New Boundary Element Formulation for 2‐D Elastoplastic Analysis
Publication: Journal of Engineering Mechanics
Volume 113, Issue 2
Abstract
A new approach is outlined for BEM formulations for elastoplasticity, which exploits certain features of the constitutive relationships involved. The unknown nonlinear terms in the interior are now defined as scalar variables. A new direct numerical solution scheme comparable to the variable stiffness method used in the finite element analyses has been developed and applied to a number ol standard plasticity problems.
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References
1.
Banerjee, P. K., and Butterfield, R., Boundary Element Methods in Engineering Science, McGraw Hill, London, U.K., and New York, N.Y., 1981.
2.
Banerjee, P. K., and Cathie, D. N., “Boundary Element Methods for Axisymmetric Plasticity,” Innovative Numerical Methods for the Applied Engineering Science, R. P. Shaw, et al., Eds., University of Virginia Press, Charlottesville, N.C., 1980.
3.
Banerjee, P. K., and Cathie, D. N., “A Direct Formulation and Numerical Implementation of the Boundary Element Method for Two‐Dimensional Problems of Elastoplasticity,” International Journal of Mechanical Science, Vol. 22, 1980, pp. 233–245.
4.
Banerjee, P. K., Cathie, D. N., and Davies, T. G., “Two and Three‐Dimensional Problems of Elasto‐plasticity,” Chapter IV, Developments in Boundary Element Methods, Vol. 1, Applied Science Publishers, London, U.K., 1979.
5.
Banerjee, P. K., and Davies, T. G., “Advanced Implementation of the Boundary Element Methods for Three‐Dimensional Problems of Elastoplasticity and Viscoplasticity,” Development in Boundary Element Methods, P. K. Banerjee, and S. Mukherjee, Eds., Vol. 4, 1984.
6.
Banerjee, P. K., and Raveendra, S. T., “Advanced Boundary Element Analysis of Two and Three‐Dimensional Problems of Elasto‐plasticity,” International Journal for Numerical Methods in Engineering, Vol. 23, 1986; pp. 985–1002.
7.
Bui, H. D., “Some Remarks about the Formulation of Three‐Dimensional Thermoelastoplastic Problems by Integral Equations,” International Journal of Solids and Structures, Vol. 14, 1978, pp. 935–939.
8.
Cathie, D. N., and Banerjee, P. K., “Boundary Element Methods for Plasticity, Creep Including a Viscoplastic Approach,” Research Mechanica, Vol. 4, 1982, pp. 3–22.
9.
Chaudonneret, M., “Boundary Integral Equation Method for Viscoplasticity Analysis,” J. de Mech. Appliq., Vol. 1, No. 2, 1977, pp. 113–131 (in French).
10.
Chen, W. F., Limit Analysis and Soil Plasticity, Elsevier, New York, N.Y., 1975.
11.
Kumar, V., and Mukherjee, S., “A Boundary Integral Equation Formulation for Time Dependent Inelastic Deformation in Metals,” International Journal of Mechanical Science, Vol. 19, No. 12, 1975, pp. 713–724.
12.
Lachat, J. C., and Watson, J. O., “Effective Numerical Treatment of Boundary Integral Equation: A Formulation for Three‐Dimensional Elasto‐statics,” International Journal of Numerical Methods in Engineering, Vol. 10, 1975, pp. 991–1005.
13.
Mendelson, A., and Albers, L. V., “Application of Boundary Integral Equation Method to Elastoplastic Problems,” Proc., ASME Conference on Boundary Integral Equation Methods, T. A. Cruse, and F. J. Rizzo, Eds., AMD, Vol. 11, New York, N.Y., 1975.
14.
Morjaria, M., and Mukherjee, S., “Improved Boundary Integral Equation Method for Time Dependent Inelastic Deformation in Metals,” International Journal of Numerical Methods in Engineering, Vol. 15, 1980, pp. 97–111.
15.
Mukherjee, S., Boundary Elements in Creep and Fracture, Applied Science Publishers, London, U.K., 1982.
16.
Mustoe, G. G., “Advanced Integration Schemes over Boundary Elements and Volume Cells for Two and Three‐Dimensional Nonlinear Analysis,” Chapter IX, Developments in Boundary Element Methods, Vol. 4, P. K. Banerjee, and S. Mukherjee, Eds., Applied Science Publishers, London, U.K., 1984.
17.
Nayak, G. C., and Zienkiewicz, O. C., “Elastoplastic Stress Analysis Generalisation for Various Constitutive Relations Including Strain Softening,” International Journal of Numerical Methods in Engineering, Vol. 11, 1972, pp. 53–64.
18.
Raveendra, S. T., “Advanced Development of BEM for Two and Three‐Dimensional Nonlinear Analysis,” thesis presented to State University of New York at Buffalo, N.Y., in 1984, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
19.
Riccardella, P., “An Implementation of the Boundary Integral Technique for Planar Problems of Elasticity and Elasto‐plasticity,” thesis presented to Carnegie‐Mellon University, at Pittsburgh, Pa., in 1973, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
20.
Rzasnicki, W., and Mendelson, A., “Application of the Boundary Integral Equation Method to the Elastoplastic Analysis of υ‐notch Beams,” NASA Technical Report TMX‐71471, 1973.
21.
Swedlow, J. L., and Cruse, T. A., “Formulation of Boundary Integral Equations for Three‐Dimensional Elasto‐plastic Flow,” International Journal of Solids and Structures, Vol. 7, 1971, pp. 1673–1683.
22.
Telles, J. C. F., and Brebbia, C., “Boundary Elements in Plasticity,” Applied Mathematical Modelling, Vol. 5, 1981, pp. 275–281.
23.
Theocaris, P. S., and Marketos, E., “Elasto‐plastic Analysis of Perforated Thin Strips of Strain Hardening Material,” Journal of Mechanics and Physics of Solids, Vol. 12, 1964, pp. 377–390.
24.
Zienkiewicz, O. C., The Finite Element Method, 3rd ed., McGraw‐Hill, London, U.K., 1977.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 113 • Issue 2 • February 1987
Pages: 252 - 265
Copyright
Copyright © 1987 ASCE.
History
Published online: Feb 1, 1987
Published in print: Feb 1987
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