Beams and plates on elastic foundations: A review

Progress in Structural Engineering and Materials

Volumn 7, Issue 4, 2005, Pages 174-182

  Wang, Y H ^a   Tham, L G ^b   Cheung, Y K ^b  

^a HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^b UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Beam; Elastic foundation; Numerical method; Plate; Soil structure interaction

Indexed keywords

BEAMS AND GIRDERS; BOUNDARY ELEMENT METHOD; ELASTICITY; FINITE DIFFERENCE METHOD; FINITE ELEMENT METHOD; FOUNDATIONS; MATHEMATICAL MODELS; NUMERICAL METHODS; PLATES (STRUCTURAL COMPONENTS); STRUCTURAL DESIGN;

ELASTIC FOUNDATION; FINITE STRIP METHOD; FOUNDATION DESIGN;

SOIL STRUCTURE INTERACTIONS;

EID: 28444480666     PISSN: 13650556     EISSN: None     Source Type: Journal    
DOI: 10.1002/pse.202     Document Type: Review

References (140)

1. Donald PC. Foundation Design: Principles and Practice. New York: Prentice-Hall, 2001.
2. Selvadurai APS. Elastic Analysis of Soil-Foundation Interaction. Amsterdam: Elsevier, 1979.
3. Cheung YK & Tham LG. Recent advances in soil-structure interaction analysis. Proceedings of the Theory and Application of the Structures-Media Interaction, Nanjing: Hohai University Press, 1993: 17-27.
4. Winkler E. Die Lehre von der Elastizitat und Festigkeit. Dominicus, Prague, 1867.
5. Filonenko-Borodich MM. A very simple model of an elastic foundation capable of spreading the load. Sb. Tr. Mosk. Elektro. Inst. Inzh. Tran. No: 53, Transzhedorizdat (in Russian), 1945.
6. Pasternak PL. On a new method of analysis of an elastic foundation by means of two foundation constants. Gosudarstvennoe Izdatelstro Liberaturi po Stroitelstvui Arkhitekture, Moscow (in Russian), 1954.
7. Hetenyi M. Beams on Elastic Foundations. Michigan University of Michigan Press, 1946.
8. Kerr AD. Elastic and viscoelastic foundation models. Journal of Applied Mechanics (ASME) 1964: 31: 491-498
9. Reissner E. Deflection of plates on viscoelastic foundation. Journal of Applied Mechanics (ASME) 1958: 80: 144-145.
10. Vlazov VZ & Leontiev UN. Beams, Plates and Shells on Elastic Foundations. Israel Program for Scientific Translations, Jerusalem (translated from Russian), 1966.
11. Boussinesq J. Application des Potentiels a l'Etude de l'Equilibre et du Mouvement des Solides Elastique. Paris: Gauthier-Villars, 1885.
12. Stark RF & Booker JR. Surface displacements of a non-homogeneous elastic half-space subjected to uniform surface tractions, International Journal for Numerical and Analytical Methods in Geomechanics 1997: 21: 361-378; 379-395.
13. Gibson RG. Some results concerning displacements and stresses in a non-homogeneous elastic half-space. Geotechnique 1967: 17: 58-67.
14. Booker JR, Balaam NP & Davis EH. The behaviour of an elastic non-homogeneous half-space, Part I: Line and point loads. International Journal for Numerical and Analytical Methods in Geomechanics 1985: 9: 353-367.
15. Booker JR, Balaam NP & Davis EH. The behaviour of an elastic non-homogeneous half-space, Part II: Circular and strip footings. International Journal for Numerical and Analytical Methods in Geomechanics 1985: 9: 369-381.
16. Nayak M. Elastic settlement of a cross-anisotropic medium under axisymmetric loading. Soil and Foundations 1973: 13(2): 83-90.
17. Wang Y & Ishikawa I. A method for linear elastic-static analysis of multi-layered axisymmetrical bodies using Hankel's transform. Computational Mechanics 2001: 27: 474-483.
18. Sneddon IN. Fourier Transforms. New York: McGraw-Hill, 1951.
19. Yin YP, Wang YH & Zhu JQ. Solutions of axisymmetric load applied to layered foundation. Rock and Soil Mechanics 2001: 22(2): 156-158 (in Chinese).
