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Limit analysis of structures containing flaws based on a modified elastic compensation method

机译：基于改进弹性补偿法的含缺陷结构极限分析

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摘要

The elastic compensation method (ECM) based on the conventional linear elastic finite element method is a simple and effective method for structural limit analysis. However, for structures containing flaws, computational errors of the ECM are relatively greater and numerical singularity is often caused before a better solution can be achieved. Firstly, the present paper employs the Banach's contraction mapping theorem in mathematical analysis to discuss the convergence problem of the iterative method of the ECM. The discussions demonstrate that only when iterative elastic modulus sequences are contraction mappings can a good limit load solution be obtained. Secondly, a modified elastic compensation method (K_tECM) is proposed, in which iterative elastic modulus sequences of structural main load-carrying elements can satisfy the condition of contraction mapping. Moreover, an adjustable factor related with structural stress concentration factor (K_t) is introduced to define a rational nominal stress and to dynamically balance the computational precision and CPU time consumed. Finally, we perform limit load analyses for several representative structures containing flaws. These solutions obtained by the KtECM are compared with results from the analytical method, the elastic-plastic analysis method (EPAM) and the ECM. It reaches the conclusion that the KtECM can provide good estimations of plastic limit loads for structures containing flaws. The KtECM has the advantages of simplicity, high efficiency and convenience for engineering applications.
机译：基于常规线性弹性有限元法的弹性补偿法（ECM）是一种简单有效的结构极限分析方法。但是，对于包含缺陷的结构，ECM的计算误差相对较大，并且在实现更好的解决方案之前常常会引起数值奇异。首先，本文在数学分析中采用了Banach收缩映射定理，讨论了ECM迭代方法的收敛性问题。讨论表明，只有当迭代弹性模量序列为收缩映射时，才能获得良好的极限载荷解。其次，提出了一种改进的弹性补偿方法（K_tECM），其中结构主承载元件的迭代弹性模量序列可以满足收缩映射的条件。此外，引入了与结构应力集中因子（K_t）相关的可调因子，以定义合理的名义应力并动态平衡计算精度和CPU消耗时间。最后，我们对包含缺陷的几种代表性结构进行极限载荷分析。将通过KtECM获得的这些溶液与分析方法，弹塑性分析方法（EPAM）和ECM的结果进行比较。得出的结论是，KtECM可以很好地估计包含缺陷的结构的塑性极限载荷。 KtECM具有简单，高效和便于工程应用的优点。

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