Elasto-plastic Analysis of Two-dimensional Orthotropic Bodies with the Boundary Element Method

Abstract

Abstract: The Boundary Element Method (BEM) isintroduced to analyze the elasto-plastic problems of 2-D orthotropic bodies. With the help of known boundaryintegral equations and fundamental solutions, a numeri-cal scheme for elasto-plastic analysis of 2-D orthotropicproblems with the BEM is developed. The Hill or-thotropic yield criterion is adopted in the plastic analy-sis. The initialstress method and tangent predictor-radialreturn algorithm are used to determine the stress state insolving the nonlinear equation with the incremental iter-ation method. Finally, numerical examples show that theBEM is effective and reliable in analyzing elasto-plasticproblems of orthotropic bodies.keyword: Boundary Element Method (BEM), Elasto-plastic Analysis, Singular Integrals, 2-D OrthotropicBody, Orthotropic Yield Criterion1 IntroductionNowadays new type materials exhibiting a characteristicof anisotropy or orthotropy are widely used in the indus-tries and the corresponding numerical analysis is neces-sary to solve these complicated problems as the exper-iments are absent or the analytical methods are unfea-sible in most conditions. Elasto-plastic analysis is oneof the practical and desirable problems, which has at-tracted many interestson study. However, the anisotropicor orthotropic plastic analysis is much more complicatedthan isotropic problems. Fortunately, the development ofcomputer technologies and computational methods per-mits a more realistic and complex modelingthan ever be-fore. The finite element method (FEM) and the boundaryelement method (BEM) are twousualnumerical methodsthat are widely used in solving many engineering prob-