4.4 Article

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

Journal

MATHEMATICS AND MECHANICS OF SOLIDS
Volume 18, Issue 5, Pages 524-542

Publisher

SAGE PUBLICATIONS LTD
DOI: 10.1177/1081286512444749

Keywords

Nonlinear programming; limit analysis; non-associated plastic flow; finite element method; cohesive-frictional material

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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.

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