Elastic-viscoplastic analysis of plate bending with Reissner’s theory by the boundary element method. (English) Zbl 1521.74295
Summary: The development of a formulation of the Boundary Element Method (BEM) for application to elastic-viscoplastic analysis of plate bending is presented in this work. Reissner’s theory is used, valid for thin and thick plates. Initially, Reissner’s plate bending theory is presented, including the consideration of physical nonlinearity, and then, integral equations applied to Reissner’s plates are shown. The theory for considering viscoplasticity is presented, as well as the procedures for its use with the BEM. In order to solve the equations that govern the problem, an incremental procedure is used and von Mises’ and Tresca’s yield criteria are considered. This process offers an alternative method of solution for elasto-plastic problems, when steady-state condition is reached. Numerical examples are presented and results are compared with available solutions.
MSC:
| 74S15 | Boundary element methods applied to problems in solid mechanics |
| 74C10 | Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity) |
| 65M38 | Boundary element methods for initial value and initial-boundary value problems involving PDEs |
| 74K20 | Plates |
Software:
ABAQUSReferences:
| [1] | Dinis, LMS; Owen, DRJ., Elastic-viscoplastic analysis of plates by the finite element method, Comput Struct, 8, 207-215 (1978) · Zbl 0369.73055 |
| [2] | Owen, DRJ; Liu, GQ., Elasto-viscoplastic analysis of anisotropic laminated plates and shells, Eng Comput, 6, 90-95 (1985) |
| [3] | Moshaiov, A.; Vorus, WS., Elasto-plastic plate bending analysis by a boundary element method with initial plastic moments, Int J Solids Struct, 22, 11, 1213-1229 (1986) · Zbl 0602.73083 |
| [4] | Providakis, CP; Beskos, DE., Dynamics analysis of elasto-plastic flexural plates by the D/BEM, Eng Anal Bound Elem, 14, 1, 75-80 (1994) |
| [5] | Fortiu, PA; Irschik, H.; ZieglerF, ., Modal analysis of elastic-plastic plate vibrations by integral equations, Eng Anal Bound Elem, 14, 1, 81-97 (1994) |
| [6] | Fernandes, GR; Venturini, WS., Non-linear boundary element analysis of plates applied to concrete slabs, Eng Anal Bound Elem, 26, 169-181 (2002) · Zbl 1051.74051 |
| [7] | Karam, VJ., Analysis of plate bending by the bem including physical non-linearity (1992), UFRJ: UFRJ Rio de Janeiro, RJ, Brazil, [D.Sc. thesis] |
| [8] | Karam, VJ; Telles, JCF., The BEM applied to plate bending elastoplastic analysis using Reissner’s theory, Eng Anal Bound Elem, 9, 4, 351-375 (1992) |
| [9] | Karam, VJ; Telles, JCF., Nonlinear material analysis of Reissner’s plates, Plate bending analysis with boundary elements, 127-163 (1998), Computational Mechanic Publications, Advances in boundary elements England: EdChap. 4 · Zbl 0987.74006 |
| [10] | Ribeiro, GO; Venturini, WS., Elastoplastic analysis of Reissner’s plate using the boundary element method, Plate bending analysis with boundary elements, 101-125 (1998), Computational Mechanic Publications, Advances in boundary elements England: EdChap.3. · Zbl 0987.74006 |
| [11] | Providakis, CP; Beskos, DE, Inelastic transient dynamics analysis of Reissner- Mindlin plates by the D/BEM, Int J Numer Methods Eng, 49, 383-397 (2000) · Zbl 0976.74077 |
| [12] | Supriyono; Aliabadi, MH, Boundary element method for shear deformable plates with combined geometric and material nonlinearities, Eng Anal Bound Elem, 30, 1, 31-42 (2006) · Zbl 1195.74259 |
| [13] | Oliveira, SRC.; Karam, V. J., Elastoplastic analysis of Reissner’s plates by the boundary element method, Eng Anal Bound Elem, 64, 247-254 (2016), 2016 · Zbl 1403.74207 |
| [14] | Morjaria, M.; Mukherjee, S., Inelastic analysis of transverse deflection of plates by the boundary element method, J Appl Mech, 47, 2, 291-296 (1980) · Zbl 0436.73094 |
| [15] | Providakis, CP., Quasi-static analysis of viscoplastic plates by the boundary element method, Eng Anal Bound Elem, 11, 265-268 (1993) |
| [16] | Telles, JCF; Brebbia, CA., Elastic/viscoplastic problems using boundary elements, Int J Mech Sci, 24, 10, 605-618 (1982) · Zbl 0491.73091 |
| [17] | Telles, JCF., The boundary element method applied to inelastic problems (1983), Springer-Verlag: Springer-Verlag New York, TokyoBerlin, Heidelberg · Zbl 0533.73076 |
| [18] | Perzyna, P., Fundamental problems in viscoplaticity, Adv Appl Mech, 9, 243 (1996) |
| [19] | Reissner, E., On the theory of bending of elastic plates, J Math Phys, 23, 184-191 (1944) · Zbl 0061.42501 |
| [20] | Reissner, E., The effect of transverse shear deformation on the bending of elastic plates, J Appl Mech, 12, A69-A77 (1945) · Zbl 0063.06470 |
| [21] | Reissner, E., On bending of elastic plates, Q Appl Math, 5, 55-68 (1947) · Zbl 0030.04302 |
| [22] | Hill, R., The mathematical theory of plasticity (1950), Oxford University Press: Oxford University Press New York · Zbl 0041.10802 |
| [23] | Van der Weeën, F., Application of the boundary integral equation method to Reissner’s plate model, Int J Numer Methods Eng, 18, 1-10 (1982) · Zbl 0466.73107 |
| [24] | Van der Weeën, F., Application of the direct boundary element method to Reissner’s plate model, Bound Elem Eng, 487-499 (1982) |
| [25] | Karam, VJ; Telles, JCF., On boundary elements for Reissner’s plate theory, Eng Anal, 5, 1, 21-27 (1988) |
| [26] | Telles, JCF., A self-adaptive coordinate transformation for efficient numerical evaluation of general boundary element integrals, Int J Numer Methods Eng, 24, 959-973 (1987) · Zbl 0622.65014 |
| [27] | Kutt, HR., Quadrature formulae for finite part integrals (1975), The National Research Institute for Mathematical Sciences: The National Research Institute for Mathematical Sciences Pretoria, Report Wisk 178 · Zbl 0327.65027 |
| [28] | Comeau, I., Numerical stability in quasi-static elasto/viscoplasticity, Int J Numer Methods Eng, 9, 109 (1975) · Zbl 0293.73022 |
| [29] | Owen, DRJ; Hinton, E., Finite elements in plasticity: theory and practice (1980), Pineridge Press Limited: Pineridge Press Limited Swansea, U.K · Zbl 0482.73051 |
| [30] | Armen, H.; Pifko, AB; Levine, HS; Isakso, G., Plasticity, (Tottenham, H.; Brebbia, CA, Finite element techniques in structural mechanics (1970), Stress Analysis Publisher), 209-257, Chap. 8 |
| [31] | Hopkins, HG; Wang, AJ., Load-carrying capacities for circular plates of perfectly-plastic material with arbitrary yield condition, J Mech Phys Solids, 3, 117-129 (1954) |
| [32] | Owen, DRJ; Figueiras, JA, Elastoplastic analysis of anisotropic plates and shells by the semiloof element, Int J Numer Methods Eng, 19, 521-539 (1983) · Zbl 0508.73066 |
| [33] | Simulia: ABAQUS Software. Version 6.20-3 (2020), Dassault Systèmes |
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