A modified algorithm of linear matching method for limit analysis

Abstract

Linear matching method has been widely used for the numerical analysis of limit and shakedown. It has been proved theoretically that linear matching method could offer the monotonically reducing sequence of upper bound. Nevertheless, it still remains open whether linear matching method can obtain the conversed and reliable lower bound or not. Thus, an elastic compensation method is used generally for the evaluation of lower bound, but limit analysis using linear matching method and elastic compensation method needs double iterative computations. Moreover, the convergence can be checked only after the computation is finished because linear matching method and elastic compensation method cannot be performed simultaneously. From this, we propose a simple method in order to improve the numerical solution of lower bound by linear matching method. The Young’s modulus varying spatially is determined in every iteration such that not only the stress state lies on the yielding surface but also the strain state does not exceed a certain value of reference strain, leading to the evaluation of lower bound based on the strain state but not the stress one. The proposed method can improve the numerical solution of lower bound by linear matching method without any affection on the upper bound. ANSYS UserMat is used for implementing the current method. The limit analysis is performed like the general elastic finite element analysis in ANSYS. Some numerical examples are considered in order to confirm the effectiveness of proposed approach. Numerical examples showed the validity and improvement of numerical accuracy of our approach. It should be mentioned that our approach can predict the lower bound and upper one simultaneously within the framework of only linear matching method without using the elastic compensation method.