A nonlinear programming approach to limit analysis of non-associated plastic flow materials

Abstract

A nonlinear programming approach, along with finite element implementation, has been developed to perform plastic limit analysis for materials under non-associated plastic flow, so the plastic stability condition of non-standard materials can be directly calculated. In the framework of Radenkovic’s theorems, a decoupled material model with non-associated plastic flow was introduced into kinematic limit analysis so that the classic limit theorems were extended for non-standard plastic flow materials, such as cohesive-frictional materials. A non-associated plastic dissipation power is derived, and a purely kinematic formulation is obtained for limit analysis. Based on the mathematical programming theory and the finite element method, the numerical implementation of kinematic limit analysis is formulated as a nonlinear programming problem subject only to one equality constraint. An extended direct iterative algorithm is proposed to solve the resulting programming problem. The developed method has a wide applicability for limit analysis. The effectiveness and efficiency of the proposed method are validated through numerical examples and the influence of non-associated plastic flow on stability conditions of structures is numerically investigated.

Statistical Analyses of the Strengths of Particulate Reinforced Metal Matrix Composites (PRMMCs) Subjected to Multiple Tensile and Shear Stresses

“…Using direct methods (DM) constructed from static theorem in conjunction with the finite element (FE) based homogenization techniques, Weichert et al [9], Magoariec et al [10], Bourgeois et al [11], Zhang et al [12], You et al [13], Chen et al [14], Zhang et al [15,16] elucidated in their works how the macroscopic feasible load domains of different heterogeneous materials can be calculated. Similarly, macroscopic strengths were also evaluated from numerical methods developed based on kinematic theorem, Carvelli [17], Chen and Ponter [18], Barrera et al [19], Li and Yu [20,21], Canh et al [22].…”