20. Wang YH, Tham LG, Tsui Y & Yue ZQ. Plate on layered foundation analyzed by a semi-analytical and semi-numerical method. Computers and Geotechnics 2003: 30: 409-418.
21. Hetenyi M. Analysis of Bars on Elastic Foundation. Final report of the 2nd International Congress for Bridge and Structure Engineering, Berlin-Munich, 1936.
22. Wright W. Beams on elastic foundations - solution by relaxation methods. Structural Engineering 1952: 30: 169-171.
23. Gazis DC. Analysis of finite beams on elastic foundation. Journal of Structural Engineering (ASCE) 1958: 84: Paper No. 1722.
24. Penzien J. Discontinuity stresses in beams of elastic foundations. Journal of Structural Engineering (ASCE) 1960: 86(4): 67-93.
25. Blaszkowiak S & Kaczkowski Z. Iterative Methods in Structural Analysis (Translated by Kacner A and Olesiak Z), Oxford: Pergamon Press, 1966.
26. Yankelevsky DZ, Eisenberge M & Adin MA. Analysis of beams on nonlinear Winkler foundation. Computers and Structures 1989: 31(2): 287-292.
27. Iwinski T. Theory of Beams. Oxford: Pergamon Press (edited and translated by Bernat EP), 1967.
28. Iyengar KTSR. Matrix analysis of finite beams on elastic foundations. Journal of the Institution of Engineers (India) 1965: 45: 837-855.
29. Bowles JE. Analytical and Computer Methods in Foundation Engineering. New York: McGraw-Hill, 1974.
30. Bowles JE. Foundation Analysis and Design. New York: McGraw-Hill, 2nd edn, 1977.
31. Lee SY & Yang CC. Non-conservative instability of a Timoshenko beam resting on Winkler elastic foundation. Journal of Sound and Vibration 1993: 162(1): 177-184.
32. Aydogan M. Stiffness-matrix formulation of beams with shear effect on elastic foundation. Journal of Structural Engineering (ASCE) 1995: 121(9): 1265-1270.
33. Miranda C & Nair K. Finite beams on elastic foundations. Journal of Structural Engineering (ASCE) 1966: 92: 131-142.
34. Gao J, Selvarathinam A & Weitsman YJ. Analysis of adhesively jointed composite beams. Journal of Sandwich Structures and Materials 1999: 1: 323-339.
35. Guo YJ & Weitsman YJ. Solution method for beams on nonuniform elastic foundations. Journal of Engineering Mechanics 2002: 128(5): 592-594.
36. Ioakimidis NI. Inequality constraints in one-dimensional finite elements for an elastic beam on a tensionless Winkler foundation. Finite Elements in Analysis and Design 1996: 24(2): 67-75.
37. Kaschiev MS & Mikhajlov K. Beam resting on a tensionless Winkler foundation. Computers and Structures 1995: 55(2): 261-264.
38. Erguven ME & Gedikli A. A mixed finite element formulation for Timoshenko beam on Winkler foundation. Computational Mechanics 2003: 31(3-4): 229-237.
39. Akoz AY & Kadioglu F. Mixed finite element solution of circular beam on elastic foundation. Computers and Structures 1996: 60(4): 643-651.
40. Horibe T. Boundary integral equation method analysis for beam-columns on elastic foundation. Transactions of the Japan Society of Mechanical Engineers, Part A 1996: 62: 2067-2071.
41. Yin JH. Comparative modeling study of reinforced beam on elastic foundation. Journal of Geotechnical and Geoenvironmental Engineering 2000: 126(3): 265-271.
42. Yin JH. Closed-form solution for reinforced Timoshenko beam on elastic foundation. Journal of Engineering Mechanics 2000: 126(8): 868-874.
43. Zhaohua F & Cook RD. Beam element on two-parameter elastic foundations. Journal of Engineering Mechanics (ASCE) 1983: 109(6): 1390-1402.
44. Onu G. Shear effect in beam finite element on two-parameter elastic foundation. Journal of Structural Engineering 2000: 126(9): 1104-1107.
45. Gulkan P & Alemdar BN. Exact finite element for a beam on a two-parameter elastic foundation: a revisit. Structural Engineering and Mechanics 1999: 7(3): 259-276.
