An effective boundary element algorithm for 2D and 3D elastoplastic problems

International Journal of Solids and Structures

Volumn 37, Issue 36, 2000, Pages 4987-5008

  Gao, Xiao Wei ^a   Davies, Trevor G ^a  

^a UNIVERSITY OF GLASGOW   (United Kingdom)

Author keywords

Boundary element method; Elastoplastic problem; Plastic multiplier; Singular domain integral; Variable stiffness iteration

Indexed keywords

EID: 0000850190     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7683(99)00188-2     Document Type: Article

References (61)

1. Banerjee P.K., Cathie D.N., Davies T.G. Two and three-dimensional problems of elasto-plasticity. Developments in Boundary Element Methods. 1979;Elsevier, London.
2. Banerjee P.K., Davies T.G. Analysis of some case histories of laterally loaded pile groups. Proc. of Int. Conf. On Numerical Methods in Offshore Piling :1979;Institution of Civil Engineers, London.
3. Banerjee P.K., Davies T.G. Advanced implementation of the boundary element methods for three-dimensional problems of elasto-plasticity. Developments in Boundary Element Methods. 1984;Elsevier, London.
4. Banerjee P.K., Raveendra S.T. Advanced boundary element analysis of two- and three-dimensional problems of elasto-plasticity. Int. J. Num. Meth. Engng. 23:1986;985-1002.
5. Banerjee P.K., Henry D.P., Raveendra S.T. Advanced inelastic analysis of solids by the boundary element method. Int. J. Mech. Sci. 31:1989;309-322.
6. Banerjee P.K. The Boundary Element Methods in Engineering. 1994;73-75 McGraw-Hill, New York.
7. Bonnet M., Mukherjee S. Implicit BEM formulations for usual and sensitivity problems in elasto-plasticity using the consistent tangent operator concept. Int. J. Solids Structures. 33:1996;4461-4480.
8. Brebbia C.A., Telles J.C.F., Wrobel L.C. Boundary Element Techniques. 1984;Springer, Berlin, New York.
9. Bui H.D. Some remarks about the formulation of three-dimensional thermoelastoplastic problems by integral equations. Int. J. Solids and Structures. 14:1978;935-939.
10. Burghardt, B., Van, A.L., 1998. A fully regularized direct boundary formulation for three-dimensional elastoplastic problems. In: Kassab, A., Brebbia, C.A., Chopra, M. (Eds.), Boundary Element XX, Computational Mechanics Publications, Southampton, U.K.
11. Chandra A., Saigal S. A boundary element analysis of the axisymmetric extrusion process. In. J. Nonlinear Mech. 26:1991;1-13.
12. Chandra A., Mukherjee S. Boundary Element Methods in Manufacturing. 1996;Oxford University Press, Oxford, UK.
13. Chen W.F., Han D.J. Plasticity for Structural Engineers. 1988;Springer-Verlag, London.
14. Chen Z.Q., Ji X. Boundary element analysis of finite deformation problems of elasto-plasticity. Tanaka M., Du Q. Theory and Application of Boundary Element Methods, Proc. First Japan-China Symp. On Boundary Element Methods. 1987;261-270 Pergamon, Oxford.
15. Chen H., Wang Y.C., Lu P. Stress rate integral equations of elastoplasticity. ACTA Mechanica Sinica (English Series). 12:1996;55-64.
16. Chopra M.B., Dargush G.F. Development of BEM for thermoplasticity. Int. J. Solids Structures. 31:1994;1635-1656.
17. Cisilino A.P., Aliabadi M.H., Otegui J.L. A three-dimensional boundary element formulation for the elastoplastic analysis for cracked bodies. Int. J. Numer. Meth. Engng. 42:1998;237-256.
18. Crisfield M.A. Non-linear Finite Element Analysis of Solids and Structures. 1997;Wiley, Chichester, UK.
