In this paper, a new and simple boundary element method without internal cells is presented for the analysis of elastoplastic problems, based on an effective transformation technique from domain integrals to boundary integrals. The strong singularities appearing in internal stress integral equations are removed by transforming the domain integrals to the boundary. Other weakly singular domain integrals are transformed to the boundary by approximating the initial stresses with radial basis functions combined with polynomials in global coordinates. Three numerical examples are presented to demonstrate the validity and effectiveness of the proposed method.
Issue Section:
Technical Papers
1.
Swedlow
, J. L.
, and Cruse
, T. A.
, 1971
, “Formulation of Boundary Integral Equations for Three-Dimensional Elasto-Plastic Flow
,” Int. J. Solids Struct.
, 7
, pp. 1673
–1683
.2.
Mukherjee
, S.
, 1977
, “Corrected Boundary Integral Equations in Planar Thermo-Elastoplasticity
,” Int. J. Solids Struct.
, 13
, pp. 331
–335
.3.
Telles
, J. C. F.
, and Brebbia
, C. A.
, 1979
, “On the Application of the Boundary Element Method to Plasticity
,” Appl. Math. Model.
, 3
, pp. 466
–470
.4.
Banerjee
, P. K.
, and Raveendra
, S. T.
, 1986
, “Advanced Boundary Element Analysis of Two- and Three-Dimensional Problems of Elasto-Plasticity
,” Int. J. Numer. Methods Eng.
, 23
, pp. 985
–1002
.5.
Riccardella, P., 1973, “An Implementation of the Boundary Integral Technique for Planar Problems of Elasticity and Elastoplasticity,” Ph.D thesis, Carnegie-Mellon University, Pittsurgh, PA.
6.
Mendelson, A., and Albers, L. V., 1975, “An Application of the Boundary Integral Equation Method to Elastoplastic Problems,” Proc. ASME Conf. On Boundary Integral Equation Methods, T. A. Cruse and F. J. Rizzo, eds., AMD-Vol. 11, ASME, New York.
7.
Telles, J. C. F., 1983, The Boundary Element Method Applied to Inelastic Problems, Springer-Verlag, Berlin.
8.
Lee
, K. H.
, and Fenner
, R. T.
, 1986
, “A Quadratic Formulation for Two-Dimensional Elastoplastic Analysis Using the Boundary Integral Equation Method
,” J. Strain Anal.
, 21
, pp. 159
–175
.9.
Chandra
, A.
, and Saigal
, S.
, 1991
, “A Boundary Element Analysis of the Axisymmetric Extrusion Process
,” Int. J. Non-Linear Mech.
, 26
, pp. 1
–13
.10.
Guiggiani
, M.
, Krishnasamy
, G.
, Rudolphi
, T. J.
, and Rizzo
, F. J.
, 1992
, “General Algorithm for the Numerical Solution of Hyper-Singular Boundary Integral Equations
,” ASME J. Appl. Mech.
, 59
, pp. 604
–614
.11.
Daller
, R.
, and Kuhn
, G.
, 1993
, “Efficient Evaluation of Volume Integrals in Boundary Element Method
,” Comput. Methods Appl. Mech. Eng.
, 109
, pp. 95
–109
.12.
Okada
, H. O.
, and Atluri
, S. N.
, 1994
, “Recent Developments in the Field-Boundary Element Method for Finite/Small Strain Elastoplasticity
,” Int. J. Solids Struct.
, 31
, pp. 1737
–1775
.13.
Huber
, O.
, Dallner
, R.
, Partheymuller
, P.
, and Kuhn
, G.
, 1996
, “Evaluation of the Stress Tensor in 3-D Elastoplasticity Direct Solving of Hypersingular Integrals
,” Int. J. Numer. Methods Eng.
, 39
, pp. 2555
–2573
.14.
Aliabadi
, M. H.
, and Martin
, D.
, 2000
, “Boundary Element Hyper-Singular Formulation for Elastoplastic Contact Problems
,” Int. J. Numer. Methods Eng.
, 48
, pp. 995
–1014
.15.
Gao
, X. W.
, and Davies
, T. G.
