Boundary methods: Elements, contours, and nodes

Boundary Methods: Elements, Contours, and Nodes

Volumn , Issue , 2005, Pages 1-220

  Mukherjee, Subrata ^a   Mukherjee, Yu Xie ^a  

^a Department of Obstetrics Gynecology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85057682692     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Book

References (190)

1. Aluru, N.R. and White, J. (1997). An efficient numerical technique for electromechanical simulation of complicated microelectromechanical structures. Sensors and Actuators A 58:1-11.
2. Aluru, N.R. and Li, G. (2001). Finite cloud method: a true meshless technique based on a fixed reproducing kernel approximation. International Journal for Numerical Methods in Engineering 50:2373-2410.
3. Atluri, S.N. and Shen, S. (2002). The Meshless Local Petrov-Galerkin (MLPG) Method. Tech Science Press, Encino, CA.
4. Banerjee, P.K. (1994). The Boundary Element Methods in Engineering. McGraw Hill Europe, Maidenhead, Berkshire, UK.
5. Banichuk, N.V. (1983). Problems and Methods of Optimal Structural Design. Plenum, New York.
6. Bao, Z. and Mukherjee, S. (2004). Electrostatic BEM for MEMS with thin conducting plates and shells. Engineering Analysis with Boundary Elements. 28:1427-1435.
7. Bao, Z. and Mukherjee, S. (2005). Electrostatic BEM for MEMS with thin beams. Communications in Numerical Methods in Engineering. In press.
8. Bao, Z., Mukherjee, S., Roman, M. and Aubry, N. (2004). Nonlinear vi-brationsof beamsstringsplatesand membraneswithout initial tension. ASME Journal of Applied Mechanics 71:551-559.
9. Becker, A.A. (1992). The Boundary Element Method in Engineering. Mc-Graw Hill International, Singapore.
10. Belytschko, T., Lu, Y.Y. and Gu, L. (1994). Element-free Galerkin methods. International Journal for Numerical Methods in Engineering 37:229-256.
11. Belytschko, T., Krongauz, Y., Organ, D., Fleming, M. and Krysl, P. (1996). Meshless methods: An overview and recent developments. Computer Methods in Applied Mechanics and Engineering 139:3-47.
12. Bobaru, F. and Mukherjee, S. (2001). Shape sensitivity analysis and shape optimization in planar elasticity using the element-free Galerkin method. Computer Methods in Applied Mechanics and Engineering 190:4319-4337.
13. Bobaru, F. and Mukherjee, S. (2002). Meshless approach to shape optimization of linear thermoelastic solids. International Journal for Numerical Methods in Engineering 53:765-796.
14. Bonnet, M. (1995). Boundary Integral Equation Methods for Solids and Fluids. Wiley, Chichester, UK.
15. Bonnet, M. and Xiao, H. (1995). Computation of energy release rate using material differentiation of elastic BIE for 3-D elastic fracture. Engineering Analysis with Boundary Elements 15:137-149.
16. Brebbia, C.A. and Dominguez, J. (1992). Boundary Elements: An Introductory Course. 2nd edition. Computational MechanicsPublications, Southampton, UK, and McGraw Hill, New York.
17. Bui, H.D. (1975). Application despotentielsélastiques à l’étude des fissures planesde forme arbitrare en milieu tridimensionnel. Comptes Rendus de l’Académie des Sciences Paris Série A 280:1157-1160.
18. Carstensen, C. (1995). Adaptive boundary element methods and adaptive finite element methodsand boundary element coupling. Boundary Value Problems and Integral Equations in Nonsmooth Domains. M. Costabel, M. Dauge and S. Nicaise eds., 47-58. Marcel Dekker.
19. Carstensen, C. and Stephan, E.P. (1995). A posteriori error estimates for boundary element methods. Mathematics of Computation 64:483-500.
20. Carstensen, C., Estep, D. and Stephan, E.P. (1995). h-adaptive boundary element schemes. Computational Mechanics 15:372-383.
21. Carstensen, C. (1996). Efficiency of a posteriori BEM error estimates for first kind integral equations on quasi-uniform meshes. Mathematics of Computation 65:69-84.
22. Chandra, A. and Mukherjee, S. (1997). Boundary Element Methods in Manufacturing. Oxford University Press, NY.
23. Chati, M.K. (1999). Meshless Standard and Hypersingular Boundary Node Method-Applications in Three-Dimensional Potential Theory and Linear Elasticity. Ph.D. Dissertation, Cornell University, Ithaca, NY.
