关键词: 结构力学, 有限元分析, 结构动力响应, 多重网格方法, 迭代

Abstract: 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.

Key words: structural mechanics, finite element analysis(FEA), structural dynamic response, multigrid method, iteration