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A Nonlinear Optimization Algorithm for Lower Bound Limit and Shakedown Analysis

G. Gang1, Y.H. Liu2
China Special Equipment Inspection and Research Center, Beijing 100013, China
Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China

Computers, Materials & Continua 2010, 20(3), 251-272. https://doi.org/10.3970/cmc.2010.020.251

Abstract

Limit and shakedown analysis theorems are the theories of classical plasticity for the direct computation of the load-carrying capacity under proportional and varying loads. Based on Melan's theorem, a solution procedure for lower bound limit and shakedown analysis of three-dimensional (3D) structures is established making use of the finite element method (FEM). The self-equilibrium stress fields are expressed by linear combination of several basic self-equilibrium stress fields with parameters to be determined. These basic self-equilibrium stress fields are elastic responses of the body to imposed permanent strains obtained through elastic-plastic incremental analysis by the three-dimensional finite element method (3D-FEM). The Complex method is used to solve the resulting nonlinear programming directly and determine the maximal load amplifier. The numerical results show that it is efficient and accurate to solve three-dimensional limit and shakedown analysis problems by using the 3D-FEM and the Complex method. The limit analysis is treated here as a special case of shakedown analysis in which only proportional loading is considered.

Keywords

Limit and shakedown analysis, 3D-FEM, self-equilibrium stress, nonlinear programming, the Complex method

Cite This Article

G. . Gang and Y. . Liu, "A nonlinear optimization algorithm for lower bound limit and shakedown analysis," Computers, Materials & Continua, vol. 20, no.3, pp. 251–272, 2010.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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