Advanced finite element method in structural engineering

Advanced Finite Element Method in Structural Engineering

Volumn , Issue , 2009, Pages 1-706

  Long, Yu Qiu ^a   Cen, Song ^a   Long, Zhi Fei ^b  

^a TSINGHUA UNIVERSITY   (China)

^b CHINA UNIVERSITY OF MINING AND TECHNOLOGY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84885770432     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/978-3-642-00316-5     Document Type: Book

References (475)

1. Courant R (1943) Variational methods for the solution of problems of equilibrium and vibration. Bull Am Math Soc 49: 1-23
2. Turner MJ, Clough RW, Martin HC, Toop LC (1956) Stiffness and deflection analysis of complex structures. J Aeronaut Sci 23(9): 805-823
3. Clough RW (1960) The finite element method in plane stress analysis. In: Proc 2nd Conference on Electronic Computation. Pittsburgh: ASCE, pp 345-377
4. Melosh RJ (1963) Basis for derivation for the direct stiffness method. AIAA Journal 1(7): 1631-1637
5. Zienkiewicz OC, Taylor RL (2000) The finite element method, 5th edn. Oxford: Butterworth-Heinemann
6. Cook RD, Malkus DS, Plesha ME (1989) Concepts and applications of finite element analysis, 3rd edn. John Wiley & Sons Inc, New York
7. Huebner KH, Thornton EA, Byrom TG (1995) The finite element method for engineers. John Wiley & Sons Inc, New York
8. Bathe KJ (1996) Finite element procedures. Prentice-Hall Inc, New Jersey
9. Belytschko T, Liu WK, Moran B (2000) Nonlinear finite elements for continua and structures. Wiley, Chichester
10. Chien WZ (1980) Calculus of variations and finite elements (Vol. I). Science Press, Beijing (in Chinese)
11. Hu HC (1984) Variational principles of theory of elasticity with applications. Science Press, Beijing
12. Long YQ (1978, 1991) Introduction to finite element method. 1st edn, 2nd edn. Higher Education Press, Beijing (in Chinese)
13. Long YQ (1992) Introduction to new finite element method. Tsinghua University Press, Beijing (in Chinese)
14. Long ZF, Cen S (2001) New monograph of finite element method: principle, programming, developments. China Hydraulic and Water-power Press, Beijing (in Chinese)
15. Hu HC (1955) On some variational principles in the theory of elasticity and the theory of plasticity. Scientia Sinica 49(1): 33-42
16. Feng K (1965) Difference scheme based on variational principle. Chinese Journal of Applied Mathematics and Computational Mathematics 2(4): 238-262 (in Chinese)
17. Washizu K (1968, 1975, 1982) Variational Methods in Elasticity and Plasticity, 1st edn, 2nd edn, 3rd edn. Pergamon Press
18. Long YQ (1981) Piecewise generalized variational principles in elasticity. Shanghai Mechanics 2(2): 1-9 (in Chinese)
19. Long YQ (1986) Several patterns of functional transformation and generalized variational principles with several arbitrary parameters. International Journal of Solids and Structures 22(10): 1059-1069
20. Long YQ (1987) Generalized variational principles with several arbitrary parameters and the variable substitution and multiplier method. Applied Mathematics and Mechanics (English Edition) 8(7): 617-629
21. Long YQ, Xin KG (1987) Generalized conforming element. Tumu Gongcheng Xuebao/China Civil Engineering Journal 20(1): 1-14 (in Chinese)
22. Long YQ, Xin KG (1989) Generalized conforming element for bending and buckling analysis of plates. Finite Elements in Analysis and Design 5: 15-30
23. Long YQ, Long ZF, Xu Y (1997) The generalized conforming element (GCE) theory and applications. Advances in Structural Engineering 1(1): 63-70
24. Shi ZC (1990) On the accuracy of the quasi-conforming and generalized conforming finite elements. Chinese Annals of Mathematics Series B 11(2): 148-155
25. Long YQ, Bu XM, Long ZF, Xu Y (1995) Generalized conforming plate bending elements using point and line compatibility conditions. Computers & Structures 54(4): 717-723
26. Long ZF (1992) Triangular and rectangular plate elements based on generalized compatibility conditions. Computational Mechanics 10(3/4): 281-288 (Pubitemid 23605497)
27. Long ZF (1993) Two generalized conforming plate elements based on SemiLoof constraints. Computers & Structures 47(2): 299-304
28. Long YQ, Xi F (1992) A universal method for including shear deformation in the thin plate elements. International Journal for Numerical Methods in Engineering 34: 171-177
29. Long YQ, Zhi BC, Kuang WQ, Shan J (1982) Sub-region mixed finite element method for the calculation of stress intensity factor. In: He GQ et al. (eds) Proceedings of International Conference on FEM. Science Press, Shanghai, pp 738-740
30. Long YQ, Fu XR (2002) Generalized conforming elements based on analytical trial functions. In: Proceedings of the Eleventh National Conference on Structural Engineering (Vol. I), plenary lecture. China, Changsha, pp 28-39 (in Chinese)
31. Long YQ, Li JX, Long ZF, Cen S (1997) Area-coordinate theory for quadrilateral elements. Gong Cheng Li Xue/Engineering Mechanics 14(3): 1-11 (in Chinese)
32. Yuan S (1984) Spline elements in stress analysis [Doctoral Dissertation]. Tsinghua University, Beijing
33. Fan Z (1988) Applications of spline elements and sub-region mixed elements in structural engineering [Doctoral Dissertation]. Tsinghua University, Beijing (in Chinese)
34. Washizu K (1968, 1975, 1982) Variational methods in elasticity and plasticity. 1st edn, 2nd edn, 3rd edn, Pergamon Press, Oxford
35. Chien WZ (1980) Calculus of variations and finite elements (Vol. I). Science Press, Beijing (in Chinese)
36. Hu HC (1984) Variational principles of theory of elasticity with applications. Science Press, Beijing
37. Finlayson BA (1972) The method of weighted residuals and variational principles. Academic Press, New York
38. Pian THH (1964) Derivation of element stiffness matrices by assumed stress distributions. AIAA Journal, 2: 1333-1335
39. Atluri SN, Gallagher RH, Zienkiewicz OC (1983) (eds). Hybrid and mixed finite element method. Wiley, Chichester
40. Zienkiewicz OC (1983) The generalized finite element method-state of the art and future directions. Journal of Applied Mechanics (50th anniversary issue), 50: 1210-1217 (Pubitemid 14501747)
41. Long YQ (1985) Advances in variational principles in China. In: Zhao C et al (eds). Proceedings of the Second International Conference on Computing in Civil Engineering. Elsevier Science Publishers, Hangzhou, pp 1207-1215
42. Long YQ (1981) Piecewise generalized variational principles in elasticity. Shanghai Mechanics, 2(2): 1-9 (in Chinese)
43. Long YQ, Zhi BC, Yuan S (1982) Sub-region, sub-item and sub-layer generalized variational principles in elasticity. In: He GQ et al (eds). Proceedings of international conference on FEM. Science Press, Shanghai, pp 607-609
44. Long YQ (1987) Sub-region generalized variational principles and sub-region mixed finite element method. In: Chien WZ (eds). The advances of applied mathematics and mechanics in China. China Academic Publishers, Beijing, 157-179
45. Long YQ (1987) Sub-region generalized variational principles in elastic thin plates. In: Yeh KY eds. Progress in Applied Mechanics. Martinus Nijhoff Publishers, Dordrecht, Netherlands, pp 121-134
46. Long YQ (1983) Sub-region generalized variational principles for elastic thick plates. Applied Mathematics and Mechanics (English Edition) 4(2): 175-184
47. Long YQ, Long ZF, Xu Y (1996) Sub-region generalized variational principles in shallow shells and applications. In: Zhong WX, Cheng GD and Li XK (eds). The Advances in computational mechanics. International Academic Publishers, Beijing, pp 69-77
48. Long YQ (1995) Sub-region mixed energy partial derivative theorem. In: Long YQ (ed). Proceedings of the Fourth National Conference on Structural Engineering. Quangzhou, pp 188-194 (in Chinese)
49. Prager W (1968) Variational principles of elastic plates with relaxed continuity requirements. International Journal of Solids and Structures 4(9): 837-844
50. Long YQ (1986) Several patterns of functional transformation and generalized variational principle with several arbitrary parameters. International Journal of Solids and Structures 22(10): 1059-1069
51. Long YQ (1987) Generalized variational principles with several arbitrary parameters and the variable substitution and multiplier method. Applied mathematics and Mechanics (English Edition) 8(7): 617-629
52. Chien WZ (1983) Method of high-order Lagrange multiplier and generalized variational principles of elasticity with more general forms of functionals. Applied mathematics and Mechanics (English Edition) 4(2): 143-157
53. Xiong ZH, Liu ZT (1988) Variational principles in elasticity. Hunan University Press, Changsha, pp 88-99 (in Chinese)
54. DU QH et al (1994) (eds) An encyclopedia of engineering mechanics. Higher Education Press, Beijing, pp 2304-2306 (in Chinese)
55. Wang HD, Wu DL (1997) The finite element method and its computational program. China Architecture & Building Press, Beijing, pp 227-232 (in Chinese)
56. Zienkiewicz OC (1974) Constrained variational principles and penalty function methods in finite element analysis. In: Lecture Notes in Mathematics. Springer-Verlag, Berlin, 363: pp 207-214
57. Wu CC, Pian THH (1997) Incompatible numerical analysis and hybrid finite element method. Science Press, Beijing, pp 118-121 (in Chinese)
58. Long ZF, Cen S, Long YQ, Luo JH (2004) Hamiltonian variational principle with arbitrary parameters for thin plates. Gong Cheng Li Xue/Engineering Mechanics 21(4): 1-5 (in Chinese)
59. Hu HC (1992) On the connections between the functionals of equivalent variational principles. Acta Mechanica Solida Sinica (English Edition) 5(2): 175-182
60. Long YQ, Xin KG (1987) Generalized conforming element. Tumu Gongcheng Xuebao/China Civil Engineering Journal 20(1): 1-14 (in Chinese)
61. Long YQ, Xin KG (1989) Generalized conforming element for bending and buckling analysis of plates. Finite Elements in Analysis and Design 5: 15-30
62. Long YQ, Long ZF, Xu Y (1997) The generalized conforming element (GCE)-theory and applications. Advances in Structural Engineering 1(1): 63-70
63. Bazeley GP, Cheung YK, Irons BM, Zienkiewicz OC (1965) Triangular elements in bending-conforming and nonconforming solution. In: Proceedings of the Conference on Matrix Methods in Structural Mechanics. Air Force Institute of Technology, Ohio: Wright-Patterson A. F. Base, pp 547-576
64. Batoz JL, Bathe KJ, Ho LW (1980) A study of three-node triangular plate bending elements. International Journal for Numerical Methods in Engineering 15: 1771-1812
65. Stricklin JA, Haisler WE, Tisdale PR, Gunderson R (1969) A rapidly converging triangular plate element. AIAA Journal 7: 180-181
66. Allman DJ (1971) Triangular finite element plate bending with constant and linearly varying bending moments. In: BF de Veubeke (ed) High Speed Computing of Elastic Structures. Liege, Belgium, pp 105-136