46. Morfidis K. Formulation of a generalized beam element on a two-parameter elastic foundation with semi-rigid connections and rigid offsets. Computers and Structures 2002: 80(25): 1919-1934.
47. Borowicka H. Druckverteilung under elastischen platen. Ingenieur-Archiv 1939: 10(2): 113-125.
48. Gorbunov-Posadov MI. Analysis of structures on an elastic foundations. Moskova, Goss. izd. Lit. stroit. Arkh. 1953 (in Russian).
49. Al-Gahtain HJ. Finite beams on nonhomogeneous elastic foundations. Boundary Elements Communications 1997: 8(3): 168-170.
50. Zemochkin BN & Sinitsyn AP. Practical Method for Calculation of Beams and Plates on Elastic Foundation (without using Winkler's Hypothesis). Strouzdat, Moscow, 1947 (in Russian).
51. Barden L. Distribution of contact pressure under foundations. Geotechnique 1962: 12: 181-198; 1963: 13: 87-88.
52. Barden L. Stresses and displacements in a cross-anisotropic soil. Geotechnique 1963: 13: 198-210.
53. Ohde J. Die Berechnung der Sohldruckverteilung unter Grundungskorpern. Bauingenieur 1942: 23: 99-107.
54. Cheung YK & Zienkiewicz OC. Plates and tanks on elastic foundation - an application of the finite element method. International Journal of Solids and Structures 1965: 1: 451-461.
55. Cheung YK & Nag DK. Plates and beams on elastic foundations: linear and nolinear behaviour. Geotechnique 1968: 18: 250-260.
56. Timoshenko S & Goodier JN. Theory of Elasticity, New York: McGraw-Hill, 1970.
57. Reissner E. On the bending of elastic plates. Quarterly of Applied Mathematics 1947: 5: 55-68.
58. Szilard R. Theories and Applications of Plate Analysis: Classical, Numerical, and Engineering Methods, NJ: John Wiley, 2004.
59. Hertz H. On the equilibrium of floating elastic plates (in German). Annals of Physics and Chemistry 1884: 22: 449-455.
60. Wyman M. Deflections of an infinite plate. Canadian Journal of Research, Section A, Physical Sciences 1950: 28: 293-302.
61. Thimoshenko SP & Woinowsky-Krieger S. Theory of Plates and Shells. New York: McGraw-Hill, 1959.
62. Kerr AD. Elastic plates on a liquid foundation. Journal of Engineering Mechanics (ASCE) 1963: 89: EM3, 59-71.
63. Fryba L. Vibration of Solids and Structures under Moving Loads. Groningen: Noordhoff, 1972.
64. Panc V. Theories of Elastic Plates. Leyden: Noordhoff, 1975.
65. Kneifati MC. Analysis of plates on a Kerr foundation model. Journal of Engineering Mechanics 1985: 111(1): 1325-1342.
66. Livesley RK. Some notes on the mathematical theory of a loaded elastic plate resting on an elastic foundation. Quarterly Journal of Mechanics and Applied Mathematics 1953: 6: 32-44.
67. Hemsley JA. Plane elastostatic flexure of an infinite plate on a half-space. Proceedings of the Institution of Civil Engineers (London) Part I-Design & Construction, 1988: 85(2): 629-663.
68. Sneddon IN, Gladwell GML & Coen S. Bonded contact of an infinite plate and an elastic foundation. Letters in Applied and Engineering Sciences 1975: 3: 1-13.
69. Pister KS & Westmann RA. Bending of plates on an elastic foundation. Journal of Applied Mechanics (ASME) 1962: 29(2): 369-374.
70. Arora MG & Khanna SK. Numerical analysis of rigid pavament resting over Hookean subgrade continuum. Proceedings of the 2nd Internatinal Conference on Numerical Methods in Geomechanics (ASCE) Blackburg, USA, 1976: Vol. 1, 511-525.
71. Selvadurai APS. The influence of a Mindlin force on the axisymmetric interaction between an infinite plate and an elastic half space. Letters in Applied and Engineering Sciences 1977: 5: 379-388.
72. Reissman H. Bending of circular and ring-shaped plates on an elastic foundation. Journal of Applied Mechanics (ASME) 1954: 21: 45-51