19. Dallner R., Kuhn G. Efficient evaluation of volume integrals in boundary element method. Comp. Methods in Appl. Mech. and Engng. 109:1993;95-109.
20. Dong C.Y., Antes H. An improved inner point stress integral equation and its application in 2-D elastoplastic problems. Engineering Analysis with Boundary Elements. 22:1998;133-139.
21. Fox E.N. The mean elastic settlement of a uniformly loaded area at a depth below the ground surface. Proc. 2nd Int. Conf. Soil Mechs. Fndn. Eng. 1:1948;129.
22. Gao, X.W., Davies, T.G., 1999a. 3D multi-region BEM with corners and edges. International Journal of Solids and Structures, in press.
23. Gao, X.W., Davies, T.G., 1999b. Adaptive algorithm in elasto-plastic boundary element analysis. Journal of the Chinese Institute of Engineers, submitted.
24. Gao X.W., Davies T.G. 3-D infinite boundary elements for half-space problems. Engineering Analysis with Boundary Elements. 21:1998;207-213.
25. Gao, X.W., 1999. 3D non-linear and multi-region boundary element stress analysis. PhD Thesis, University of Glasgow, UK.
26. Gao, X.W., Zhong, Z.Q., 1992. Elastoplastic damage theory in isotropic medium. Chinese Journal of Theoretical and Applied Mechanics 4.
27. Gao X.W., Lu J.T. A combination method of FEM and BEM for elastoplastic problems. Proc. of Forth Int. Conf. on EPMESC, Dalian, China, August :1992.
28. Gao X.W., Zheng Y.R. An accelerating convergence method for elastoplastic iterative computation in strain space. Proc. of Third Int. Conf. on EPMESC, MACAU :1990;84-90.
29. Guiggiani M., Gigante A. A general algorithm for multidimensional Cauchy principal value integrals in the boundary element method. J. Appl. Mech. 57:1990;906-915.
30. Guiggiani M., Krishnasamy G., Rudolphi T.J., Rizzo F.J. General algorithm for the numerical solution of hyper-singular boundary integral equations. ASME J. Appl. Mech. 59:1992;604-614.
31. Henry, D.P., 1987. Advanced development of the boundary element method for elastic and inelastic thermal stress analysis. PhD Dissertation, State University of New York at Buffalo.
32. Henry D.P., Banerjee P.K. A variable stiffness type boundary element formulation for axisymmetric elastoplastic media. Int. J. Num. Meth. Engng. 26:1988;1005-1027.
33. Huber O., Dallner R., Partheymuller P., Kuhn G. Evaluation of the stress tensor in 3-D elastoplasticity direct solving of hypersingular integrals. Int. J. Num. Meth. Engng. 39:1996;2555-2573.
34. Huang Q., Du Q. An improved formulation for domain stress evaluation by boundary element methods in elastoplastic problems. Proc. China-US Seminar on Boundary Integral Equations and Finite Element Methods in Physics and Engineering, Xian, China :1988.
35. Il'iushin A.A. On the postulate of plasticity. Prikl. Mat. Meh. 25:1961;503-507.
36. Kane J.H. Boundary Element Analysis in Engineering Continuum Mechanics. 1994;Prentice-Hall, Englewood Cliffs, NJ.
37. Krishnasamy G., Rizzo F.J., Rudolphi T.J. Hypersingular boundary integral equations: Their occurrence, interpretation, regularization and computation. Banerjee P.K., Kobayashi S. Advanced Dynamic Analysis by Boundary Element Methods. 1992;207-252 Elsevier, London and New York.
38. Kumar V., Mukherjee S. A boundary-integral equation formulation for time-dependent inelastic deformation in metals. Int. J. Mechanical Science. 19:1977;713-724.
39. Lachat, J.C., 1975, A further development of the boundary integral technique for elastostatics. PhD Thesis, University of Southampton.