24. Chati, M.K. and Mukherjee, S. (1999). Evaluation of gradientson the boundary using fully regularized hypersingular boundary integral equations. Acta Mechanica 135:41-55.
25. Chati, M.K., Mukherjee, S. and Mukherjee, Y.X. (1999). The boundary node method for three-dimensional linear elasticity. International Journal for Numerical Methods in Engineering 46:1163-1184.
26. Chati, M.K. and Mukherjee, S. (2000). The boundary node method for three-dimensional problems in potential theory. International Journal for Numerical Methods in Engineering 47:1523-1547.
27. Chati, M.K., Mukherjee, S. and Paulino, G.H. (2001). The meshless hypersingular boundary node method for three-dimensional potential theory and linear elasticity problems. Engineering Analysis with Boundary Elements 25:639-653.
28. Chati, M.K., Mukherjee, S. and Paulino, G.H. (2001). The meshless standard and hypersingular boundary node methods-applicationsto error estimation and adaptivity in three-dimensional problems. International Journal for Numerical Methods in Engineering 50:2233-2269.
29. Chen, G. and Zhou, J. (1992). Boundary Element Methods. Academic Press.
30. Chen, J.T. and Hong, H.K. (1999). Review of dual boundary element methods with emphasis on hypersingular integrals and divergent series. ASME Applied Mechanics Reviews 52:17-33.
31. Chen, S.Y., Tang, W.X., Zhou, S.J., Leng, X. and Zheng, W. (1999). Evaluation of J integrals and stress intensity factors in a 2D quadratic boundary contour method. Communications in Numerical Methods in Engineering 15:91-100.
32. Chen, W. and Tanaka, M. (2002). A meshless, integration-free, boundary-only RBF technique. Computers and Mathematics with Applications 43:379-391.
33. Choi, J.H. and Kwak, B.M. (1988). Boundary integral equation method for shape optimization of elastic structures. International Journal for Numerical Methods in Engineering 26:1579-1595.
34. Ciarlet, P.G. (1991). Basic error estimates for elliptic problems. Finite Element Methods (Part 1)-Vol. 2 of Handbook of Numerical Analysis. P. G. Ciarlet and J. L. Lions eds., Elsevier Science Publishers.
35. Costabel, M. and Stephan, E. (1985). Boundary integral equations for mixed boundary value problemsin polygonal domainsand Galerkin approximation. Mathematical Models and Methods in Mechanics Vol. 15. W. Fiszdon and K. Wilmanski eds., Banach Center Publications.
36. Costabel, M., Dauge, M. and Nicaise, S. eds. (1995). Boundary Value Problems and Integral Equations in Non-smooth Domains. Number 167 in Lecture Notes in Pure and Applied Mathematics. Marcel Dekker Publications.
37. Cruse, T.A. (1969). Numerical solutions in three-dimensional elastostatics. International Journal of Solids and Structures 5:1259-1274.
38. Cruse, T.A. (1988). Boundary Element Analysis in Computational Fracture Mechanics. Kluwer, Dordrecht, The Netherlands.
39. Cruse, T.A. and Richardson, J.D. (1996). Non-singular Somigliana stress identitiesin elasticity. International Journal for Numerical Methods in Engineering 39:3273-3304.
40. De, S. and Bathe, K.J. (2000). The method of finite spheres. Computational Mechanics 25:329-345.
41. Dolbow, J., Möes, N. and Belytschko, T. (2000). Modeling fracture in Mindlin-Reissner plates with the extended finite element method. International Journal of Solids and Structures 37:7161-7183.
42. Duarte, C.A.M. and Oden, J.T. (1996). H-p clouds-an h-p meshless method. Numerical Methods in Partial Differential Equations 12:673-705.
43. Duarte, C.A.M. and Oden, J.T. (1996). An h-p adaptive method using clouds. Computer Methods in Applied Mechanics and Engineering 139:237-262.
44. Eriksson, K., Estep, D., Hansbo, P. and Johnson, C. (1995). Introduction to adaptive methodsfor partial differential equations. Acta Numerica Chapter 3. A. Iserles ed., 105-158, Cambridge University Press, UK.
45. Feistaur, M., Hsiao, G.C. and Kleinman, R.E. (1996). Asymptotic and a posteriori error estimates for boundary element solutions of hypersingular integral equations. SIAM Journal of Numerical Analysis 32:666-685.