73. Conway HD. Analysis of some circular plates on elastic foundations and the flexural vibration of some circular plates. Journal of Applied Mechanics (ASME) 1955: 22: 275-276.
74. Celep Z & Guler K. Static and dynamic responses of a rigid circular plate on a tensionless Winkler foundation. Journal of Sound and Vibration 2004: 276(1-2): 449-458.
75. Korenev BG. Structures resting on an elastic foundation. In: Rabinovich IM (editor), Structural Mechanics in the USSR, 1917-1957. Oxford: Pergamon Press, 1960: 160-190.
76. Yu YY & Syracuse NY. Axisymmetrical bending of circular plates under simultaneous action of lateral load, force in the middle plane, and elastic foundation. Journal of Applied Mechanics (ASME) 1957: 24(1): 141-143.
77. Saygun A & Celik M. Analysis of circular plates on two-parameter elastic foundation. Structural Engineering and Mechanics 2003: 15(2): 249-267.
78. Guler K. Circular elastic plate resting on tensionless Pasternak foundation. Journal of Engineering Mechanics 2004: 130(10): 1251-1254.
79. Popov GY. Plates on a linearly elastic foundation (a survey). Soviet Applied Mechanics 1971: 8(3): 3-17.
80. Selvadurai APS. Axial loading of a rigid circular anchor plate embedded in an elastic half-space. International Journal for Numerical and Analytical Methods in Geomechanics 1993: 17(5): 343-353.
81. Rajapakese RKND. Interaction between a circular elastic plate and a transversly isotropic elastic half-space. International Journal for Numerical and Analytical Methods in Geomechanics 1988: 12(4): 419-436.
82. Zemochkin BN. Analysis of Circular Plates on Elastic Foundation. Mosk. Izd. Voenno. Inzh. Akad., 1939 (in Russian).
83. Ishkova AG. On some generalizations of the solution of the problems concerning a circular plate and an infinite strip on the elastic halfspace. Prikl. Mat. Mekh. 1957: 21: 287-290 (in Russian).
84. Malter H. Numerical solutions for beams on elastic foundations. Journal of Structural Engineering (ASCE) 1958: 84: ST2, paper No. 1562.
85. Wang PC. Numerical and Matrix Methods in Structural Engineering. New York: Wiley, 1966.
86. Ghali A & Neville AM. Structural Analysis: A unified Classical and Matrix Approach. Intext Educational Publishers, Scranton, Penn, USA, 1972.
87. Cividini A. Application of Numerical Methods to Geotechnical Problems. Proceedings of the fourth European Conference on Numerical Methods in Geotechnical Engineering. NUMGE98, Udine, Italy, 1998.
88. Allen DN & Seven RT. The stresses in foundation rafts-I,II,III. Proceedings of the Institution of Civil Engineers 1960: 15: 35-48; 1961: 20: 293-304; 1963: 25: 257-266.
89. Bobritskii GM. Flexure of slabs of variable rigidity on a nonhomogeneous elastic foundation. Soviet Applied Mechanics 1967: 3: 50-59.
90. Bowles JE. Analytical and Computer Methods in Foundation Engineering. New York: McGraw-Hill, 1974.
91. Paramasivam P. Computer analysis of flat-slab type mat foundations using finite difference method. In: Valliappan S et al. (editors), Analysis of Soil Behaviour and its Application to Geotechnical Structures, Unisearch, NSW, Australia, 1975: 99-112.
92. Vallabhan CVG & Das YC. Analysis of circular tank foundations. Journal of Engineering Mechanics 1991: 117(4): 789-797.
93. Pickett G & McCormick FJ. Circular and rectangular plates under lateral load and supported by an elastic solid foundation. Proceeding of the 1st US Natural Congress of Applied Mechanics 1951: 331-338.
94. Janes RL. Digital computer solution for pavement deflections. Journal of Portland Cement Association 1962: 4(3): 30-36.
95. Bosakov SV. Calculation of a plate of finite stiffnese in an elastic half space. Soil Mechanics and Foundation Engineering 1992: 28(5): 229-232.
