Upper-bound limit analysis based on the element-free Galerkin method

摘要

In most practical engineering applications, limit analysis offers a direct and effective method for determining the load-carrying capacity of structures and provides the theoretical foundation necessary for engineering design and safety assessment. Up to now, great efforts have been devoted to develop efficient and reliable computational methods of limit analysis, and most of these numerical methods are mesh-based, such as the finite element method (FEM) and boundary element method (BEM). Recently, a novel numerical method called meshless method received much attention in computational mechanics field. This method is much less mesh-dependency and can avoid potential mesh distortion and entanglement in mesh-based numerical methods. As a flexible alternative method to mesh-based methods, meshless method shows particular advantages in some scopes. Based on the static limit analysis theorem, this paper intends to employ element-free Galerkin (EFG) method to solve the upper-bound limit analysis of the rigid-perfectly plastic structures governed by the von Mises criterion. In the developed method, moving least-squares interpolants are used to construct the trial and test function, and penalty function are used to deal with the essential boundary conditions. The algorithm of the mathematical programming procedure for determining the upper-bound limit analysis is a no searching process, the rigid and plastic zones are recognized and the objective function is revised correspondingly in every iteration step. In this way, the difficulties caused by undetermined rigid zones and nondifferentiable objective function are overcome, and the iterative process ensures the upper-bound of the load multiplier to be obtained step by step. Numerical examples show that the developed method is feasible and effective to solve the problems of limit analysis by using the EFG method and nonlinear programming.