67. Clough R W, Tocher J L (1965) Finite element stiffness matrices for analysis of plate bending. In: Proceedings of the Conference on Matrix Methods in Structural Mechanics. Air Force Institute of Technology, Ohio: Wright-Patterson A. F. Base, pp 515-545
68. Long YQ, Zhi BC, Yuan S (1982) Sub-region, sub-item and sub-layer generalized variational principles in elasticity. In: He GQ et al. (eds) Proceedings of International Conference on FEM, Shanghai Science Press, pp 607-609
69. Long YQ (1987) Sub-region generalized variational principles in elastic thin plates. In: Yeh KY (eds) Progress in Applied Mechanics. Martinus Nijhoff Publishers, pp 121-134
70. Washizu K (1968, 1975, 1982) Variational methods in elasticity and plasticity. 1st edn, 2nd edn, 3rd edn. Pergamon Press
71. Long YQ, Zhao JQ (1992) Combined application of the energy method and the weighted residual method-a new way to construct the finite elements. Chinese Journal of Aeronautics 5(2): 130-136
72. Shi ZC, Chen SC (1991) Convergence of a nine parameter generalized conforming element. Ji Suan Shu Xue/Mathematica Numerica Sinica 13(2): 193-203 (in Chinese)
73. Shi ZC (1990) On the accuracy of the quasi-conforming and generalized conforming finite elements. Chinese Annals of Mathematics Series B 11(2): 148-155
74. Specht B (1988) Modified shape functions for the three-node plate bending element passing the patch test. International Journal for Numerical Methods in Engineering 26: 705-715 (Pubitemid 18589408)
75. Shi ZC (1987) The FEM test for convergence of nonconforming finite element. Mathematics of Computation 49: 391-405
76. Li JX, Long YQ (1996) The convergence of the generalized conforming element method. Gong Cheng Li Xue/Engineering Mechanics 13(1): 75-80 (in Chinese)
77. Hrabok MM, Hrudey TM (1984) A review and catalogue of plate bending finite elements. Computers & Structures 19: 474-498
78. Yang HTY, Saigal S, Liaw DG (1990) Advances of thin shell finite elements and some applications-version I. Computers & Structures 35: 481-504
79. Kardestuncer H (1987) Finite eelement handbook. McGraw-Hill
80. Long YQ, Xin KG (1987) Generalized conforming element. Tumu Gongcheng Xuebao/China Civil Engineering Journal 20(1): 1-14 (in Chinese)
81. Long YQ, Xin KG (1989) Generalized conforming element for bending and buckling analysis of plates. Finite Elements in Analysis and Design 5: 15-30
82. Xu Y, Long ZF (1995) A simple generalized conforming rectangular plate bending element. In: Proceedings of the Fourth National Conference on Structural Engineering 315-319 (in Chinese)
83. Bu XM, Long YQ (1991) A high-precise rectangular element for thin plate bending analysis. Tumu Gongcheng Xuebao/China Civil Engineering Journal 24(1): 17-22 (in Chinese)
84. Long ZF (1993) Generalized conforming triangular elements for plate bending. Communications in Numerical Methods in Engineering 9: 53-65
85. Long YQ, Bu XM, Long ZF, Xu Y (1995) Generalized conforming plate bending elements using point and line compatibility conditions. Computers & Structures 54(4): 717-723
86. Bu XM, Long YQ (1991) A triangular displacement element based on modified potential energy functional. Journal of Tsinghua University 31(2): 9-16 (in Chinese)
87. Bu XM, Long YQ (1991) A quadrilateral element for thin plate bending. Acta Mechanica Sinica 23(1): 53-60 (in Chinese)
88. Bu XM, Long YQ (1991) A generalized conforming sector element for thin plate bending. Computational Structural Mechanics and Applications 8(2): 208-213 (in Chinese)
89. Long YQ, Bu XM (1990) A family of efficient elements for thin plate bending. Journal of Tsinghua University 30(5): 9-15 (in Chinese)
90. Long ZF (1991) Low-order and high-precision triangular elements for plate bending. In: Cheung, Lee & Leung (eds) Computational Mechanics. Rotterdam: Balkema, pp 1793-1797
91. Long ZF (1992) An improved quadrilateral element for thin plate bending. Journal of Northern Jiaotong University 16(2): 39-45 (in Chinese)
92. Long ZF (1993) Two generalized conforming plate elements based on SemiLoof constraints. Computers & Structures 47(2): 299-304
93. Long ZF (1993) Generalized conforming quadrilateral plate element by using SemiLoof constraints. Communications in Numerical Methods in Engineering 9: 417-426
94. Long ZF (1992) Triangular and rectangular plate elements based on generalized compatibility conditions. Computational Mechanics 10(3/4): 281-288 (Pubitemid 23605497)
95. Zhang YQ, Zheng ZB, Long YQ (1992) A generalized conforming element for thin plates by Coons surface approach. Gong Cheng Li Xue/Engineering Mechanics 9(2): 86-90 (in Chinese)
96. Long YQ, Zhao JQ (1988) A new generalized conforming triangular element for thin plates. Communications in Applied Numerical Methods 4: 781-792
97. Bu XM, Long YQ (1991) A generalized conforming technique using the least squares method. Gong Cheng Li Xue/Engineering Mechanics 8(2): 20-24 (in Chinese)
98. Sun JH, Long ZF, Long YQ, Zhang CS (2001) Geometrically nonlinear stability analysis of shells using generalized conforming shallow shell element. International Journal of Structural Stability and Dynamics 1(3): 313-332
99. Sun JH, Xia HX, Long YQ (199) A generalized conforming retangular shallow shell element. In: Long YQ, ed. The Proceedings of the First International Conference on Structural Engineering. KunMing, China, pp 803-810
100. Sun JH, Long ZF, Long YQ (1999) A generalized conforming element with vertex rotational freedoms for thin shell analysis. In: Long YQ, ed. The Proceedings of the First International Conference on Structural Engineering. KunMing, China, pp 811-818
101. Bazeley GP, Cheung YK, Irons BM, Zienkiewicz OC (1965) Triangular elements in bending-conforming and nonconforming solution. In: Proceedings of the Conference on Matrix Methods in Structural Mechanics. Air Force Institute of Technology, Ohio: Wright-Patterson A. F. Base pp 547-576
102. Batoz JL, Bathe KJ, Ho LW (1980) A study of three-node triangular plate bending elements. International Journal for Numerical Methods in Engineering 15: 1771-1812
103. Stricklin JA, Haisler WE, Tisdale PR, Gunderson R (1969) A rapidly converging triangular plate element. AIAA Journal 7: 180-181
104. Allman DJ (1971) Triangular finite element plate bending with constant and linearly varying bending moments. In: BF de Veubeke (ed) High Speed Computing of Elastic Structures. Liege Belgium, pp 105-136
105. Clough RW, Tocher JL (1965) Finite element stiffness matrices for analysis of plate bending. In: Proceedings of the Conference on Matrix Methods in Structural Mechanics. Air Force Institute of Technology, Ohio: Wright-Patterson A. F. Base, pp 515-545
106. Melosh RJ (1963) Basis for derivation of matrices for the direct stiffness method. AIAA Journal 1(7): 1631-1637
107. Tocher JL, Kapur KK (1965) Comment on "basis of derivation of matrices for direct stiffness method". AIAA Journal 3(6): 1215-1216
108. Kapur KK, Hartz BJ (1966) Stability of thin plates using the finite element method. In: Proceedings of American Socity of Civil Engineering, pp 177-195
109. Xu Y, Long ZF (1995) A simple generalized conforming rectangular plate bending element. In: Proceedings of the Fourth National Conference on Structural Engineering, pp 315-319 (in Chinese)
110. Long ZF (1993) Generalized conforming triangular elements for plate bending. Communications in Numerical Methods in Engineering 9: 53-65
111. Fricker AJ (1985) An improved three-node triangular element for plate bending. International Journal for Numerical Methods in Engineering 21: 105-114 (Pubitemid 15541666)
112. Jeyachandrabose C, Kirkhope J (1986) Construction of new efficient three-node triangular thin plate bending elements. Computers & Structures 23(5): 587-603
113. Long YQ, Bu XM, Long ZF, Xu Y (1995) Generalized conforming plate bending elements using point and line compatibility conditions. Computers & Structures 54(4): 717-723
114. Felippa CA, Bergan PG (1987) Triangular bending FE based on energy-orthogonal free formulation. Computer Methods in Applied Mechanics and Engineering 61: 129-160 (Pubitemid 17574686)
115. Razzaque A (1973) Program for triangular bending element with derivative smoothing. International Journal for Numerical Methods in Engineering 6: 333-343
116. Zienkiewicz OC, Lefebvre D (1988) A robust triangular plate bending element of the Reissner-Mindlin type. International Journal for Numerical Methods in Engineering 26: 1169-1184 (Pubitemid 18617261)
117. Long YQ, Bu XM (1990) A family of efficient elements for thin plate bending. Journal of Tsinghua University 30(5): 9-15 (in Chinese)
118. Long ZF (1991) Low-order and high-precision triangular elements for plate bending. In: Cheung, Lee & Leung (eds) Computational Mechanics. Rotterdam: Balkema, pp 1793-1797
119. Specht B (1988) Modified shape functions for the three-node plate bending element passing the patch test. International Journal for Numerical Methods in Engineering 26: 705-715 (Pubitemid 18589408)
120. Irons BM (1976) The SemiLoof shell element. In: Gallagher RH, Ashwell DG (eds) Finite Element for Thin and Curved Member. Wiley, pp 197-222
121. Long ZF (1992) Two generalized conforming plate elements based on SemiLoof constraints. Computers & Structures 9(1): 53-65
122. Long ZF (1993) Generalized conforming quadrilateral plate element by using SemiLoof constraints. Communications in Numerical Methods in Engineering 9: 417-426
123. Long ZF (1992) Triangular and rectangular plate elements based on generalized compatibility conditions. Computational Mechanics 10(3/4): 281-288 (Pubitemid 23605497)
124. Long ZF (1992) Triangular and rectangular plate elements based on generalized compatibility conditions. Computational Mechanics 10(3/4): 281-288 (Pubitemid 23605497)
125. Melosh RJ (1963) Basis for derivation of matrices for the direct stiffness method. AIAA Journal 1(7): 1631-1637
126. Bazeley GP, Cheung YK, Irons BM, Zienkiewicz OC (1965) Triangular elements in bending-conforming and nonconforming solution. In: Proceedings of the Conference on Matrix Methods in Structural Mechanics. Air Force Institute of Technology, Ohio: Wright-Patterson A. F. Base, pp 547-576
127. Long YQ, Zhao JQ (1988) A new generalized conforming triangular element for thin plates. Communications in Applied Numerical Methods 4: 781-792
128. Bu XM, Long YQ (1991) A generalized conforming technique using the least squares method. Gong Cheng Li Xue/Engineering Mechanics 8(2): 20-24 (in Chinese)
129. Reissner E (1995) The effect of transverse deformation on the bending of elastic plates. Journal of Applied Mechanics 12: A69-77