46. Fung, Y-C. (1965). Foundations of Solid Mechanics. Prentice Hall, Englewood Cliffs, NJ.
47. Gaul, L., Kögl, M. and Wagner, M. (2003). Boundary Element Methods for Engineers and Scientists. Springer Verlag, Heidelberg, Germany.
48. Ghosh, N. and Mukherjee, S. (1987). A new boundary element method formulation for three dimensional problems in linear elasticity. Acta Mechanica 67:107-119.
49. Gilbert, J.R., Legtenberg, R. and Senturia, S.D. (1995). 3D coupled elec-tromechanicsfor MEMS-applicationsof CoSolve EM. Proceedings of IEEE MEMS pp.122-127.
50. Glushkov, E., Glushkova, N. and Lapina, O. (1999). 3-D elastic stress analysis at polyhedral corner points. International Journal of Solids and Structures 36:1105-1128.
51. Goldberg, M.A. and Bowman, H. (1998). Superconvergence and the use of the residual as an error estimator in the BEM-I. Theoretical Development. Boundary Element Communications 8:230-238.
52. Gowrishankar, R. and Mukherjee, S. (2002). A “pure” boundary node method in potential theory. Communications in Numerical Methods in Engineering 18:411-427.
53. Gray, L.J. (1989). Boundary element method for regionswith thin internal cavities. Engineering Analysis with Boundary Elements 6:180-184.
54. Gray, L.J., Martha, L.F. and Ingraffea, A.R. (1990). Hypersingular integrals in boundary element fracture analysis. International Journal for Numerical Methods in Engineering 29:1135-1158.
55. Gray, L.J., Balakrishna, C. and Kane, J.H. (1995). Symmetric Galerkin fracture analysis. Engineering Analysis with Boundary Elements 15:103-109.
56. Gray, L.J. and Paulino, G.H. (1997). Symmetric Galerkin boundary integral formulation for interface and multizone problems. International Journal for Numerical Methods in Engineering 40:3085-3101.
57. Gray, L.J. and Paulino, G.H. (1997). Symmetric Galerkin boundary integral fracture analysis for plane orthotropic elasticity. Computational Mechanics 20:26-33.
58. Gray, L.J. and Paulino, G.H. (1998). Crack tip interpolation revisited. SIAM Journal of Applied Mathematics 58:428-455.
59. Guidera, J.T. and Lardner, R.W. (1975). Penny shaped cracks. Journal of Elasticity 5:59-73.
60. Guiggiani, M. (1994). Hypersingular formulation for boundary stress evaluation. Engineering Analysis with Boundary Elements 13:169-179.
61. Harrington, R.F. (1993). Field Computation by Moment Methods. IEEE Press, Piscataway, NJ.
62. Hartmann, F. (1989). Introduction to Boundary Elements: Theory and Applications. Springer Verlag, Berlin, New York.
63. Haug, E.J., Choi, K.K. and Komkov, V. (1986). Design Sensitivity Analysis of Structural Systems. Academic Press, New York.
64. Hayami, K. and Matsumoto, H. (1994). A numerical quadrature for nearly singular boundary element integrals. Engineering Analysis with Boundary Elements 13:143-154.
65. Heck, A. (1993). Introduction to Maple. Springer Verlag, New York.
66. Hughes, T.J.R. (2000). The Finite Element Method-Linear Static and Dynamic Finite Element Analysis. Dover, Mineola, NY.
67. Kaljevic, I. and Saigal, S. (1997). An improved element free Galerkin formulation. International Journal for Numerical Methods in Engineering 40:2953-2974.
68. Kane, J.H. (1994). Boundary Element Analysis in Engineering Continuum Mechanics. Prentice Hall, Englewood Cliffs, NJ.
69. Kaplan, W. (1984). Advanced Calculus 3rd. ed. Addison-Wesley, Reading, MA.
70. Kita, E. and Kamiya, N. (1994). Recent studies on adaptive boundary element methods. Advances in Engineering Software 19:21-32.
71. Ko, S.C., Kim, Y.C., Lee, S.S., Choi, S.H. and Kim, S.R. (2003). Micro-machined piezoelectric membrane acoustic device. Sensors and Actuators A 103:130-134.
72. Kothnur, V., Mukherjee, S. and Mukherjee, Y.X. (1999). Two-dimensional linear elasticity by the boundary node method. International Journal of Solids and Structures 36:1129-1147.