96. Chattopadhyay R & Ghosh A. Analysis of circular plates on semi-infinite elastic subgrade. Indian Journal of Technology 1969: 7: 312-319.
97. Chakravorty AK & Ghosh A. Finite difference solution for circular plates on elastic foundations. International Journal for Numerical Methods in Engineering 1975: 9: 73-84.
98. Melerski ES. Simple computer analysisof circular rafts under various axisymmetric loading and elastic foundation conditions. Proceedings of Institute of Civil Engineers, Part 2: Research and Theory 1990: 89: 407-431.
99. Cheung YK. Finite Strip Method in Structural Analysis. New York: Pergamon Press, 1976.
100. Cheung YK & Tham LG. Finite Strip Method. New York: CRS Press, 1998.
101. Booker JR & Small JC. Finite layer analysis of settlement creep and consolidation using microcomputer. Proceedings of the 5th International Conference on Numerical Methods in Geomechanics, Nagoya, 1985: 3-18.
102. Booker JR & Small JC. The use of microcomputers to solve problems in geomechanics using finite finite layer methods. Proceedings of the 5th International Conference on Numerical Methods in Geomechanics Nagoya, 1985: 1683-1689.
103. Booker JR & Small JC. The behaviour of an impermeable flexible raft on a deep layer of consolidating soil. International Journal for Numerical and Analytical Methods in Geomechanics 1986: 10: 311-327.
104. Booker JR & Small JC. Finite layer analysis of layered pavements subjected to horizontal loading. Proceedings of the 6th International Conference on Numerical Methods in Geomechanics, Innsbruck, 1989: 2109-2113.
105. Rajapakse RKND. The interaction between circular elastic plate and a transversely isotropic half space. International Journal for Numerical and Analytical Methods in Geomechanics 1988: 12: 419-436.
106. Cheung YK & Fan SC. Analysis of pavement and layered foundations by finite layer method. Proceedings of the 3th International Conference on Numerical Methods in Geomechanics, Aachen, 1979: 1129-1135.
107. Cheung YK, Tham LG & Guo DJ. Applications of finite strip and layer methods in geomechanics. Proceedings of the 5th International Conference on Numerical Methods in Geomechanics, Nagoya, 1985: 1755-1762.
108. Oskoorouchi AM, Novrouzian B, De Roeck G & Van Den Broeck J. Zoned finite strip method and its application in geomechanics. Computers and Geotechnics 1991: 11(4): 265-294.
109. Huang MH & Thambiratnam DP. Analysis of plate resting on elastic supports and elastic foundation by finite strip method. Computers and Structures 2001: 79(29-30): 2547-2557.
110. Chow YK, Swaddiwudhipong S & Phoon KF. Finite strip analysis of strip footings. Horizontal loading. Computers and Geotechnics 1989: 8(1): 65-86.
111. Tham LG, Man KR & Cheung YK. Analysis of rectangular footing resting on non-homogeneous soil by double spline element. Computers and Geotechnics 1988: 5(3): 249-268.
112. Cheung YK, Tham LG & Man KR. Analysis of circular footing resting on non-homogeneous soil. Proceedings of the 2nd East Asia-Pacific Conference on Structural Engineering and Constructures, Chiang Mai, 1989: 715-720.
113. Chow YK. Vertical deformation of rigid foundation of arbitrary shape on layered soil media. International Journal for Numerical and Analytical Methods in Geomechanics 1987: 11: 1-16.
114. Zienkiewicz OC & Cheung YK. The Finite Element Method in Structural and Continuum Mechanics, London: McGraw-Hill, 1967.
115. Zienkiewicz OC. The Finite Element Method in Engineering Science. London: McGraw-Hill, 1971.
116. Desai CS & Christian JT. Numerical Methods in Geotechnical Engineering. New York: McGraw-Hill, 1977.