130. Mindlin R D (1951) Influence of rotatory inertia and shear on flexural motion of isotropic elastic plates. Journal of Applied Mechanics 18: 31-38
131. Hu HC (1984) Variational principles of theory of elasticity with applications. Science Press, Beijing
132. Cen S, Long ZF (1998) A Mindlin triangular plate element with improved interpolation for the rotation and shear strain fields. Gong Cheng Li Xue/Engineering Mechanics 15(3): 1-14 (in Chinese)
133. Zienkiewicz OC, Taylor RL, Too JM (1971) Reduced integration techniques in general analysis of plates and shells. International Journal for Numerical Methods in Engineering 3(2): 275-290
134. Hughes TJR, Cohen M, Haron M (1978) Reduced and selective integration technique in finite element analysis of plates. Nuclear Eng. and Design 46: 203-222
135. Hinton E, Huang HC (1986) A family of quadrilateral Mindlin plate elements with substitute shear strain fields. Computers & Structures 23(3): 409-431 (Pubitemid 17481093)
136. Katili I (1993) A new discrete Kirchhoff-Mindlin element based on Mindlin-Reissner plate theory and assumed shear strain fields-part I: An extended DKT element for thick-plate bending analysis. International Journal for Numerical Methods in Engineering 36: 1859-1883
137. Cen S, Long ZF, Long YQ (1999) A Mindlin quadrilateral plate element with improved interpolation for the rotation and shear strain fields. Gong Cheng Li Xue/Engineering Mechanics 16(4): 1-15 (in Chinese) (Pubitemid 30569930)
138. Cen S, Long ZF (1998) A new triangular generalized conforming element for thin-thick plates. Gong Cheng Li Xue/Engineering Mechanics 15(1): 10-22 (in Chinese)
139. Cen S, Long YQ, Yao ZH, Chiew SP (2006) Application of the quadrilateral area coordinate method: a new element for Mindlin-Reissner plate. International Journal for Numerical Methods in Engineering 66(1): 1-45
140. Long YQ, Fu XR (2002) Two generalized conforming quadrilateral thick plate elements based on analytical trial functions. Gong Cheng Li Xue/Engineering Mechanics 19(3): 10-15 (in Chinese)
141. Chen YL, Cen S, Yao ZH, Long YQ, Long ZF (2003) Development of triangular flat-shell element using a new thin-thick plate bending element based on SemiLoof constrains. Structural Engineering and Mechanics 15(1): 83-114
142. Long YQ, Bu XM, Long ZF, Xu Y (1995) Generalized conforming plate bending elements using point and line compatibility conditions. Computers & Structures 54(4): 717-723
143. Fricker AJ (1986) A simple method for including shear deformation in thin plate elements. International Journal for Numerical Methods in Engineering 23: 1355-1366 (Pubitemid 16604138)
144. Long YQ, Xi F (1992) A universal method for including shear deformation in the thin plate elements. International Journal for Numerical Methods in Engineering 34: 171-177
145. Long ZF (1992) Locking-free thick plate rectangular element. Gong Cheng Li Xue/Engineering Mechanics 9(1): 88-93 (in Chinese)
146. Cen S, Long ZF, Kuang WQ (1997) Improved thick plate elements by introducing generalized bubble displacement fields. In: Han DJ, Mo HH (eds) Computational Methods in Engineering and Science-Theory and Application (Proceedings of the Sixth EPMESC Conference). South China University of Technology Press, China, Guangzhou, pp 517-522
147. Cen S, Long ZF, Long YQ, Kuang WQ (1997) Two robust generalized conforming rectangular element for thin-thick plates. In: Han DJ, Mo HH (eds) Computational Methods in Engineering and Science-Theory and Application (Proceedings of the Sixth EPMESC Conference). South China University of Technology Press, China, Guangzhou, pp 523-527
148. Long ZF (1992) Triangular and rectangular plate elements based on generalized compatibility conditions. Computational Mechanics 10(3/4): 281-288 (Pubitemid 23605497)
149. Melosh RJ (1963) Basis for derivation of matrices for the direct stiffness method. AIAA Journal 1(7): 1631-1637
150. Reddy JN (1997) Mechanics of laminated composite plates-theory and analysis. CRC Press, Boca Raton
151. Calcote LR (1969) The analysis of laminated composite structures. Van Nostrand Reinhold, New York
152. Jones RM (1975) Mechanics of composite material. MacGraw-Hill Kogakusha, Tokyo
153. Medwadowski SJ (1958) A refined theory of elastic orthotropic plates. ASME J Appl Mech, 25: 437-443
154. Yang PC, Norris CH, Stavsky Y (1966) Elastic wave propagation in heterogeneous plates. International Journal of Solids and Structures 2: 665-684
155. Lo KH, Christensen RM, Wu EM (1977) A higher-order theory of plate deformation, Part II: Laminated plates. Journal of Applied Methanics 44(4): 663-668
156. Reddy JN (1984) A simple higher-order theory for laminated composite plates. Journal of Applied Methanics 51: 745-752 (Pubitemid 15422865)
157. Phan ND, Reddy JN (1985) Analysis of laminated composite plates using a higher-order shear deformation theory. International Journal for Numerical Methods in Engineering 21: 2201-2219 (Pubitemid 15602723)
158. 0 plate bending elements. Computer Methods in Applied Mechanics and Engineering 66: 173-198 (Pubitemid 18562216)
159. 0 plate bending element. Computers & Structures 15: 177-183 (Pubitemid 12538478)
160. Reddy JN (1987) A generalization of two-dimensional theories of laminated composite plates. Communications in Applied Numerical Methods 3: 173-180 (Pubitemid 17606670)
161. Robbins DH, Reddy JN (1993) Modelling of thick composites using a layerwise laminate theory. International Journal for Numerical Methods in Engineering 36: 655-677 (Pubitemid 23643573)
162. Pryor CW, Barker RM (1971) A finite element analysis including transverse shear effects for application to laminated plates. AIAA Journal 9: 912-917
163. Vlachoutsis S (1992) Shear correction factors for plates and shells. International Journal for Numerical Methods in Engineering 33: 1537-1552
164. Auricchio F, Sacco E (199) A mixed-enhanced finite-element for the analysis of laminated composite plates. International Journal for Numerical Methods in Engineering 44: 1481-1504
165. Rolfes R, Rohwer K (1997) Improved transverse shear stresses in composite finite elements based on first order shear deformation theory. International Journal for Numerical Methods in Engineering 40: 51-60 (Pubitemid 127571724)
166. Rolfes R, Rohwer K, Ballerstaedt M (1998) Efficient linear transverse normal stress analysis of layered composite plates. Computers & Structures 68: 643-652 (Pubitemid 128416307)
167. Singh G, Raju KK, Rao GV (1998) A new lock-free, material finite element for flexure of moderately thick rectangular composite plates. Computers & Structures 69: 609-623 (Pubitemid 128430636)
168. Sadek EA (1998) Some serendipity finite element for the analysis of laminated plates. Computers & Structures 69: 37-51 (Pubitemid 128423643)
169. Alfano G, Auricchio F, Rosati L, Sacco E (2001) MITC finite elements for laminated composite plates. International Journal for Numerical Methods in Engineering 50: 707-738 (Pubitemid 32138364)
170. Wu CC, Pian THH (1997) Incompatible Numerical Analysis and Hybrid Finite Element Method. Beijing: Science Press (in Chinese)
171. Cen S, Long YQ, Yao ZH (2002) A new element based on the first-order shear deformation theory for the analysis of laminated composite plates. Gong Cheng Li Xue/Engineering Mechanics 19(1): 1-8 (in Chinese) (Pubitemid 35020776)
172. Cen S, Long YQ, Yao ZH (2002) A new hybrid-enhanced displacement-based element for the analysis of laminated composite plates. Computers & Structures 80 (9-10): 819-833 (Pubitemid 34715397)
173. Cen S, Long ZF, Long YQ (1999) A Mindlin quadrilateral plate element with improved interpolation for the rotation and shear strain fields. Gong Cheng Li Xue/Engineering Mechanics 16(4): 1-15 (in Chinese) (Pubitemid 30569930)
174. Soh AK, Cen S, Long YQ, Long ZF (2001) A new twelve DOF quadrilateral element for analysis of thick and thin plates. European Journal of Mechanics A/Solids 20: 299-326 (Pubitemid 32248381)
175. Cen S, Long YQ, Yao ZH (2001) An enhanced hybrid post-processing procedure for improving stress solutions of displacement-based plate bending elements. Gong Cheng Li Xue/Engineering Mechanics 18(3): 21-27 (in Chinese) (Pubitemid 32618275)
176. Ayad R, Dhatt G, Batoz JL (1998) A new hybrid-mixed variational approach for Reissner-Mindlin plates: The MiSP model. International Journal for Numerical Methods in Engineering 42: 1149-1179 (Pubitemid 128500010)
177. Pian THH, Sumihara K (1984) Rational approach for assumed stress finite element. International Journal for Numerical Methods in Engineering 20: 1685-1695 (Pubitemid 14651258)
178. Pagano NJ, Hatfield SJ (1972) Elastic behavior of multilayered bidirectional composites. AIAA Journal 10: 931-933
179. Lardeur P, Batoz JL (1989) Composite plate analysis using a new discrete shear triangular finite element. International Journal for Numerical Methods in Engineering 27: 343-359 (Pubitemid 20645032)
180. Pagano NJ (1970) Exact solutions for rectangular bidirectional composites and sandwich plates. J Compos Mater 4: 20-34
181. Benjeddou A (2000) Advances in piezoelectric finite element modeling of adaptive structural elements: a survey. Computers & Structures 76: 347-363 (Pubitemid 30589541)
182. Sze KY, Yao LQ, Yi S (2000) A hybrid stress ANS solid-shell element and its generalization for smart structure modeling. Part II-smart structure modeling. International Journal for Numerical Methods in Engineering 48: 565-582
183. Chee C, Tong L, Steven G (2000) A mixed model for adaptive composite plates with piezoelectric for anisotropic actuation. Computers & Structures 77: 253-268
184. Sheikh AH, Topdar P, Halder S (2001) An appropriate FE model for through-thickness variation of displacement and potential in thin/moderately thick smart laminates. Composite Structures 51: 401-409 (Pubitemid 32376198)
185. Tzou HS (1993) Piezoelectric Shells: Distributed Sensing and Control of Continua. Netherlands: Kluwer Academic Publishers
186. Ha SK, Keilers C, Chang FK (1992) Finite element analysis of composite structures containing distributed piezoelectric sensors and actuators. AIAA Journal 30(3): 772-780
187. Reddy JN (1999) On laminated composite plates with integrated sensors and actuators. Engineering Structures 21: 568-593
188. Huang JH, Wu TL (1996) Analysis of hybrid multilayered piezoelectric plates. International Journal of Engineering Science 34(2): 171-181 (Pubitemid 126342989)
189. Jonnalagadda KD, Blandford GE, Tauchert TR (1992) Piezothermoelastic composite plate analysis using first-order shear deformation theory. Computers & Structures 5(1): 79-89
190. Detwiler DT, Shen MHH, Venkayya VB (1995) Finite element analysis of laminated composite structures containing distributed piezoelectric actuators and sensors. Finite Elements in Analysis and Design 20: 87-100
