Shakedown analysis of circular plates using a yield criterion of the mean

Abstract

Structural optimization based on the shakedown theory is a powerful and promising technique. However, due to the nonlinearities of physical materials and the number of variable loads in real structures, it is computationally complex and time-consuming. To simplify the occurring non-linear, non-convex optimization problems, the paper suggests reducing the number of yield conditions. The so-called a yield criterion of the mean (integral yield condition) is analysed and explained in detail, which allows taking into account one yield condition for the entire finite element instead of multiple point-wise conditions. This approach shows promising results in numerical application to the optimization of a circular plate, considering a possibility of employing the yield criteria of the mean or pointwise yield conditions in different areas of the plate in particular. The methods applied are based on the assumptions of perfect plasticity and small deformations.