A Finite Element Technique for Limit Analysis of Structures

Abstract

Limit analysis provides an alternative to incremental elastic-plastic analysis for determining a limit load. The limit load is obtained from the lower and upper-bound theorems. These theorems, which are based on variational principles, establish the static and kinematic methods, respectively, and are particularly attractive for finite element implementation. A finite element approach using the definition of the p-norm is developed for calculating upper and lower bounds of the limit load multiplier for two-dimensional, rigid perfectly plastic structures which obey the von Mises yield criterion. Displacement and equilibrium building block quadrilateral elements are used in these dual upper and lower-bound formulations, respectively. The nonlinear finite element equations are transformed into systems of linear algebraic equations during the iteration process, and the solution vectors are determined using a frontal equation solver. The upper and lower-bound solutions are obtained in a reasonable number of iteration steps, and provide a good estimate of the limit load multiplier. Numerical results are provided to demonstrate this finite element procedure. In addition, this procedure is particularly applicable to the solution of complex problems using parallel processing on a supercomputer.