191. Suleman A, Venkayya VB (1995) A simple finite element formulation for a laminated composite with piezoelectric layers. Journal of Intelligent Material Systems and Structures 6: 776-782
192. Cen S, Soh AK, Long YQ, Yao ZH (2002) A new 4-node quadrilateral FE model with variable electrical degrees of freedom for the analysis of piezoelectric laminated composite plates. Composite Structures 58(4): 583-599 (Pubitemid 35400198)
193. Wu CC, Sze KY, Huang YQ (2001) Numerical solutions on fracture of piezoelectric materials by hybrid element. International Journal of Solids and Structures 38: 4315-4329 (Pubitemid 32480822)
194. Tzou HS, Ye R (1996) Analysis of piezoelastic structures with laminated piezoelectric triangle shell element. AIAA Journal 34(1): 110-115 (Pubitemid 126499199)
195. ABAQUS/Standard User's Manual, Version 5.8 (1998) Hibbitt, Karlsson & Sorensen, Inc.: Rawtucket, Rhode Island
196. Ray MC, Bhattacharya R, Samanta B (1972) Exact solutions for static analysis of intelligent structures. AIAA Journal 31(9): 1684-1691
197. Pagano NJ, Hatfield SJ (1992) Elastic behavior of multilayered bidirectional composites. AIAA Journal 10: 931-933
198. Vlachoutsis S (1992) Shear correction factors for plates and shells. International Journal for Numerical Methods in Engineering 33: 1537-1552
199. Pagano NJ (1970) Exact solutions for rectangular bidirectional composites and sandwich plates. Journal of Composite Materials 4: 20-34
200. Manjunatha BS, Kant T (1994) A comparison of 9 and 16 noded quadrilateral elements based on higher order laminated theories for estimation of transverse stresses. Journal of Reinforced Plastics and Composites 11: 986-1002
201. Heyliger P (1994) Static behavior of laminated elastic/piezoelectric plates. AIAA Journal 32(12): 2481-2484
202. Long YQ, Huang MF (1988) A generalized conforming isoparametric element. Applied mathematics and Mechanics (English Edition) 9(10): 929-936
203. Long YQ, Xu Y (1994) Generalized conforming quadrilateral membrane element with vertex rigid rotational freedom. Computers & Structures 52(4): 749-755
204. Long YQ, Xu Y (1994) Generalized conforming triangular membrane element with vertex rigid rotational freedom. Finite Elements in Analysis and Design 17: 259-271
205. Long YQ, Xu Y (1993) Generalized conforming triangular flat shell element. Gong Cheng Li Xue/Engineering Mechanics 10(4): 1-7 (in Chinese)
206. Long YQ, Xu Y (1994) Generalized conforming flat rectangular thin shell element. Computational Structural Mechanics and Applications 11(2): 154-160 (in Chinese)
207. Xu Y, Long YQ, Long ZF (1994) A triangular shell element with drilling freedoms based on generalized compatibility conditions. In: Proc. WCCMIII. Japan, pp 1234-1235
208. Xu Y, Long ZF (1996) Advances of membrane and thin shell elements with the generalized conforming approach. In: Yuan Si, Ma Zhiliang (eds) New Developments in Structural Engineering, pp 218-223
209. Xu Y, Long YQ, Long ZF (1999) A generalized conforming triangular flat shell element with high accuracy. In: Long YQ (ed) The Proceedings of the First International Conference on Structural Engineering. China, KunMing, pp 700-706
210. Chen YL, Cen S, Yao ZH, Long YQ, Long ZF (2003) Development of triangular flat-shell element using a new thin-thick plate bending element based on SemiLoof constraints. Structural Engineering and Mechanics 15(1): 83-114
211. Sun JH, Xia HX, Long YQ (1999) A generalized conforming rectangular shallow shell element. In: Long YQ (ed) The Proceedings of the First International Conference on Structural Engineering. China, KunMing, pp 803-810
212. Sun JH, Long ZF, Long YQ (1999) A generalized conforming element with vertex rotational freedoms for thin shell analysis. In: Long YQ (ed) The Proceedings of the First International Conference on Structural Engineering. China, KunMing, pp 811-818
213. Sun JH, Long ZF, Long YQ, Zhang CS (2001) Geometrically nonlinear stability analysis of shells using generalized conforming shallow shell element. International Journal of Structural Stability and Dynamics 1(3): 313-332
214. Wilson EL, Taylor RL, Doherty WP, Ghabussi T (1973) Incompatible displacement models. In: Fenven ST et al (eds) Numerical and Computer Methods in Structural Mechanics. Academic Press, New York, pp 43-57
215. Long YQ, Xin KG (1989) Generalized conforming element for bending and buckling analysis of plates. Finite Elements in Analysis and Design 5: 15-30
216. Taylor RL, Beresford PJ, Wilson EL (1976) A non-conforming element for stress analysis. International Journal for Numerical Methods in Engineering 10: 1211-1219
217. Wachspress EL (1978) Incomptiable quadrilateral basis functions. International Journal for Numerical Methods in Engineering 12: 589-595
218. Pian THH, Wu CC (1986) General formulation of incompatible shape function and an incompatible isoparametric element. In: Proc of the Invitational China-American Workshop on FEM. Chengde, pp 159-165
219. Chen WJ, Tang LM (1981) Isoparametric quasi-conforming element. Journal of Dalian Institute of Technology 20(1): 63-74 (in Chinese)
220. Cook RD (1974) Improved two-dimensional finite element. Journal of the Structural Division ASCE, 100, ST9: 1851-1863
221. Zienkiewicz OC, Taylor RL (1991) The finite element method, 4th edn. Volume 2-Solid and Fluid Mechanics & Dynamics and Non-linearity. McGRAW-HILL Book Company, London
222. Clough RW, Johnson CP (1968) A finite element approximation for the analysis of thin shells. International Journal of Solids and Structures 4: 43-60
223. Olsen MD, Bearden TW (1979) A simple flat shell element revisited. International Journal for Numerical Methods in Engineering 14: 51-68
224. Allman DJ (1988) A quadrilateral finite element including vertex rotation for plane elasticity analysis. International Journal for Numerical Methods in Engineering 26: 717-730 (Pubitemid 18589409)
225. Felippa CA, Alexander S (1992) Membrane triangles with corner drilling freedom-III. Implementations and performane evolution. Finite Element in Analysis and Design 12: 203-249
226. Bergan PG, Felippa CA (1985) A triangular membrane element with rotational degrees of freedom. Computer Methods in Applied Mechanics and Engineering 50: 25-69 (Pubitemid 15588703)
227. Long ZF, Cen S (1992) New monograph of finite element method: principle, programming, developments. Hydraulic and Water-power Press, China, Beijing (in Chinese)
228. Long YQ, Bu XM, Long ZF, Xu Y (1995) Generalized conforming plate bending elements using point and line compatibility conditions. Computers & Structures 54(4): 717-723
229. Fish J, Belytshko T (1992) Stabilized rapidly convergent 18-degree-of-freedom flat shell triangular element. International Journal for Numerical Methods in Engineering 33: 149-162
230. Chen WJ, Cheung YK (1999) Refined non-conforming triangular elements for analysis of shell structures. International Journal for Numerical Methods in Engineering 46: 433-455
231. Providas E, Kattis MA (2000) An assessment of two fundamental flat triangular shell elements with drilling rotations. Computers & Structure 77(2): 129-139
232. Carpenter N, Stolarski H, Belyschko T (1986) Improvements in 3-node triangular shell elements. International Journal for Numerical Methods in Engineering 23: 1643-1667 (Pubitemid 16630615)
233. ABAQUS/Standard User's Manual, Version 5.8 (1998) Hibbitt, Karlsson & Sorensen, Inc.: Rawtucket, Rhode Island
234. MacNeal RH, Harder RL (1985) A proposed standard set of problems to test finite element accuracy. Finite Element in Analysis and Design 1: 3-20
235. Aminpour MA (1992) An assumed-stress hybrid 4-node shell element with drilling degrees of freedom. International Journal for Numerical Methods in Engineering 33: 19-38
236. Guan Y, Tang L (1992) A quasi-conforming nine-node degenerated shell finite element. Finite Elements in Analysis and Design 11: 165-176 (Pubitemid 23568369)
237. Batoz JL, Tahar MB (1982) Evaluation of a new quadrilateral thin plate bending element. International Journal for Numerical Methods in Engineering 18: 1655-1677
238. Bathe KJ, Dvorkin EN (1985) Short communication: a four-node plate bending element based on Mindlin/Ressiner plate theory and mixed interpolation. International Journal for Numerical Methods in Engineering 21: 367-383
239. Chen WJ (2001) Advances in finite element with high performances. In: Yuan MW, Sun SL (eds) Computational Mechanics in Engineering and Science (Proceedings of the Chinese Conference on Computational Mechanics'2001). Peking Univerisuty Press, China, Guangzhou, pp 136-151 (in Chinese)
240. Parish HA (1979) Critical survey of the 9-node degenerated shell element with special emphasis on thin shell application and reduced integration. Computer Methods in Applied Mechanics and Engineering 20: 323-350
241. Long YQ, Zhao JQ (1992) Generalized conforming curved rectangular element for shallow shells. Gong Cheng Li Xue/Engineering Mechanics, 9(1): 3-10 (in Chinese)
242. Long YQ, Xi F (1992) A universal method for including shear deformation in thin plate elements. International Journal for Numerical Methods in Engineering 34: 171-177
243. Sun JH (1998) Research on generalized conforming shallow shell element and nonlinear analysis of plate and shell structures [Doctoral Dissertation]. Tsinghua University, Beijing (in Chinese)
244. Bu XM, Long YQ (1991) A high-precise rectangular element for thin plate bending analysis. Tumu Gongcheng Xuebao/China Civil Engineering Journal 24(1): 17-22 (in Chinese)
245. Bonnes G, Dhatt G, Giroux Y, Robichaud (1968) Curved triangular elements for analysis of shell. In: Proceedings of Conference on Matrix Method in Structural Mechanics. A. F. Base, Ohio: Wright Patterson pp 617-640
246. Cowper G, Lindberg GM, Olson MD (1970) A shallow shell finite element of triangular shape. International Journal of Solids and Structures 6: 1133-1156
247. Cook RD (1974) Concept and Applications of Finite Element Analysis. John Wiley & Sons, Inc, New York
248. Badiansky B (1974) Theory of buckling and post-buckling behavior of elastic structure. In: Yih Chia-Shun (eds) Advances in Applied Mechanics (Vol. 14), Academic Press, New York, pp 2-63
249. Jiang HY (1984) Nonlinear finite element method of quasi-conforming technique model. Computational Structural Mechanics and Applications 1(2): 49-59 (in Chinese)
250. Pica A, Wood RD, Hinton E (1980) Finite element analysis of geometrically nonlinear plate behaviour using a Mindlin formulation. Computers & Structures 11: 203-215
251. Sabir AB, Lock AC (1972) The application of finite element to the large deflection geometrically nonlinear behavior of cylindrical shells. In: Brebbia CA (ed) Variational Methods in Engineering, Southampton University Press, Southampton pp 54-65
