基于自然单元法的轴对称结构极限上限分析

自然单元法是一种以自然邻近插值为试函数的新兴无网格数值方法,其形函数的计算不涉及矩阵求逆,也不需要任何人为参数。为了充分发挥自然单元法的优势,本文基于极限分析上限定理建立了轴对称结构极限上限分析的整套求解算法。轴对称结构的位移场由自然邻近插值构造,并且采用罚函数法处理材料的不可压条件。为了消除目标函数非光滑所引起的数值困难,采用逐步识别刚性区和塑性区,并对两者用不同方法进行处理。数值算例结果表明,本文提出的轴对称结构极限上限分析方法是行之有效的。

Upper bound limit analysis of axisymmetric structures based on natural element method

As a recently developed meshless method,the natural element method (NEM) constructs its shape function by the natural neighbour interpolation,which does not involve the computation of complex matrix inversion and requires no artificial parameters.In order to fully exploit the advantage of natural element method,a solution procedure for upper bound limit analysis of axisymmetric structures is presented based on the upper bound theorem of limit analysis.The displacement field of the axisymmetric structure is constructed by the natural neighbour interpolation and the plastic incompressibility is well covered by the penalty function method.In order to avoid the difficulties caused by non-differentiable objective function,the rigid zone is distinguished from the plastic zone generally and they are dealt with differently.Numerical examples show that the proposed method for upper bound limit analysis of axisymmetric structures is effective.