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对于厚度变化比较平缓,而且平分厚度的中面仍然是平面的薄板弯曲分析。首先在板上布置节点,选定支持域半径和适当的权函数,然后利用移动最小二乘法(MLS)得到支持域内节点的形函数,将形函数代入控制微分方程,得到支持域内节点的刚度和作用在节点上的力,将节点刚度和力装配成系统的刚度矩阵和力的列向量,求解方程得到各节点的位移以及内力,并用有限元分析软件(ANSYS)对同一问题进行研究,对两种方法所得结果进行了比较,数值结果表明应用无网格Local Petrov-Galerkin法计算变厚度薄板弯曲具有足够的精度和效率。
For the change of thickness is relatively flat, and the middle of the bisecting thickness is still flat sheet bending analysis. Firstly, the nodes are arranged on the board, the radius of the support domain and the appropriate weight function are selected, and then the shape functions of the nodes in the support domain are obtained by using the moving least square method (MLS). The shape function is substituted into the control differential equation to obtain the stiffness and The force acting on the node is used to assemble the node stiffness and force into the system stiffness matrix and the column vector of force. The displacement and internal force of each node are obtained by solving the equation. The same problem is studied by using the finite element analysis software (ANSYS) The numerical results show that the method of Local Petrov-Galerkin meshless method can be used to calculate the bending of variable thickness sheet with enough accuracy and efficiency.