, 2000
, “An Effective Boundary Element Algorithm for 2D and 3D Elastoplastic Problems
,” Int. J. Solids Struct.
, 37
, pp. 4987
–5008
.16.
Gao, X. W., and Davies, T. G., 2001, Boundary Element Programming in Mechanics, Cambridge University Press, Cambridge, UK.
17.
Nardini, D., and Brebbia, C. A., 1982, “A New Approach for Free Vibration Analysis Using Boundary Elements,” Boundary Element Methods in Engineering, C. A. Brebbia, ed., Springer, Berlin, pp. 312–326.
18.
Partridge, P. W., Brebbia, C. A., and Wrobel, L. C., 1992, The Dual Reciprocity Boundary Element Method, Computational Mechanics Publications, Southampton, UK.
19.
Zhu
, S.
, and Zhang
, Y.
, 1994
, “Improvement on Dual Reciprocity Boundary Element Method for Equations With Convective Terms
,” Commun. Numer. Meth. Eng.
, 10
, pp. 361
–371
.20.
Golberg
, M. A.
, Chen
, C. S.
, and Bowman
, H.
, 1999
, “Some Recent Results and Proposals for the Use of Radial Basis Functions in the BEM
,” Eng. Anal. Boundary Elem.
, 23
, pp. 285
–296
.21.
Power
, H.
, and Mingo
, R.
, 2000
, “The DRM Subdomain Decomposition Approach to Solve the Two-Dimensional Navier-Stokes System of Equations
,” Eng. Anal. Boundary Elem.
, 24
, pp. 107
–119
.22.
Cheng
, A. H. D.
, Young
, D. L.
, and Tsai
, C. C.
, 2000
, “Solution of Poisson’s Equation by Iterative DRBEM Using Compactly Supported, Positive Definite Radial Basis Function
,” Eng. Anal. Boundary Elem.
, 24
, pp. 549
–557
.23.
Sensale
, B.
, Partridge
, P. W.
, and Creus
, G. J.
, 2001
, “General Boundary Elements Solutions for Ageing Viscoelastic Structures
,” Int. J. Numer. Methods Eng.
, 50
, pp. 1455
–1468
.24.
Henry
, D. P.
, and Banerjee
, P. K.
, 1988
, “A New Boundary Element Formulation for Two- and Three-Dimensional Elastoplasticity Using Particular Integrals
,” Int. J. Numer. Methods Eng.
, 26
, pp. 2079
–2096
.25.
Kane, J. H., 1994, Boundary Element Analysis in Engineering Continuum Mechanics, Prentice-Hall, Englewood Cliffs, NJ.
26.
Ochiai
, Y.
, and Kobayashi
, T.
, 1999
, “Initial Stress Formulation for Elastoplastic Analysis by Improved Multiple-Reciprocity Boundary Element Method
,” Eng. Anal. Boundary Elem.
, 23
, pp. 167
–173
.27.
Banerjee, P. K., and Davies, T. G., 1984, “Advanced Implementation of the Boundary Element Methods for Three-Dimensional Problems of Elasto-Plasticity,” Developments in Boundary Element Methods, Elsevier, London.
28.
Partridge
, P. W.
, and Sensale
, B.
, 1997
, “Hybrid Approximation Functions in the Dual Reciprocity Boundary Element Method
,” Commun. Numer. Meth. Eng.
, 13
, pp. 83
–94
.29.
Golberg
, M. A.
, Chen
, C. S.
, and Karur
, S. R.
, 1996
, “Improved Multiquadric Approximation for Partial Differential Equations
,” Eng. Anal. Boundary Elem.
, 18
, pp. 9
–17
.30.
Partridge
, P. W.
, 2000
, “Towards Criteria for Selecting Approximation Functions in the Dual Reciprocity Method
,” Eng. Anal. Boundary Elem.
, 24
, pp. 519
–529
.31.
Fox, E. N., 1948, “The Mean Elastic Settlement of a Uniformly Loaded Area at a Depth Below the Ground Surface,” Proc. 2nd Int. Conf. Soil Mechanics and Foundation Engng., Vol. 1, FNDN, p. 129.
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