73. Kress, R. (1989). Linear Integral Equations. Springer Verlag.
74. Krishnamoorthy, C.S. and Umesh, K.R. (1993). Adaptive mesh refinement for two-dimensional finite element stress analysis. Computers and Structures 48:121-133.
75. Krishnasamy, G., Schmerr, L.W., Rudolphi, T.J. and Rizzo, F.J. (1990). Hypersingular boundary integral equations: some applications in acoustic and elastic wave scattering. ASME Journal of Applied Mechanics 57:404-414.
76. Krishnasamy, G., Rizzo, F.J. and Rudolphi, T.J. (1992). Hypersingular boundary integral equations: their occurrence, interpretation, regularization and computation. Developments in Boundary Element Methods-7. P.K. Banerjee and S. Kobayashi eds., Elsevier Applied Science, London, pp. 207-252.
77. Kulkarni, S.S., Telukunta, S. and Mukherjee, S. (2003). Application of an accelerated boundary-based mesh-free method to two-dimensional problemsin potential theory. Computational Mechanics 32:240-249.
78. Lancaster, P. and Salkauskas, K. (1990). Curve and Surface Fitting-An Introduction. Academic Press, London.
79. Li, G. and Aluru, N.R. (2002). Boundary cloud method: a combined scattered point/boundary integral approach for boundary only analysis. Computer Methods in Applied Mechanics and Engineering 191:2337-2370.
80. Li, G. and Aluru, N.R. (2003). A boundary cloud method with a cloud-by-cloud polynomial basis. Engineering Analysis with Boundary Elements 27:57-71.
81. Liapis, S. (1995). A review of error estimation and adaptivity in the boundary element method. Engineering Analysis with Boundary Elements 14:315-323.
82. Liu, G.R. (2002). Mesh Free Methods-Moving beyond the Finite Element Method. CRC Press, Boca Raton, FL.
83. Liu, W.K., Chen, Y., Uras, R.A. and Chang, C.T. (1996). Generalized multiple scale reproducing kernel particle methods. Computer Methods in Applied Mechanics and Engineering 139:91-157.
84. Liu, W.K., Chen, Y., Jun, S., Belytschko, T., Pan, C., Uras, R.A. and Chang, C.T. (1996). Overview and applicationsof the reproducing kernel particle methods. Archives of Computational Methods in Engineering 3, 3-80.
85. Liu, Y.J. and Rizzo, F.J. (1993). Hypersingular boundary integral equations for radiation and scattering of elastic wavesin three dimensions. Computer Methods in Applied Mechanics and Engineering 107:131-144.
86. Liu, Y.J., Zhang, D. and Rizzo, F.J. (1993). Nearly singular and hypersingular integrals in the boundary element method. Boundary Elements XV. C.A. Brebbia and J.J. Renciseds., 453-468, Computational Mechanics Publications, Southampton and Elsevier, Barking, Essex, UK.
87. Liu, Y.J. (1998). Analysis of shell-like structures by the boundary element method based on 3-D elasticity: formulation and verification. International Journal for Numerical Methods in Engineering 41:541-558.
88. Lutz, E.D. (1991). Numerical Methods for Hypersingular and Near-Singular Boundary Integrals in Fracture Mechanics. Ph.D. Dissertation, Cornell University, Ithaca, NY.
89. Lutz, E.D., Ingraffea, A.R. and Gray, L.J. (1992). Use of ‘simple solutions’ for boundary integral methods in elasticity and fracture analysis. International Journal for Numerical Methods in Engineering 35:1737-1751.
90. Lutz, E., Ye, W. and Mukherjee, S. (1998). Elimination of rigid body modes from discretized boundary integral equations. International Journal of Solids and Structures 35:4427-4436.
91. Mackerele, J. (1993). Mesh generation and refinement for FEM and BEM-a bibliography (1990-1993). Finite Elements in Analysis and Design 15:177-188.
92. Martin, P.A. and Rizzo, F.J. (1996). Hypersingular integrals: how smooth must the density be ? International Journal for Numerical methods in Engineering 39:687-704.
93. Martin, P.A., Rizzo, F.J. and Cruse, T.A. (1998). Smoothness-relaxation strategies for singular and hypersingular integral equations. International Journal for Numerical Methods in Engineering 42:885-906.
94. MantiČc, V. (1993). A new formula for the C-matrix in the Somigliana identity. Journal of Elasticity 33:191-201.
95. Menon, G. (1996). Hypersingular Error Estimates in Boundary Element Methods. M.S. Thesis, Cornell University, Ithaca, NY.