252. Ramesh G, Krishnamoorthy CS (1993) Post-buckling analysis of structures by dynamic relaxation. International Journal for Numerical Methods in Engineering 36: 1339-1364
253. Wei G, Zhao CX (1990) A large deflection quasi-conforming rectangular shallow shell element and applications. Computational Structural Mechanics and Applications 7(1): 15-43 (in Chinese)
254. Crisfield MA (1981) A fast incremental/iterative solution procedure that handles "snap-through". Computers & Structures 13: 55-62 (Pubitemid 11504717)
255. Horrigmoe G, Bergan PG (1978) Nonlinear analysis of free-form shells by flat finite elements. Computer Methods in Applied Mechanics and Engineering 16: 11-35 (Pubitemid 9408107)
256. Long YQ, Zhi BC, Kuang WQ, Shan J (1982) Sub-region mixed finite element method for the calculation of stress intensity factor. In: He GQ et al (eds) Proceedings of International Conference on FEM. Science Press, Shanghai, pp 738-740
257. Benzley SE (1974) Representation of singularities with isoparametric finite elements. International Journal for Numerical Methods in Engineering 8: 537-545
258. Chien WZ, Xie ZC, Gu QL, Yang ZF, Zhou CT (1980) The superposition of the finite element method on the singularity terms in determining the stress intensity factors. Journal of Tsinghua University 2: 15-24 (in Chinese)
259. Long YQ, Zhao YQ (1985) Calculation of stress intensity factors in plane problems by the sub-region mixed finite element method. Engineering Software 7(1): 32-35
260. Huang MF, Long YQ (1988) Calculation of stress intensity factors of cracked Reissner plates by the sub-region mixed finite element method. Computers & Structures 30(4): 837-840
261. Long YQ, Qian J (1992) Calculation of stress intensity factors for surface cracks in a 3D body by the subregion mixed FEM. Computers & Structures 44(1/2): 75-78 (Pubitemid 23557064)
262. Fan Z, Long YQ (1992) Sub-region mixed finite element analysis of V-notched plates. International Journal of Fracture 56: 333-344
263. Long YQ, Qian J (1990) Fracture analysis of V-notch in composite material. In: Proceeding of WCCM-II. Stuttgart, pp 332-335
264. Long YQ, Qian J (1992) Sub-region mixed finite element analysis of V-notches in a bimaterial. In: Zhu DC (ed) Advances in Engineering Mechanics. Peking University Press, Beijing, pp 54-59
265. Qian J, Long YQ (1992) The expression of stress and strain at the tip of notch in Reissner plate. Applied mathematics and Mechanics (English Edition) 13(4): 315-324
266. Qian J, Long YQ (1994) The expression of stress and strain at the tip of 3-D notch. Applied mathematics and Mechanics (English Edition) 15(3): 211-221
267. Bao SH, Yang C, Fan Z (1984) Analysis of shear wall supported by beam column system and shear wall with opening by subregion mixed FEM. In: Proc. 3rd Int. Conf. on Tall Buildings. Hong Kong, pp 586-591
268. Atluri SN, Kobayashi AS, Nakagaki M (1975) An assumed displacement hybrid finite element model for linear fracture mechanics. International Journal of Fracture 11: 257-271
269. Kelly JW, Sun CT (1977) A singular finite element for computing stress intensity factors. In: Sih GC (ed) Proceedings of an International Conference on Fracture Mechanics and Technology (Vol 2), Sijthoff and Noordhoff International Publishers, Hong Kong, pp 1483-1498
270. Gross B, Strawley JE, Brown WE (1964) Stress intensity factors for a single edge notch tension specimen by boundary collocation of a stress function. NASA, TN-D-2395
271. Isida M (1971) Effect of width and length on stress intensity factors of internally cracked plates under various boundary conditions. International Journal of Fracture 7: 301-316
272. Rooke DP, Cartwright DJ (1976) Compendium of Stress Intensity Factors. Her Majesty's Stationery Office, London
273. Wilson WK (1971) Numerical methods for determining stress intensity factors of an interior crack in a finite plate. ASME Journal of Basic Engineering 93: 685-690
274. Barsoum RS (1976) A degenerate solid element for linear fracture analysis of plate bending and general shells. International Journal for Numerical Methods in Engineering 10: 551-564
275. Yagawa G (1979) Finite element analysis of stress intensity factors for plate extension and plate bending problems. International Journal for Numerical Methods in Engineering 14(5): 727-740 (Pubitemid 9451049)
276. Li YZ, Liu CT (1983) Analysis of Reissner's plate bending fracture problem. Acta Mechanica Sinica 15(4): 366-375 (in Chinese)
277. Hartranft RJ, Sih GC (1968) Effect of plate thickness on the bending stress distribution around through cracks. Journal of Mathematics and Physics 47: 276-291
278. Wang NM (1970) Twisting of an elastic plate containing a crack. International Journal of Fracture 6: 367-378
279. Nishioka T, Atluri SN (1983) An alternating method for analysis of surface flawed aircraft structural components. AIAA Journal 21(5): 749-757 (Pubitemid 13561476)
280. Niu X, Glinka G (1989) Stress intensity factors for semi-elliptical surface cracks in welded joints. International Journal of Fracture 40: 255-270 (Pubitemid 20609902)
281. Heliot J, Labbens R, Pellissier-Tannon A (1979) Semi-elliptical cracks in a cylinder subjected to stress gradients. In: Smith GW (eds) Fracture Mechanics. ASTM STP 677, American Society for Testing and Materials, Philadelphia, pp 341-364 (Pubitemid 10424096)
282. Li YZ (1988) Crack tip stress and strain fields for surface cracks in 3D boby and the calculation of stress intensity factors. Chinese Science (A) 8: 828-842
283. Newman JC, Raju IS (1979) NASA, TP-1578
284. Fan Z, Long YQ (1992) Sub-region mixed finite element analysis of V-notched plates. International Journal of Fracture 56: 333-344
285. Long YQ, Qian J (1992) Sub-region mixed finite element analysis of V-notches in a bimaterial. In: Zhu DC (ed) Advances in Engineering Mechanics, Peking University Press, Beijing, pp 54-59
286. Qian J, Long YQ (1992) The expression of stress and strain at the tip of notch in Reissner plate. Applied mathematics and Mechanics (English Edition) 13(4): 315-324
287. Qian J, Long YQ (1994) The expression of stress and strain at the tip of 3-D notch. Applied mathematics and Mechanics (English Edition) 15(3): 211-221
288. Williams ML (1952) Stress singularities resulting from various boundary conditions in angular corners of plates in extension. Journal of Applied Mechanics 14: 526-528
289. Gross B, Mendelson A (1972) Plane elastostatic analysis of V-notched plates. International Journal of Fracture 8: 267-276
290. Rzasnicki W, Mendelson A, Albers LU (1973) Application of boundary integral method to elastic analysis of V-notched beams. NASA TN-F-7424
291. Carpenter WC (1984) A collocation procedure for determining fracture mechanics parameters at a corner. International Journal of Fracture 24: 255-266
292. Carpenter WC (1985) The eigenvector solution for a general corner or finite opening crack with further studies on the collocation procedure. International Journal of Fracture 27: 63-74
293. Carpenter WC (1987) A path independent integral for computing stress intensities for V-notched cracks in a bi-material. International Journal of Fracture 35: 245-268
294. Lin KY, Tong P (1980) Singular finite element for the fracture analysis of V-notch plate. International Journal for Numerical Methods in Engineering 15: 1343-1354 (Pubitemid 11444948)
295. Awaji H, Yokobori AT, Yokobori T (1986) The variation of the stress singularity at the notch-tip as notch angle and radius of curvature. Computers & Structures 22(1): 25-30 (Pubitemid 16518111)
296. Long YQ (1987) Variational Principles ·Finite Element Method ·;Shell Analysis. Liaoning Science and Technology Publishing House, Shenyang (in Chinese)
297. Lin KY, Mar JW (1976) Finite element analysis of stress intensity factors for cracks at a bi-material interface. International Journal of Fracture 12: 521-531
298. Rice JR, Sih GC (1965) Plane problems of cracks in dissimilar media. Journal of Applied Mechanics 32: 418-423
299. Qian J, Long YQ (1991) Sub region mixed FEM for calculating stress intensity factor of antiplane notch in bi-material. Computational Structural Mechanics and Applications 8(3): 325-330 (in Chinese)
300. Sham TL, Bueckner HF (1988) The weight function theory for piecewise homogeneous isotropic notches in antiplane strain. Journal of Applied Mechanics 55: 956-603
301. Sham TL (1988) Weight functions for piecewise homogeneous isotropic notches in antiplane strain by finite element method. Engineering Fracture Mechanics 31(4): 567-576
302. Schovanec L (1989) An antiplane shear crack in a nonhomogeneous elastic material. Engineering Fracture Mechanics 33: 745-751 (Pubitemid 20612132)
303. Hwang KC, Yu SW (1985) Fracture mechanics in elasticity and plasticity. Tsinghua University Press, Beijing (in Chinese)
304. Liu CT (1983) Stresses and deformations near the crack tip for bending plate. Acta Mechanica Solida Sinica 3: 441-448 (in Chinese)
305. Knowles JK, Wang NM (1960) On the bending of an elastic plate containing a crack. Journal of Mathematics and Physics 39: 223-236
306. Hartanft RJ, Sih GC (1968) Effect of plate thickness on the bending stress distribution around through cracks. Journal of Mathematics and Physics 47: 276-291
307. Hartranft RJ, Sih GC (1969) The use of eigenfunction expansions in the general solution of three dimensional crack problems. Journal of Mathematics and Mechanics 19: 123-138
308. Long YQ, Zhi BC, Kuang WQ, Shan J (1982). Sub-region mixed finite element method for the calculation of stress intensity factor. In: He GQ et al. (eds). Proceedings of International Conference on FEM. Science Press, Shanghai, pp 738-740
309. Zhong WX, Ji Z (1996). Rational finite element. Computational Structural Mechanics and Applications 1: 1-8 (in Chinese)
310. Long YQ, Fu XR (2002) Two generalized conforming quadrilateral thick plate elements based on analytical trial functions. Gong Cheng Li Xue/Engineering Mechanics 19(3): 10-15 (in Chinese)
311. Fu XR, Long YQ (2002) Generalized conforming quadrilateral plane elements based on analytical trial functions. Gong Cheng Li Xue/Engineering Mechanics 19(4): 12-16 (in Chinese)
312. MacNeal RH (1989) Toward a defect-free four-noded membrane element. Finite Elements in Analysis and Design 5: 31-37
313. Long YQ, Fu XR (2002) Generalized conforming elements based on analytical trial functions. In: Proceedings of the Eleventh National Conference on Structural Engineering (Vol. I), plenary lecture. China, Changsha, pp 28-39 (in Chinese)
314. Taylor RL, Beresford PJ, Wilson EL (1976) A non-conforming element for stress analysis. International Journal for Numerical Methods in Engineering 10: 1211-1219.