117. Gudehns G. Finite Elements in Geomechanics. London: John Wiley, 1977.
118. Celik M & Saygun A. A method for the analysis of plates on a two-parameter foundation. International Journal of Solids and Structures 1999: 36: 2891-2918.
119. Silva ARD, Silveira RAM & Goncalves PB. Numerical methods for analysis of plates on tensionless elastic foundations. International Journal of Solids and Structures 2001: 38(10-13): 2083-2100.
120. Karpurapu GR & Bathrust RJ. Comparative analysis of some geomechanics problems using finite and infinite methods. Computers and Geotechnics 1988: 5(4): 269-284.
121. Cheung YK, Guo DJ, Tham LG & Cao ZY. Infinite ring elements. International Journal for Numerical Methods in Engineering 1986: 23: 369-385.
122. Viladkar MN, Godbole PN & Noorzaei J. Some new three-dimensional infinite elements. Computers and Structures 1990: 34: 455-467.
123. Godbole PN, Viladkar MN & Noorzaei J. Nonlinear soil-structure interaction analysis using couble finite-infinite elements. Computers and Structures 1990: 36: 1089-1096.
124. Haggblad Band Nordgren G. Modelling nonlinear soil-structure interaction using interface elements, elastic-plastic elements and absorbing infinite elements. Computers and Structures 1987: 26: 307-324.
125. Sadecka L. Finite/infinite element analysis of thick plate on a layered foundation. Computers and Structures 2000: 76(5): 603-610.
126. Auersch L. Dynamic plate-soil interaction-finite and infinite, flexible and rigid plates on homogeneous, layered or Winkler soil. Soil Dynamics and Earthquake Engineering 1996: 15(1):51-59.
127. Severn RT. The solution of foundation of foundation mat problems by finite element methods. Structural Engineering 1966: 44: 223-228.
128. Smith IM. A finite element approach to elastic soil-structure interaction. Canadian Geotechnical Journal 1970: 7: 95-105.
129. Svec OJ & McNeice GM. Finite element analysis of finite sized plates bonded to an elastic halfspace. Computer Methods in Applied Mechanics and Engineering 1972: 1: 265-277.
130. Svec OJ & Gladwell GML. A triangular plate bending element for contact problems. International Journal of Solids and Structures 1973: 9: 435-446.
131. Wood LA. The economic analysis of raft foundation, International Journal for Numerical and Analytical Mechods in Geomechanics 1977: 1: 397-405.
132. Yang TY. A finite element analysis of plates on a two-parameter foundation model. Computers and Structures 1972: 2: 593-614.
133. Liu Q, Wang YH. A triangular finite element in the study of finite plate on elastic foundation. Proceedings of the Second International Conference on Soft Soil Engineering (eds. by Z.J. Shen et al.), 1996: Nanjing: Hohai University Press, 351-356.
134. Wang YH, Qiu XM & Cheung YK. Bending plate on an elastic halfspace analyzed by isoparametric elements. Chinese Journal of Geotechnical Engineering 1998: 20(4): 7-1.
135. Wang YH & Cheung YK. Plate on cross-anisotropic foundation analyzed by the finite element method. Computers and Geotechnics 2001: 28: 37-54.
136. Wang YH, Ni J & Cheung YK. Plate on non-homogeneous elastic half-space analyzed by FEM. Structural Engineering and Mechanics 2000: 9(2): 127-139.
137. Beskos DE. Boundary element methods in geomechanics. In: Boundary Elements X, Vol. 4 (ed: Brebbia CA), 1988: 3-28.
138. Beskos DE. Boundary element methods in dynamic analysis: Part II (1986-1996). Applied Mechanics Reviews 1997: 50(3): 149-197.
139. Karabalis DL. Dynamic soil-structure interaction by BEM. In: Boundary Elements X, Vol. 4 (ed: Brebbia CA), 1988: 351-375.
140. Providakis CP & Beskos DE. Dynamic analysis of plates by boundary elements. Applied Mechanics Reviews 1999: 52(7): 213-236.