96. Menon, G., Paulino, G.H. and Mukherjee, S. (1999). Analysis of hypersingular residual error estimates in boundary element methods for potential problems. Computational Methods in Applied Mechanics and Engineering 173:449-473.
97. Moës, N., Dolbow, J. and Belytschko, T. (1999). A finite element method for crack growth without remeshing. International Journal for Numerical Methods in Engineering 46:131-150.
98. Mukherjee, S. (1982). Boundary Element Methods in Creep and Fracture. Elsevier, London.
99. Mukherjee, S. and Mukherjee, Y. X. (1998). The hypersingular boundary contour method for three-dimensional linear elasticity. ASME Journal of Applied Mechanics 65:300-309.
100. Mukherjee, S., Shi, X. and Mukherjee, Y.X. (1999). Surface variablesand their sensitivities in three-dimensional linear elasticity by the boundary contour method. Computer Methods in Applied Mechanics and Engineering 173:387-402.
101. Mukherjee, S. (2000). CPV and HFP integralsand their applicationsin the boundary element method. International Journal of Solids and Structures 37:6623-6634.
102. Mukherjee, S. (2000). Finite parts of singular and hypersingular integrals with irregular boundary source points. Engineering Analysis with Boundary Elements 24:767-776.
103. Mukherjee, S., Shi, X. and Mukherjee, Y.X. (2000). Internal variables and their sensitivities in three-dimensional linear elasticity by the boundary contour method. Computer Methods in Applied Mechanics and Engineering 187:289-306.
104. Mukherjee, S., Chati, M.K. and Shi, X. (2000). Evaluation of nearly singular integralsin boundary element contour and node methodsfor three-dimensional linear elasticity. International Journal of Solids and Structures 37:7633-7654.
105. Mukherjee, S. (2001). On boundary integral equationsfor cracked and for thin bodies. Mathematics and Mechanics of Solids 6:47-64.
106. Mukherjee, S. (2002). Regularization of hypersingular boundary integral equations: a new approach for axisymmetric elasticity. Engineering Analysis with Boundary Elements 26:839-844.
107. Mukherjee, Y.X. and Mukherjee, S. (1997). The boundary node method for potential problems. International Journal for Numerical Methods in Engineering 40:797-815.
108. Mukherjee, Y.X. and Mukherjee, S. (1997). On boundary conditionsin the element-free Galerkin method. Computational Mechanics 19:264-270.
109. Mukherjee, Y.X., Mukherjee, S., Shi, X. and Nagarajan, A. (1997). The boundary contour method for three-dimensional linear elasticity with a new quadratic boundary element. Engineering Analysis with Boundary Elements 20:35-44.
110. Mukherjee, Y.X., Shah, K. and Mukherjee, S. (1999). Thermoelastic fracture mechanicswith regularized hypersingular boundary integral equations. Engineering Analysis with Boundary Elements 23:89-96.
111. Mukherjee, Y.X. and Mukherjee, S. (2001). Error analysis and adaptivity in three-dimensional linear elasticity by the usual and hypersingular boundary contour method. International Journal of Solids and Structures 38:161-178.
112. Nabors, K. and White, J. (1991). FastCap: a multi-pole accelerated 3-D capacitance extraction program. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 10:1447-1459.
113. Nabors, K., Kim, S., White, J. and Senturia, S. (1992). FastCap User’s Guide. MIT, Cambridge, MA.
114. Nagarajan, A. and Mukherjee, S. (1993). A mapping method for numerical evaluation of two-dimensional integrals with 1/r singularity. Computational Mechanics 12:19-26.
115. Nagarajan, A., Lutz, E.D. and Mukherjee, S. (1994). A novel boundary element method for linear elasticity with no numerical integration for 2-D and line integralsfor 3-D problems. ASME Journal of Applied Mechanics 61:264-269.
116. Nagarajan, A., Mukherjee, S. and Lutz, E.D. (1996). The boundary contour method for three-dimensional linear elasticity. ASME Journal of Applied Mechanics 63:278-286.
117. Nayroles, B., Touzot, G. and Villon, P. (1992). Generalizing the finite element method: diffuse approximation and diffuse elements. Computational Mechanics 10:307-318.
118. Nishimura, N., Yoshida, K. and Kobayashi, S. (1999). A fast multipole boundary integral equation method for crack problemsin 3D. Engineering Analysis with Boundary Elements 23:97-105.
