Lower Bound Shakedown Analysis by Using the EFG Method and Nonlinear Programming

Abstract

Shakedown theorems are exact theories of classical plasticity for the direct computation of the load-carrying capacity under varying loads. Based on the classical Melan’s theorem, a numerical solution procedure for determining the shakedown load of elasto-perfectly plastic structure is presented firstly making use of the element free Galerkin (EFG) method. The numerical implementation is very simple and convenient because it is only necessary to construct an array of nodes in the domain under consideration. The reduced-basis technique is adopted here to solve the mathematical programming iteratively in a sequence of reduced self-equilibrium stress subspaces with very low dimensions. The self-equilibrium stress field is expressed by linear combination of several self-equilibrium stress basis vectors with parameters to be determined. These self-equilibrium stress basis vectors can be generated by performing equilibrium iteration procedure during elasto-plastic incremental analysis. The Complex method is used to solve nonlinear programming and determine the maximal load amplifier. The numerical results show that it is efficient and accurate to solve shakedown analysis problems by using the EFG method and nonlinear programming.