结构动力响应分析的多重网格方法

Multigrid method for structure dynamic response analysis

提出了一种适合于有限元分析中求解结构动力响应的多重网格方法,该方法利用初始网格下的结果,通过双线性插值技术得到网格变化后新的近似位移向量,然后由多重网格迭代过程求解结构动力响应问题。在多重网格迭代的前光滑过程中,选择了共轭梯度法提高其收敛率;在粗网格校正过程中,给出了一种近似求解位移向量误差的方程;在后光滑过程中,选择了Jacobi松弛迭代提高解的光滑性。该方法将网格离散过程和数值求解过程结合在一起,建立了一个网格细分后结构动力响应问题的快速重分析方法,与传统有限元方法相比较,具有计算简便、迭代步骤少,运算时间短等特点,可以作为结构动力问题自适应有限元分析的一种十分有效的工具。同时,本文还给出了一种简单实用的时间步长划分的自适应方法。

A multigrid method with a simple adaptive time stepping technique was proposed to solve the structure dynamic response in the finite element analysis（FEA）. By the method the results of the initial mesh were utilized sufficienlty, the new approximate displacement vectors in the changed mesh were obtained by the bilinear interpolation technique, and the solution for the structure dynamic response problem was accomplished by the multigrid iteration procedure. The conjugate gradient method was applied in the prior smoothing process of the multigrid iteration procedure to improve the convergence rate. An equation to estimate approximately the error of the displacement vector was given in the correction of the coarse mesk. In the post-smoothing process of the multigrid iteration procedure, Jacobi relaxation iterations were chosen to improve the evenness of the solution. Combining the discretization of mesh with the numerical solution, a fast reanalysis procedure after the mesh refinement was established. Compared with the traditional FEA, the proposed method is characterized by simple calculation, fast iteration and timesavingness. It can be used as an effective tool for solving the structure dynamic response problem by the adaptive FEA.