119. Novati, G. and Springhetti, R. (1999). A Galerkin boundary contour method for two-dimensional linear elasticity. Computational Mechanics 23:53-62.
120. Oden, J.T., Duarte, C.A.M. and Zienkiewicz, O.C. (1998). A new cloud based hp finite element method. Computer Methods in Applied Mechanics and Engineering 153:117-126.
121. París, F. and Cañas, J. (1997). Boundary Element Method: Fundamentals and Applications. Oxford University Press, UK.
122. Paulino, G.H. (1995). Novel Formulations of the Boundary Element Method for Fracture Mechanics and Error Estimation. Ph.D. Dissertation, Cornell University, Ithaca, NY.
123. Paulino, G.H., Gray, L.J. and Zarkian, V. (1996). Hypersingular residuals-a new approach for error estimation in the boundary element method. International Journal for Numerical Methods in Engineering 39:2005-2029.
124. Paulino, G.H., Shi, F., Mukherjee, S. and Ramesh, P. (1997). Nodal sensitivities as error estimates in computational mechanics. Acta Mechanica 121:191-213.
125. Paulino, G.H. and Gray, L.J. (1999). Galerkin residuals for adaptive symmetric-Galerkin boundary element methods. ASCE Journal of Engineering Mechanics 125:575-585.
126. Paulino, G.H., Menezes, I.F.M., Cavalcante Neto, J.B. and Martha, L.F. (1999). A methodology for adaptive finite element analysis: towards an integrated computational environment. Computational Mechanics 23:361-388.
127. Paulino, G.H., Menon, G. and Mukherjee S. (2001). Error estimation using hypersingular integrals in boundary element methods for linear elasticity. Engineering Analysis with Boundary Elements 25:523-534.
128. Petryk, H. and Mróz, Z. (1986). Time derivativesof integralsand functionals defined on varying volume and surface elements. Archives of Mechanics 5-6:697-724.
129. Phan, A.-V., Mukherjee, S. and Mayer, J.R.R. (1997). The boundary contour method for two-dimensional linear elasticity with quadratic boundary elements. Computational Mechanics 20:310-319.
130. Phan, A.-V., Mukherjee, S. and Mayer, J.R.R. (1998). A boundary contour formulation for design sensitivity analysis in two-dimensional linear elasticity. International Journal of Solids and Structures 35:1981-1999.
131. Phan, A.-V., Mukherjee, S. and Mayer, J.R.R. (1998). The hypersingular boundary contour method for two-dimensional linear elasticity. Acta Mechanica 130:209-225.
132. Phan, A.-V., Mukherjee, S. and Mayer, J.R.R. (1998). Stresses, stress sensitivities and shape optimization in two-dimensional linear elasticity by the boundary contour method. International Journal for Numerical Methods in Engineering 42:1391-1407.
133. Phan, A.-V. and Mukherjee, S. (1999). On design sensitivity analysis in linear elasticity by the boundary contour method. Engineering Analysis with Boundary Elements 23:195-199.
134. Phan, A.-V. and Phan, T.-N. (1999). Structural shape optimization system using the two-dimensional boundary contour method. Archive of Applied Mechanics 69:481-489.
135. Phan, A.-V. and Liu, Y.J. (2001). Boundary contour analysis of thin films and layered coatings. Sixth U.S. National Congress of Applied Mechanics, Detroit, MI.
136. Phan, A.-V., Gray, L.J., Kaplan, T. and Phan, T.-N. (2002). The boundary contour method for two-dimensional Stokes flow and incompressible elastic materials. Computational Mechanics 28:425-433.
137. Pickett, G. (1944). Application of the Fourier method to the solution of certain boundary value problemsin the theory of elasticity. Transactions of the ASME (Journal of Applied Mechanics) 66:A176-A182.
138. Poon, H., Mukherjee, S. and Ahmad, M.F. (1998). Use of simple solutions in regularizing hypersingular boundary integral equations in elastoplastic-ity. ASME Journal of Applied Mechanics 65:39-45.
139. Radin, C. (1994). The pinwheel tilingsof the plane. Annals of Mathematics 139:661-702.
140. Rank, E. (1989). Adaptive h-, p-, and hp-versions for boundary integral element methods. International Journal for Numerical Methods in Engineering 28:1335-1349.
141. Rizzo, F.J. (1967). An integral equation approach to boundary value problems of classical elastostatics. Quarterly of Applied Mathematics 25:83-95.