315. Pian THH, Sumihara K (1984) Rational approach for assumed stress finite element. International Journal for Numerical Methods in Engineering 20: 1685-1695 (Pubitemid 14651258)
316. Andelfinger U, Ramm E (1993) EAS-elements for two dimensional, three dimensional, plate and shell structures and their equivalence to HR-elements. International Journal for Numerical Methods in Engineering 36: 1311-1337
317. Cao YP, Hu N, Yao ZH (2002) Improved EAS elements. Gong Cheng Li Xue/Engineering Mechanics 19(1): 47-51 (in Chinese) (Pubitemid 35020783)
318. Hu HC (1984) Variational principles of theory of elasticity with applications. Science Press, Beijing
319. Zienkiewicz OC, Taylor RL, Too JM (1971) Reduced integration techniques in general of plates and shells. International Journal for Numerical Methods in Engineering 3: 275-290
320. Hughes TJ, Cohen M, Haroun M (1978) Reduced and selective integration techniques in finite element analysis of plates. Nuclear Engineering and Design 46: 203-222
321. Soh AK, Long ZF, Cen S (1999) A Mindlin plate triangular element with improved interpolation based on Timoshenko's beam theory. Communications in Numerical Methods in Engineering 15(7): 527-532 (Pubitemid 32213149)
322. Soh AK, Long ZF, Cen S (1999) A new nine dof triangular element for analysis of thick and thin plates. Computational Mechanics 24(5): 408-417 (Pubitemid 30546713)
323. Soh AK, Cen S, Long YQ, Long ZF (2001) A new twelve DOF quadrilateral element for analysis of thick and thin plates. European Journal of Mechanics A/Solids 20(2): 299-326 (Pubitemid 32248381)
324. Cen S, Long YQ, Yao ZH, Chiew SP (2006) Application of the quadrilateral area coordinate method: a new element for Mindlin-Reissner plate. International Journal for Numerical Methods in Engineering 66(1): 1-45
325. Long ZF, Cen S (2001) New monograph of finite element method: principle, programming, developments. China Hydraulic and Water-power Press, Beijing (in Chinese)
326. Long YQ, Bu XM, Long ZF, Xu Y (1995) Generalized conforming plate bending elements using point and line compatibility conditions. Computers & Structures 55(4): 717-728
327. Taylor RL, Auricchio F (1993) Linked interpolation for Reissner-Mindlin plate element: part II-a simple triangle. International Journal for Numerical Methods in Engineering 36: 3057-3066
328. Katili I (1993) A new discrete Kirchhoff-Mindlin element based on Mindlin-Reissner plate theory and assumed shear strain fields-Part I: An extended DKT element for thick-plate bending analysis. International Journal for Numerical Methods in Engineering 36: 1859-1883
329. Batoz JL, Katili I (1992) On a simple triangular Reissner/Mindlin plate element based on incompatible modes and discrete constraints. International Journal for Numerical Methods in Engineering 35: 1603-1632 (Pubitemid 23605010)
330. Batoz JL, Lardeur P (1989) A discrete shear triangular nine d.o.f element for the analysis of thick to very thin plates. International Journal for Numerical Methods in Engineering 28: 533-560
331. Williams ML (1957) On the stress distribution at the base of a stationary crack. Journal of Applied Mechanics 24: 109-114
332. Fu XR, Long YQ (2001) Fracture analysis with the sub-region mixed element method. Gong Cheng Li Xue/Engineering Mechanics 18(6): 39-46 (in Chinese)
333. Williams ML (1952) Stress singularities resulting from various boundary conditions in angular corners of plates in extention. Journal of Applied Mechanics 14: 526-528
334. Fan Z, Long YQ (1992) Sub-region mixed finite element analysis of V-notched plates. International Journal of Fracture 56: 333-344
335. Fu XR, Long YQ (2002) Calculation of the eigenvalues-the sub-region accelerated Müller method. In: Proceedings of the Eleventh National Conference on Structural Engineering (Vol. I). China, Changsha, pp 226-232 (in Chinese)
336. Gross B, Mendelson A (1972) Plane elastostatic analysis of V-notched plates. International Journal of Fracture 8: 267-276
337. Long YQ, Li JX, Long ZF, Cen S (1997) Area-coordinate theory for quadrilateral elements. Gong Cheng Li Xue/Engineering Mechanics 14(3): 1-11 (in Chinese)
338. Long ZF, Li JX, Cen S, Long YQ (1997) Differential and integral formulas for area coordinates in quadrilateral element. Gong Cheng Li Xue/Engineering Mechanics 14(3): 12-22 (in Chinese)
339. Long YQ, Li JX, Long ZF, Cen S (1999) Area coordinates used in quadrilateral elements. Communications in Numerical Methods in Engineering 15(8): 533-545
340. Long ZF, Li JX, Cen S, Long YQ (1999) Some basic formulae for Area coordinates used in quadrilateral elements. Communications in Numerical Methods in Engineering 15(12): 841-852 (Pubitemid 30526327)
341. Long YQ, Long ZF, Cen S (1999) Method of area coordinate-from triangular to quadrilateral elements. In: Long YQ (ed) The proceedings of the first international conference on structural engineering (Invited paper). China, KunMing, pp 57-66
342. Long YQ, Long ZF, Cen S (2001) Method of area coordinate-from triangular to quadrilateral elements. Advances in Structural Engineering 4(1): 1-11 (Pubitemid 32271397)
343. Chen XM, Cen S, Long YQ, Fu XR (2007) A two-component area coordinate method for quadrilateral elements. Gong Cheng Li Xue/Engineering Mechanics 24(Sup. I): 32-35 (in Chinese) (Pubitemid 47060385)
344. Chen XM, Cen S, Fu XR, Long YQ (2008) A new quadrilateral area coordinate method (QACM-II) for developing quadrilateral finite element models. International Journal for Numerical Methods in Engineering 73(13): 1911-1941 (Pubitemid 351454755)
345. Taig IC (1961) Structural analysis by the matrix displacement method. Eng1. Electric Aviation Report No. S017
346. Irons BM (1966) Engineering application of numerical integration in stiffness method. AIAA Journal 14: 2035-2037
347. Hua C (1990) An inverse transformation for quadrilateral isoparametric elements: analysis and application. Finite Elements in Analysis and Design 7: 159-166
348. Lee NS, Bathe KJ (1993) Effects of element distortions on the performance of isoparametric elements. International Journal in Numerical Methods in Engineering 36: 3553-3576
349. Mertie JB (1964) Transformation of trilinear and quadriplanar coordinates to and from Cartesian coordinates. The American Mineralogist 49(7/8): 926-936
350. Eisenberg MA, Malvern LE (1973) On finite element integration in natural coordinates. International Journal in Numerical Methods in Engineering 7(4): 574-575
351. Zhong ZH (1993) Finite element procedures for contact-impact problems. Oxford University Press, Oxford
352. Long YQ, Long ZF, Wang L (2009) The third version of area coordinate systems for quadrilateral elements. Gong Cheng Li Xue/Engineering Mechanics 26(2): 1-5 (in Chinese)
353. Pian THH, Sumihara R (1984) Rational approach for assumed stress finite elements. International Journal for Numerical Methods in Engineering 20: 1685-1695 (Pubitemid 14651258)
354. Wilson EL, Ibrahimbegovic A (1990) Use of incompatible displacement modes for the calculation of element stiffness or stresses. Finite Elements in Analysis and Design 7: 229-241
355. Xu Y, Long ZF, Long YQ (1998) A generalized conforming quadrilateral membrane element insensitive to geometric distortion. Advances in Structural Engineering 1(3): 185-191
356. Lee NS, Bathe KJ (1993) Effects of element distortions on the performance of isoparametric elements. International Journal for Numerical Methods in Engineering 36: 3553-3576
357. Cen S, Long ZF, Zhang CS (1998) Two eight-node quadrilateral elements constructed by area coordinates. In: Proceedings of the Seventh National Conference on Structural Engineering (Vol. I). China, ShijiaZhuang, pp 237-241 (in Chinese)
358. Long YQ, Long ZF, Cen S (2001) Several problems and advances in finite element method. In: Proceedings of the Tenth National Conference on Structural Engineering (Vol. I). China, Nanjing, pp 34-51 (in Chinese)
359. Chen XM, Cen S, Long YQ, Yao ZH (2004) Membrane elements insensitive to distortion using the quadrilateral area coordinate method. Computers & Structures 82(1): 35-54
360. Cen S, Du Y, Chen XM, Fu XR (2007) The analytical element stiffness matrix of a recent 4-node membrane element formulated by the Quadrilateral Area Coordinate method. Communications in Numerical Methods in Engineering 23(12): 1095-1110 (Pubitemid 350268756)
361. Du Y, Cen S (2008) Geometrically nonlinear analysis with a 4-node membrane element formulated by the quadrilateral area coordinate method. Finite Elements in Analysis and Design 44(8): 427-438
362. Cen S, Chen XM, Fu XR (2007) Quadrilateral membrane element family formulated by the quadrilateral area coordinate method. Computer Methods in Applied Mechanics and Engineering 196(41-44): 4337-4353 (Pubitemid 47194338)
363. Chen XM, Cen S, Fu XR, Long YQ (2008) A new quadrilateral area coordinate method (QACM-II) for developing quadrilateral finite element models. International Journal for Numerical Methods in Engineering 73(13): 1911-1941 (Pubitemid 351454755)
364. Chen XM, Long YQ, XU Y (2003) Construction of quadrilateral membrane elements with drilling DOF using area coordinate method. Gong Cheng Li Xue/Engineering Mechanics 20(6): 6-11 (in Chinese)
365. Soh AK, Long YQ, Cen S (2000) Development of eight-node quadrilateral membrane elements using the area coordinates method. Computational Mechanics 25(4): 376-384
