Linear matching method for limit load problems using the Drucker–Prager yield condition

Abstract

The paper discusses the application of the linear matching method to the evaluation of the limit load for the Drucker–Prager yield condition. The method involves the sequential matching of an appropriate linear material to the yield condition. This results in a programming method where the linear solution required for each iteration can be interpreted as a standard problem of the type for which finite element codes are designed. Convergence may be proven for a wide range of yield conditions. For the Drucker–Prager condition, however, the existing sufficient condition for convergence is not satisfied, but convergent iterative methods may still be derived. In this paper, solutions for both an associated and a non-associated flow rule are discussed for indentation problems. Comparisons with analytical solutions and step-by-step finite element calculations demonstrate the accuracy and efficiency of the method.