科研之友
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摘要
In the present paper a robust computational procedure is proposed for the finite element solution of elasto-plastic boundary value problems in the structural analysis of ductile materials. An implicit numerical scheme is detailed based on a return mapping algorithm. In the present computational scheme the local constitutive equations lead to the solution of a nonlinear scalar equation which ultimately reduces to a single variable algebraic (polynomial) equation in the plastic rate parameter. The proposed integration scheme allows to find the analytical solution of the algebraic equation in closed form. Consequently, in the present algorithmic procedure no iterative method is required to solve the local constitutive problem. The algorithmic scheme presented herein is also characterized by an alternative formulation of the algorithmic counterpart of the plastic consistency condition. Furthermore, in the algorithmic strategy a suitable procedure is presented for the consistent linearization of elasto-plastic boundary value problems. In fact an alternative procedure is proposed herein for the consistent derivation of the tangent operator associated to the algorithmic scheme so that in the present approach the consistent tangent operator is determined without the necessity of computing matrix inversions. The presented computational approach combined with the proposed consistent tangent operator ensures a quadratic rate of asymptotic convergence when an iterative method is pursued for the global solution procedure of elasto-plastic boundary value problems. Numerical applications and illustrative examples are finally reported to show the robustness and effectiveness of the proposed computational procedure in the finite element analysis of elasto-plastic boundary value problems.
- 出版日期2016-5
