A FEM optimal design method for the problem of dynamic response amplitude

The characteristic of dynamic optimal design is heavy in workload and inefficient in computation because of re-analysis. To avoid or reduce re-analysis, we derived the augmentative matrix variation only in summation of the previous matrices time the outside-perturbed parameters by decomposing the element stiffness and mass matrix. The implicit function of amplitude about design variables such as cross-areas and lengths is changed into simplistic function about the perturbed parameters of design variables. Several methods for determining the value of perturbed parameters are detailed. