动力弹塑性分析的无网格自然单元法

APPLICATION OF MESHLESS NATURAL ELEMENT METHOD TO DYNAMIC ELASTOPLASTIC ANALYSIS

基于无网格自然单元法,提出了结构动力弹塑性响应分析的一条新途径.自然单元法是一种新兴的无网格数值计算方法,其实质是基于自然邻近插值的伽辽金法.自然单元法在本质边界条件的施加上较采用移动最小二乘法的无网格法具有明显的优势.在空间域上采用自然单元法离散,并运用加权余量法推导了动力弹塑性分析的离散控制方程.然后,采用预校正形式的Newmark法在时间域上进行求解.最后给出了数值算例,并验证了所提方法的有效性和正确性.

A new algorithm for dynamic elastoplastic analysis is put forward on the basis of the meshless natural element method. The natural element method（NEM） is a recently developed meshless method and is essentially the Galerkin method based on natural neighbour interpolation. Compared with the meshless methods based on the moving least squares approximation,The NEM possesses notable advantages in the enforcement of essential boundary conditions. The space domain is discretized with the NEM and the discretized governing equations for dynamic elastoplastic analysis are derived using weighted residual technique. Then the predictor-corrector form of the Newmark algorithm is employed to solve the discretized governing equations. At last, numerical examples are presented to demonstrate the effectiveness and accuracy of the proposed method for dynamic elastoplastic analysis.