基于承载比的弹性补偿有限元法分析杆系结构的极限承载力

Modified Elastic Compensation Method Based on Bearing Ratio for Load Carrying Capacity Analysis of Frame Structures

常规的弹性补偿有限元法通常建立于结构单元应力分析的基础上,应用于土木工程结构的极限承载力分析时存在局限性。文中以构件承载比为控制参数,结合塑性极限分析的下限定理,提出了建筑杆系结构塑性极限分析的修正弹性补偿有限元法:首先利用构件承载比和承载比均匀度确定基准承载比,进而通过有策略地调整单元的弹性模量来降低高承载比构件的内力,使得结构的承载比和内力发生重分布,从而形成一系列静力容许应力场,并据此确定结构的塑性极限荷载下限值。该方法可以研究由不同抗力构件组成的杆系结构,且只需利用弹性有限元迭代分析即可求得结构的塑性极限承载力。算例分析说明,该方法计算格式简单、计算精度高。

The traditional elastic compensation method, generally based on stress analysis, has limitation for plastic limit analysis of civil engineering structures. In this paper, a modified elastic compensation method for plastic limit analysis of frame structures is proposed based on lower bOund theory of plastic limit analysis. In this method, the reference bearing ratio for elastic modulus adjustment is determined according to the Element Bearing Ratio （EBR） and the uniform degree of EBR. The elastic modulus of elements with high EBR are decreased systematically, so that a sets of statically admissible stress fields are established, therefore, the lower bound of limit loads can be determined for frame structures. It is practical for plastic limit analysis of civil engineering structures assembled by various components with different bearing capacity and it can determine the plastic limit bearing capacity of structures by only a few conventional linear elastic finite element analyses. Numerical examples demonstrate the correctness of the proposed method with a simple formulation.