366. Guan NX, Cen S, Chen XM (2007) Quadrilateral axisymmetric elements formulated by the area coordinate method. In: Yao ZH, Yuan MW (eds) Computational Mechanics (Proceedings of the ISCM 2007). Tsinghua University Press & Springer, China, Beijing, CD Rom pp 1055-1059
367. Long ZF, Li JX, Cen S, Long YQ (1997) A quadrilateral plate bending element by using area coordinate method. Gong Cheng Li Xue/Engineering Mechanics 14(4): 1-10 (in Chinese)
368. Soh AK, Long ZF, Cen S (2000) Development of a new quadrilateral thin plate element using area coordinates. Computer Methods in Applied Mechanics and Engineering 190(8-10): 979-987 (Pubitemid 32029474)
369. Cen S, Long YQ, Yao ZH, Chiew SP (2006) Application of the quadrilateral area coordinate method: A new element for Mindlin-Reissner plate. International Journal for Numerical Methods in Engineering 66(1): 1-45
370. Cen S, Fu XR, Long YQ, Li HG, Yao ZH (2007) Application of the quadrilateral area coordinate method: a new element for laminated composite plate bending problems. Acta Mechanica Sinica 23(5): 561-575
371. Taylor RL, Beresford PJ, Wilson EL (1976) A non-conforming element for stress analysis. International Journal for Numerical Methods in Engineering 10: 1211-1219
372. Cen S, Long ZF (1998) A new triangular generalized conforming element for thin-thick plates. Gong Cheng Li Xue/Engineering Mechanics 15(1): 10-22 (in Chinese)
373. Wilson EL, Taylor RL, Doherty WP, Ghabussi T (1973) Incompatible displacement models. In: Fenven ST et al., eds. Numerical and Computer Methods in Structural Mechanics. Academic Press, New York, 43-57
374. Chen WJ, Tang LM (1981) Isoparametric quasi-conforming element. Journal of Dalian University of Technology 20(1): 63-74 (in Chinese)
375. Pian THH, Wu CC (1986) General formulation of incompatible shape function and an incompatible isoparametric element. In: Proceedings of the Invitational China-American Workshop on FEM. China, Chengde, pp 159-165
376. Piltner R, Taylor RL (1997) A systematic construction of B-bar functions for linear and nonlinear mixed-enhanced finite elements for plane elasticity problems. International Journal for Numerical Methods in Engineering 44: 615-639
377. Bassayya K, Bhattacharya K, Shrinivasa U (2000) Eight-node brick, PN340, representing constant stress fields exactly. Computers & Structures 74: 441-460 (Pubitemid 30527895)
378. Long YQ, Xu Y (1994) Generalized conforming quadrilateral membrane element with vertex rigid rotational freedom. Computers & Structures 52(4): 749-755
379. MacMeal RH, Harder RL (1985) A proposed standard set of problems to test finite element accuracy. Finite Elements in Analysis and Design 1(1): 3-20
380. Chen WJ, Cheung YK (1992) Three dimensional 8-node and 20-node refined hybrid isoparametric elements. International Journal for Numerical Methods in Engineering 35: 1871-1889 (Pubitemid 23614807)
381. Andelfinger U, Ramm E (1993) EAS-elements for two-dimensional, three-dimensional, plate and shell structures and their equivalence to HR-elements. International Journal for Numerical Methods in Engineering 36: 1311-1337
382. MacNeal RH (1987) A theorem regarding the locking of tapered four-noded membrane elements. International Journal for Numerical Methods in Engineering 24: 1793-1799
383. Wu CC, Jiao ZP (1993) Geometrically nonlinear analyses for 2-D problems based on the incompatible finite elements with internal parameters. Acta Mechanica Sinica 25 (4): 505-513 (in Chinese)
384. ABAQUS Inc. ABAQUS Documentation Version 6.5 (2004) ABAQUS Inc., Rawtucket, Rhode Island
385. Bisshopp RE, Drucker DC (1945) Large deflection of cantilever beams. Quarterly of Applied Mathematics 3(3): 272-275
386. Weissmen SL, Taylor RL (1990) Resultant fields for mixed plate bending elements. Computer Methods in Applied Mechanics in Engineering 79: 321-355
387. Batoz JL, Tahar MB (1982) Evaluation of a new quadrilateral thin plate bending element. International Journal for Numerical Methods in Engineering 18: 1655-1677
388. Hu HC (1984) Variational principles of theory of elasticity with applications. Science Press, Beijing
389. Soh AK, Cen S, Long YQ, Long ZF (2001) A new twelve DOF quadrilateral element for analysis of thick and thin plates. European Journal of Mechanics A/Solids 20(2): 299-326 (Pubitemid 32248381)
390. Kant T, Hinton E (1983) Mindlin plate analysis by the segmentation method. Journal of Engineering Mechanics, Div. ASCE, 109: 537-556 (Pubitemid 13522744)
391. Lardeur P, Batoz JL (1989) Composite plate analysis using a new discrete shear triangular finite element. International Journal for Numerical Methods in Engineering 27: 343-359 (Pubitemid 20645032)
392. Wu CC, Pian THH (1997) Incompatible numerical analysis and hybrid finite element method. Science Press, Beijing (in Chinese)
393. Pagano NJ, Hatfield SJ (1972) Elastic behavior of multilayered bidirectional composites. AIAA Journal 10: 931-933
394. Reddy JN (1997) Mechanics of laminated composite plates-theory and analysis. CRC Press, Boca Raton
395. De Boor C (1978) A practical guide to splines. Springer Verlag, New York
396. Schumaker LL (1981) Spline function: basic theory. John Wiley and Sons, New York
397. Schultz MH (1973) Spline analysis. Prentic-Hall, Englewood Cliff, New Jersey
398. Prenter PM (1975) Splines and variational methods. John Wiley and Sons, New York
399. Yuan S (1982) Finite element analysis of shell of revolution using cubic B spline. In: Proceeding of International Conference on FEM. China, Shanghai, pp 837-840
400. Yuan S (1986) Quadratic spline thick/thin plate triangular hybrid elements. In: Proceeding International Conference on Computational Mechanics. Tokyo, pp 1111-1116
401. Fan Z (1988) Applications of spline elements and sub-region mixed elements in structural engineering [Doctoral Dissertation]. Tsinghua University, Beijing (in Chinese)
402. Fan Z, Long YQ (1991) Linear analysis of tall buildings using spline element. Engineering Structure, 13: 27-33
403. Fan Z, Long YQ (1990) Large deflection and stability analysis by geometrically nonlinear spline element. In: Proceeding of International Conference on Numerical Methods in Engineering, Theory & Applications (Vol. 1). Swansea, UK, pp 414-422
404. Yuan S (1984) Spline elements in stress analysis [Doctoral Dissertation]. Tsinghua University, Beijing
405. Cheung YK (1976) Finite strip method in structural analysis. Bergamon Press, Oxford
406. Girijavallaham CV (1969) Analysis of shear wall with opening. Journal of ASCE, STR 10: 2093-2102
407. Chan HC, Cheung YK (1979) Analysis of shear walls using higher order finite element. Building & Environment, 14: 217-244
408. Fan Z, Long YQ (1989) Spline thick/thin shell element. In: Proceeding of 2nd East Asia-Pacific Conference on Structural Engineering & Construction. Thailand, Chiang Mai, pp 1195-1200
409. Coull A, Subedi NK (1975) Hull-core structures subjccted to bending and torsion. In: Proceedings of 9th Congress of International Association for Bridge and Structral Engineering, Preliminary Report, May
410. Coull A, Bose B (1975) Simplified analysis of framed-tube structures. Journal of the Structral Division, ASCE, 101(11): 2223-2240
411. Coull A, Bose B (1976) Torsion of framed-tube structures. Journal of the Structral Division, ASCE 102(12): 2366-2370
412. Long YQ, Xin KG (1985) Analysis of framed-tube structures of polygonal section by energy method. Journal of Building Structures 6(3): 10-16 (in Chinese)
413. Yuan S (1984) Spline elements in stress analysis [Doctoral Dissertation]. Tsinghua University, Beijing
414. Solid Mechanics Division, Beijing Institutie of Mechanics, China Academy of Science (1977) Bending, stability and vibration of sandwich plates. Science Press, Beijing (in Chinese)
415. Fan Z (1988) Applications of spline elements and sub-region mixed elements in structural engineering [Doctoral Dissertation]. Tsinghua University, Beijing (in Chinese)
416. Fan Z, Long YQ (1989) Spline thick/thin shell element. In: Proceeding of 2nd East Asia-Pacific Conference on Structural Engineering & Construction. Thailand, Chiang Mai, pp 1195-1200
417. Pryor CWJ, Barker RM, Frederick D (1970) Finite element bending analysis of Reissner plates. Journal of the Engineering Mechanics Division, ASCE, 96(6): 967-983
418. Timoshenko S, Woinowsky-Krieger S (1959) Theory of plates and shells. McGraw-Hill, New York
419. Alexander T (1982) An efficient conforming axisymmetric shell element including transverse shear and rotary inertia. Computers & Structures 15: 567-574
420. Fan Z, Long YQ (1990) Large deflection and stability analysis by geometrically nonlinear spline element. In: Proceeding of International Conference on Numerical Methods in Engineering, Theory & Applications (Vol. 1). Swansea, UK, pp 414-422
421. Haisler WE, Stricklin J A, Stebblins FJ (1972) Development and evaluation of solution procedures for geometrically nonlinear structural analysis. AIAA Journal 10: 264-272
422. Bathe KJ, Bolourch S (1980) A geometric and material nonlinear plate and shell element. Computers & Structures 11: 23-48
423. Budiansky B (1959) Buckling of clamped shallow spherical shells. In: Proceeding of IUTAM Symposium on the theory of thin elastic shells. The Netherlands, Delft, pp 64-85
424. Weinitschke H (1960) On the stability problem for shallow spherical shells. Journal of Mathematics and Physics 38: 208-231
