Upper Bound Limit Analysis using Linear Finite Elements and Nonlinear Programming

Limit analysis has become a key method for the optimal design of mechanical and civil structures. Unlike elastic analysis, limit analysis is able to predict material failure, thus providing some estimate of the safety factor for the imposed loading conditions. The method is based on the upper and lower bound theorems of classical plasticity and gives estimates of the limit loads directly. The technique generates the stress and velocity fields at collapse and can be implemented using finite element theory and mathematical programming algorithms. Because the limit theorems give both upper and lower bounds on the collapse load, numerical methods which use them have the advantage of an in-built error estimate. This advantage is a significant one in practical applications, where the material parameters and applied loading may be complex. This paper describes a robust numerical scheme for upper bound limit analysis which can be used for two- and three-dimensional problems. The scheme complements an efficient lower bound formulation recently proposed by Lyamin [6], and permits the collapse load to be predicted accurately.