142. Roman, M. and Aubry, N. (2003). Design and fabrication of electrically actuated synthetic microjets. ASME Paper No. IMECE2003-41579. American Society of Mechanical Engineers, New York.
143. Rudolphi, T.J. (1991). The use of simple solutions in the regularization of hypersingular boundary integral equations. Mathematical and Computer Modeling 15:269-278.
144. Saigal S. and Kane, J.H. (1990). Boundary-element shape optimization system for aircraft structural components. AIAA Journal 28:1203-1204.
145. Sandgren, E. and Wu, S.J. (1988). Shape optimization using the boundary element method with substructuring. International Journal for Numerical Methods in Engineering 26:1913-1924.
146. Schittkowski, K. (1986). NLPQL: A FORTRAN subroutine solving constrained nonlinear programming problems. Annals of Operations Research 5:485-500.
147. Senturia, S.D., Harris, R.M., Johnson, B.P., Kim, S., Nabors, K., Shul-man, M.A. and White, J.K. (1992). A computer-aided design system for microelectromechanical systems (MEMCAD). Journal of Microelectromechanical Systems 1:3-13.
148. Shi, F., Ramesh, P. and Mukherjee, S. (1995). Simulation methods for micro-electro-mechanical structures (MEMS) with application to a mi-crotweezer. Computers and Structures 56:769-783.
149. Shi, F., Ramesh, P. and Mukherjee, S. (1996). Dynamic analysis of micro-electro-mechanical systems. International Journal for Numerical Methods in Engineering 39:4119-4139.
150. Shi, X. and Mukherjee, S. (1999). Shape optimization in three-dimensional linear elasticity by the boundary contour method. Engineering Analysis with Boundary Elements 23:627-637.
151. Sladek, J. and Sladek, V. (1986). Computation of stresses by BEM in 2-D elastostatics. Acta Technica CSAV 31:523-531.
152. Sladek, J., Sladek, V. and Atluri, S.N. (2000). Local boundary integral equation (LBIE) method for solving problems of elasticity with nonhomo-geneousmaterial properties. Computational Mechanics 24:456-462.
153. Sloan, I.H. (1976). Improvement by iteration for compact operator equations. Mathematics of Computation 30:758-764.
154. Sloan, I.H. (1990). Superconvergence. Numerical Solution of Integral Equations Chapter 2. M. A. Goldberg ed., 35-70 Plenum Press, New York.
155. Sloan, I.H. (1992). Error analysis in boundary integral methods. Acta Numerica Chapter 7. A. Iserles ed., 287-339 Cambridge University Press, UK.
156. Stephan, E.P. (1996). The h-p boundary element method for solving 2-and 3-dimensional problems. Computer Methods in Applied Mechanics and Engineering 133:183-208.
157. Strouboulis, T., Babuška, I. and Copps, K. (2000). The design and analysis of the generalized finite element method. Computer Methods in Applied Mechanics and Engineering 181:43-69.
158. Sukumar, N., Moran, B. and Belytschko, T. (1998). The natural element method. International Journal for Numerical Methods in Engineering 43:839-887.
159. Sukumar, N., Möes, N., Moran, B. and Belytschko, T. (2000). Extended finite element method for three-dimensional crack modeling. International Journal for Numerical Methods in Engineering 48:1549-1570.
160. Sukumar, N., Moran, B., Semenov, A.Y. and Belytschko, T. (2001). Natural neighbour Galerkin methods. International Journal for Numerical Methods in Engineering 50:1-27.
161. Tafreshi, A. and Fenner, R.T. (1995). General-purpose computer program for shape optimization of engineering structures using the boundary element method. Computers and Structures 56:713-720.
162. Tanaka, M., Sladek, V. and Sladek, J. (1994). Regularization techniques applied to boundary element methods. ASME Applied Mechanics Reviews 47:457-499.
163. Telukunta, S. and Mukherjee, S. (2004). An extended boundary node method for modeling normal derivative discontinuities in potential theory acrosscornersand edges. Engineering Analysis with Boundary Elements 28:1099-1110.
164. Telukunta, S. and Mukherjee, S. (2004). Extended boundary node method for three-dimensional problems in potential theory. Computers and Structures. Submitted.
165. Telles, J.C.F. (1987). A self-adaptive co-ordinate transformation for efficient numerical evaluation of general boundary element integrals. International Journal for Numerical Methods in Engineering 24:959-973.
166. Telles, J.C.F. and Oliveria, R.F. (1994). Third degree polynomial transformation for boundary element integrals: Further improvements. Engineering Analysis with Boundary Elements 13:135-141.
