Modified elastic compensation method for limit analysis of complex structures

Abstract

The elastic compensation method (ECM) for struc- tural limit analysis is a simple and effective method for simple structures. However, relatively greater computational errors and divergence are often caused for complex structures. Addressing on these problems, the present paper employs the fixed point theorem in Banach space to discuss the convergence problem of the ECM for lower bound limit load calculations. It can be pointed out that a good limit load solution can be achieved only when the iterative elastic modulus sequences satisfy the condi- tion of contraction mapping. Based on this idea, a modified elastic compensation method (KtECM) is proposed. The KtECM adopts an iterative method, in which the iterative elastic modulus sequences of the main load-carrying elements in a structure satisfy the condition of contraction mapping. At the same time, an adjustable factor λ related with the stress con- centration factor (Kt) of structures is used to define a rational nominal stress. Limit loads of several complex structures are calculated by different methods. It reaches the conclusion that the KtECM can provide a good estimation of plastic limit loads for complex structures and preserves the advantages of simplic- ity, high efficiency and convenience for engineering applica- tions. The adjustable factor λ can make a balance between computational precision and time.