弯管结构塑性极限上限分析的有限元方法

Limit analysis of pipe structures using the finite element method

在管线系统中 ,弯管是一种关键的部件 ,对其进行塑性极限分析具有重要的工程意义。根据塑性极限上限定理 ,采用数学规划方法 ,建立了弯管结构塑性极限上限分析的有限元数学规划格式 ,给出了相应的优化迭代算法 ,克服了目标函数非线性非光滑所导致的数值计算困难。采用一种改进的弯管单元并利用该数值方法分析了弯管结构的塑性极限承载能力。计算结果表明 ,该方法具有数值稳定性好。

Pipe bends are critical components in a piping system. This paper presents a general computational method for the limit analysis of pipe structures formulated as a discrete nonlinear mathematical programming problem with equality constraints. The finite element technique was used with an optimal iterative algorithm to solve the problem. The method overcomes the numerical difficulties caused by the nonlinearity and nonsmoothness of the objective function. The numerical procedure was used to analyze the plastic limit of pipe structures. Numerical examples show that this method is convergent, efficient and accurate.