40. Lee K.H., Fenner R.T. A quadratic formulation for two-dimensional elastoplastic analysis using the boundary integral equation method. J. Strain Analysis. 21:(3):1986;159-175.
41. Lubliner J. Plasticity Theory. 1990;Macmillan, New York, London.
42. Mendelson, A., Albers, L.V., 1975. An application of the boundary integral equation method to elastoplastic problems. In: Cruse, T.A., Rizzo, F.J. (Eds.), Proc. ASME Conf. on boundary integral equation methods, AMD 11, New York.
43. Mukherjee S. Corrected boundary integral equations in planar thermo-elastoplasticity. Int. J. Solids Structures. 13:1977;331-335.
44. Mukherjee S. Boundary Element Method in Creep and Fracture. 1982;Applied Science Publishers, New York.
45. Mustoe G.G.W. Advanced integration schemes over boundary elements and volume cells for two- and three-dimensional non-linear analysis. Developments in Boundary Element Methods. 1984;Elsevier, London.
46. Naghdi P.M., Trapp J.A. The significance of formulating plasticity theory with reference to loading surfaces in strain space. Int. J. Eng. Sci. 13:1975;785-797.
47. Owen D.R.J., Hinton E. Finite Elements in Plasticity: Theory and Practice. 1980;Pineridge, Swansea, UK.
48. Poon H., Mukherjee S., Ahmad M.F. Use of 'simple solutions' in regularizing hypersingular boundary integral equations in elastoplasticity. ASME J. Appl. Mech. 65:1998;39-45.
49. Poon H., Mukherjee S., Bonnet M. Numerical implementation of a CTO-based implicit approach for the BEM solution of usual and sensitivity problems in elasto-plasticity. Engineering Analysis with Boundary Elements. 22:1998;257-269.
50. Raveendra, S.T., 1984. Advanced development of BEM for two and three-dimensional inelastic analysis. PhD Dissertation, State University of New York at Buffalo.
51. Riccardella, P., 1973. An implementation of the boundary integral technique for planar problems of elasticity and elastoplasticity. PhD Thesis, Carnegie-Mellon University, Pittsurgh, PA.
52. Simo J.C., Taylor R.L. Consistent tangent operators for rate-independent elastoplasticity. Comp. Meth. Appl. Mech. Engng. 48:1985;101-118.
53. Swedlow J.L., Cruse T.A. Formulation of boundary integral equations for three-dimensional elasto-plastic flow. Int. J. Solids and Structures. 7:1971;1673-1683.
54. Telles J.C.F. The Boundary Element Method Applied to Inelastic Problems. 1983;Springer-Verlag, Berlin.
55. Telles J.C.F., Brebbia C.A. On the application of the boundary element method to plasticity. Appl. Math. Modelling. 3:1979;466-470.
56. Telles J.C.F., Brebbia C.A. The boundary element method in plasticity. Proc. Second Int. Conf. on Recent Advances in Boundary Element Methods :1980;295-317 Pentech Press, Plymouth.
57. Telles J.C.F., Carrer J.A.M. Implicit procedures for the solution of elastoplastic problems by the boundary element method. Math. Comput. Modelling. 15:1991;303-311.
58. Wearing, J.L., Dimagiba, R.R.M., 1998. The development of the boundary element method for three dimensional elasto-plastic analysis. In: Brebbia (Ed.), Boundary Element Research in Europe, Computational Mechanics Publications, pp. 93-102, Southampton, U.K.
59. Zhang Q., Mukherjee S., Chandra A. Design sensitivity coefficients for elastoviscoplastic problems by boundary element methods. Int. J. Num. Meth. Engng. 34:1992;947-966.
60. Zheng, Y.R., Gao, X.W., 1986. Application of elastoplastic BEM to back analysis. Journal of Underground Technology 2.
61. Zheng, Y.R., Xu, G.C., Gao, X.W., 1989. The coupled computational method of elastoplastic BEM and FEM. Chinese Journal of Engineering Mechanics 1.