稳定相容节点积分无网格法动力学分析

Dynamic analysis of the stabilized smoothing nodal integration meshfree method

利用添加多项式项的(Radial Point Interpolation Method,RPIM)形函数,形成了动力学问题的无网格全局弱形式.生成了伴随于域节点的Voronoi图,利用基于应变光滑稳定方案的稳定相容节点积分得到了改进后的总体刚度矩阵离散化形式,并利用直接法施加位移边界条件.自由振动分析得到了与有限元参考解吻合良好的数值解,受迫振动分析采用了无条件稳定的Newmark法,从而验证了本方法在求解动力学问题所展现的稳定性、精确性及收敛性.

The meshfree global weak form of dynamic problem is formed using polynomial terms augmented RPIM shape function. A Voronoi diagram accompanied with field nodes is produced, and a discrete model of a global stiff matrix is presented by means of stabilized smoothing nodal integration based on strain smoothing sta- bilization, and the displacement boundary conditions are enforced by a direct method. The numerical results that agree well with FEM reference results were presented in free vibration analysis, and the unconditionally stable Newmark method is used in forced vibration analysis. It is proved that this method has better stability, accuracy and convergence.