425. Chien WZ (1980) Calculus of variations and finite elements (Vol. I). Science Press, Beijing (in Chinese)
426. Long YQ, (1981) Piecewise generalized variational principles in elasticity. Shanghai Mechanics 2(2): 1-9. (in Chinese)
427. Long YQ, Zhi BC, Yuan S (1982) Sub-region, sub-item and sub-layer generalized variational principles in elasticity. In: He GQ et al (eds) Proceedings of International Conference on FEM. Science Press, Shanghai, pp 607-609
428. Long YQ (1986) Several patterns of functional transformation and gcneralized variational principles with several arbitrary parameters. International Journal of Solids and Structures 22(10): 1059-1069
429. Long YQ, Xin KG (1987) Generalized conforming element. Tumu Gongcheng Xuebao/China Civil Engineering Journal 20(1): 1-14 (in Chinese)
430. Long YQ, Xin KG (1989) Generalized conforming element for bending and buckling analysis of plates. Finite Elements in Analysis and Design 5: 15-30
431. Long YQ, Zhi BC, Kuang WQ, Shan J (1982) Sub-region mixed finite element method for the calculation of stress intensity factor. In: He GQ et al (eds) Proceedings of International Conference on FEM. Science Press, Shanghai, pp 738-740
432. Long YQ, Fu XR (2002) Generalized conforming elements based on analytical trial functions. In: Proceedings of the Eleventh National Conference on Structural Engineering (Vol. I), plenary lecture. China, Changsha, pp 28-39 (in Chinese)
433. Long YQ, Li JX, Long ZF, Cen S (1997) Area-coordinate theory for quadrilateral elements. Gong Cheng Li Xue/Engineering Mechanics 14(3): 1-11 (in Chinese)
434. Long YQ, Li JX, Long ZF, Cen S (1999) Area coordinates used in quadrilateral elements. Communications in Numerical Methods in Engineering 15(8): 533-545
435. Yuan S (1984) Spline elements in stress analysis [Doctoral Dissertation]. Tsinghua University, Beijing
436. Fan Z (1988) Applications of spline elements and sub-region mixed elements in structural engineering [Doctoral Dissertation]. Tsinghua University, Beijing (in Chinese)
437. Cen S, Long ZF (1998) A Mindlin triangular plate element with improved interpolation for the rotation and shear strain fields. Gong Cheng Li Xue/Engineering Mechanics 15(3): 1-14 (in Chinese)
438. Cen S, Long ZF, Long YQ (1999) A Mindlin quadrilateral plate element with improved interpolation for the rotation and shear strain fields. Gong Cheng Li Xue/Engineering Mechanics 16(4): 1-15 (in Chinese) (Pubitemid 30569930)
439. Soh AK, Cen S, Long YQ, Long ZF (2001) A new twelve DOF quadrilateral element for analysis of thick and thin plates. European Journal of Mechanics A/Solids 20: 299-326 (Pubitemid 32248381)
440. Cen S, Long ZF (1998) A new triangular generalized conforming element for thin-thick plates. Gong Cheng Li Xue/Engineering Mechanics 15(1): 10-22 (in Chinese)
441. Chen YL, Cen S, Yao ZH, Long YQ, Long ZF (2003) Development of triangular flat-shell element using a new thin-thick plate bending element based on SemiLoof constraints. Structural Engineering and Mechanics 15(1): 83-114
442. Long ZF (1992) Locking-free thick plate rectangular element. Gong Cheng Li Xue/Engineering Mechanics 9(1): 88-93 (in Chinese)
443. Long YQ, Xi F (1992) A universal method for including shear deformation in the thin plate elements. International Journal for Numerical Methods in Engineering 34: 171-177
444. Cen S, Long YQ, Yao ZH (2002) A new element based on the first-order shear deformation theory for the analysis of laminated composite plates. Gong Cheng Li Xue/Engineering Mechanics 19(1): 1-8 (in Chinese) (Pubitemid 35020776)
445. Cen S, Long YQ, Yao ZH (2002) A new hybrid-enhanced displacement-based element for the analysis of laminated composite plates. Computers & Structures 80 (9-10): 819-833 (Pubitemid 34715397)
446. Cen S, Soh AK, Long YQ, Yao ZH (2002) A new 4-node quadrilateral FE model with variable electrical degrees of freedom for the analysis of piezoelectric laminated composite plates. Composite Structures 58(4): 583-599 (Pubitemid 35400198)
447. Long YQ, Huang MF (1988) A generalized conforming isoparametric element. Applied mathematics and Mechanics (English Edition) 9(10): 929-936
448. Xu Y, Long YQ (1993) Generalized conforming rectangular membrane elements with vertex rigid rotational freedom. In: Proceedings of the Second National Conference on Structural Engineering, pp 199-206 (in Chinese)
449. Long YQ, Xu Y (1994) Generalized conforming quadrilateral membrane element with vertex rigid rotational freedom. Computers & Structures 52(4): 749-755
450. Long YQ, Xu Y (1994) Generalized conforming triangular membrane element with vertex rigid rotational freedom. Finite Elements in Analysis and Design 17: 259-271
451. Xu Y (1994) The generalized conforming approach and the development of the membrane elements with drilling degrees of freedom and thin plate and shell elements [Doctoral Dissertation]. Tsinghua University, Beijing (in Chinese)
452. Long YQ, Xu Y (1994) Generalized conforming flat rectangular thin shell element. Computational Structural Mechanics and Applications 11(2): 154-160 (in Chinese)
453. Xu Y, Long YQ, Long ZF (1994) A triangular shell element with drilling freedoms based on generalized compatibility conditions. In: Proceeding of WCCM III. Japan pp 1234-1235
454. Long YQ, Zhao JQ (1992) Generalized conforming curved rectangular element for shallow shells. Gong Cheng Li Xue/Engineering Mechanics 9(1): 3-10 (in Chinese)
455. Sun JH (1998) Research on generalized conforming shallow shell element and nonlinear analysis of plate and shell structures [Doctoral Dissertation]. Tsinghua University, Beijing (in Chinese)
456. Sun JH, Long ZF, Long YQ, Zhang CS (2001) Geometrically nonlinear stability analysis of shells using generalized conforming shallow shell element. International Journal of Structural Stability and Dynamics 1(3): 313-332
457. Long YQ, Zhao YQ (1985) Calculation of stress intensity factors in plane problems by the sub-region mixed finite element method. Enginering Software 7(1): 32-35
458. Huang MF, Long YQ (1988) Calculation of stress intensity factors of cracked Reissner plates by the sub-region mixed finite element method. Computers & Structures 30(4): 837-840
459. Long YQ, Qian J (1992) Calculation of stress intensity factors for surface cracks in a 3D body by the subregion mixed FEM. Computers & Structures 44(1/2): 75-78 (Pubitemid 23557064)
460. Fan Z, Long YQ (1992) Sub-region mixed finite element analysis of V-notched plates. International Journal of Fracture 56: 333-344
461. Long YQ, Qian J (1992) Sub-region mixed finite element analysis of V-notches in a bimaterial. In: Zhu DC (ed) Advances in Engineering Mechanics. Peking University Press, Beijing, pp 54-59
462. Qian J, Long YQ (1991) Sub region mixed FEM for calculating stress intensity factor of antiplane notch in bi-material. Computational Structural Mechanics and Applications 8(3): 325-330 (in Chinese)
463. Qian J, Long YQ (1992) The expression of stress and strain at the tip of notch in Reissner plate. Applied mathematics and Mechanics (English Edition) 13(4): 315-324
464. Qian J, Long YQ (1994) The expression of stress and strain at the tip of 3-D notch. Applied mathematics and Mechanics (English Edition) 15(3): 211-221
465. Fu XR, Long YQ (2002) Generalized conforming quadrilateral plane elements based on analytical trial functions. Gong Cheng Li Xue/Engineering Mechanics 19(4): 12-16 (in Chinese)
466. Long YQ, Fu XR (2002) Two generalized conforming quadrilateral thick plate elements based on analytical trial functions. Gong Cheng Li Xue/Engineering Mechanics 19(3): 10-15 (in Chinese)
467. Fu XR, Long YQ (2001) Fracture analysis with the sub-region mixed element method. Gong Cheng Li Xue/Engineering Mechanics 18(6): 39-46 (in Chinese)
468. Fu XR (2002) Generalized conforming element method based on the analytical trial functions [Doctoral Dissertation]. Tsinghua University, Beijing (in Chinese)
469. Fan Z, Long YQ (1991) Linear analysis of tall buildings using spline element. Engineering Structure 13: 27-33
470. Fan Z, Long YQ (1989) Spline thick/thin shell element. In: Proceeding of 2nd East Asia-Pacific Conference on Structural Engineering & Construction. Chiang Mai, Thailand, pp 1195-1200
471. Fan Z, Long YQ (1990) Large deflection and stability analysis by geometrically nonlinear spline element. In: Proceeding of International Conference on Numerical Methods in Engineering, Theory & Applications (Vol. 1). Swansea, UK, pp 414-422
472. Soh AK, Long YQ, Cen S (2000) Development of eight-node quadrilateral membrane elements using the area coordinates method. Computational Mechanics 25(4): 376-384
473. Chen XM, Cen S, Long YQ, Yao ZH (2004) Membrane elements insensitive to distortion using the quadrilateral area coordinate method. Computers & Structures 82(1): 35-54
474. Cen S, Chen XM, Fu XR (2007) Quadrilateral membrane element family formulated by the quadrilateral area coordinate method. Computer Methods in Applied Mechanics and Engineering 196(41-44): 4337-4353 (Pubitemid 47194338)
475. Chen XM, Cen S, Fu XR, Long YQ (2008) A new quadrilateral area coordinate method (QACM-II) for developing quadrilateral finite element models. International Journal for Numerical Methods in Engineering 73(13): 1911-1941 (Pubitemid 351454755)