167. Timoshenko, S.P. and Goodier, J.N. (1970). Theory of Elasticity 3rd. ed. McGraw Hill, New York.
168. Toh, K.-C. and Mukherjee, S. (1994). Hypersingular and finite part integralsin the boundary element method. International Journal of Solids and Structures 31:2299-2312.
169. Wei, X., Chandra, A., Leu, L.J. and Mukherjee, S. (1994). Shape optimization in elasticity and elasto-viscoplasticity by the boundary element method. International Journal of Solids and Structures 31:533-550.
170. Wendland, W.L., Stephan, E.P. and Hsiao, G.C. (1979). On the integral equation method for the plane mixed boundary value problem for the Laplacian. Mathematical Methods in the Applied Sciences 1:265-321.
171. Wendland, W.L. and Yu, D-H. (1988). Adaptive boundary element methods for strongly elliptic integral equations. Numerische Mathematik 53:539-558.
172. Wendland, W.L. and Yu, D-H. (1992). A posteriori local error estimates of boundary element methods with some pseudo-differential equations on closed curves. Journal of Computational Mathematics 10:273-289.
173. Wilde, A.J. and Aliabadi, M.H. (1998). Direct evaluation of boundary stresses in the 3D BEM of elastostatics. Communications in Numerical Methods in Engineering 14:505-517.
174. Xu, Y. and Saigal, S. (1998). An element-free Galerkin formulation for stable crack growth in elastic solids. Computer Methods in Applied Mechanics and Engineering 154:331-343.
175. Xu, Y. and Saigal, S. (1998). Element-free Galerkin study of steady quasi-static crack growth in plane strain tension in elastic-plastic materials. Computational Mechanics 21:276-282.
176. Xu, Y. and Saigal, S. (1999). An element-free Galerkin analysis of steady dynamic growth of a mode I crack in elastic-plastic materials. International Journal of Solids and Structures 36:1045-1079.
177. Yamazaki, K., Sakamoto, J. and Kitano, M. (1994). Three-dimensional shape optimization using the boundary element method. AIAA Journal 32:1295-1301.
178. Yang, R.J. (1990). Component shape optimization using BEM. Computers and Structures 37:561-568.
179. Yang, T.Y. (1986). Finite Element Structural Analysis. Prentice Hall, Englewood Cliffs, NJ.
180. Yoshida, K., Nishimura, N. and Kobayashi, S. (2001). Application of a new fast multipole boundary integral equation method to crack problems in 3D. Engineering Analysis with Boundary Elements 25:239-247.
181. Yu, D.-H. (1987). A posteriori error estimates and adaptive approaches for some boundary element methods. Mathematical and Computational Aspects Vol. 1 of Boundary Elements IX. C. Brebbia, W. L. Wendland and G. Kuhn eds., 241-256. Computational Mechanics Publications and Springer Verlag.
182. Yu, D.-H. (1988). Self adaptive boundary element methods. Zeitschrift für Angewandte Mathematik und Mechanik 68:T435-T437.
183. Zhang, Q. and Mukherjee, S. (1991). Design sensitivity coefficients for linear elastic bodieswith zonesand cornersby the derivative boundary element method. International Journal of Solids and Structures 27:983-998.
184. Zhao, Z. (1991). Shape Design Sensitivity Analysis and Optimization Using the Boundary Element Method. Springer, New York.
185. Zhao, Z.Y. and Lan, S.R. (1999). Boundary stress calculation-a comparison study. Computers and Structures 71:77-85.
186. Zhou, S.J., Sun, S.X. and Cao, Z.Y. (1998). The dual boundary contour method for two-dimensional crack problems. International Journal of Fracture 92:201-212.
187. Zhou, S.J., Cao, Z.Y. and Sun, S.X. (1999). The traction boundary contour method for linear elasticity. International Journal for Numerical Methods in Engineering 46:1883-1895.
188. Zhu T., Zhang, J-D. and Atluri, S.N. (1998). A local boundary integral equation (LBIE) method in computational mechanics, and a meshless dis-cretization approach. Computational Mechanics 21:223-235.
189. Zhu, T. (1999). A new meshless regular local boundary integral equation (MRLBIE) method. International Journal for Numerical Methods in Engineering 46:1237-1252.
190. Zienkiewicz, O.C. and Taylor, R.L. (1994). The Finite Element Method. Vols. 1 and 2. McGraw Hill, Maidenhead, Berkshire, UK.