复杂结构塑性极限分析的修正弹性补偿法

MODIFIED ELASTIC COMPENSATION METHOD FOR LIMIT ANALYSIS OF COMPLEX STRUCTURES

弹性补偿法(ECM)是结构塑性极限载荷分析中一种简单有效的方法,但对复杂结构其计算结果往往存在较大误差。采用Banach不动点原理,分析ECM法计算下限极限载荷时存在的收敛性问题,指出只有在弹性模量迭代序列满足压缩映射条件时,才能得到极限载荷的较好逼近值,从而提出复杂结构极限分析的修正弹性补偿法(KtECM)。该方法采用一种结构主要承载单元的弹性模量迭代序列均满足压缩映射条件的迭代方法,并引入与结构应力集中系数相关的调整因子λ,给出名义应力的较为合理的定义方法,建立调整因子与应力集中系数之间的关系式。典型复杂结构的极限载荷分析计算表明:KtECM具有简单、高效、易于工程应用等优点,能够提高对复杂结构极限载荷的计算精度,调整因子λ的引入可以起到协调计算精度与时间的作用。

The elastic compensation method （ECM） for structural 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 condition 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 concentration 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 simplicity, high efficiency and convenience for engineering applications. The adjustable factor λ. can make a balance between computational precision and time.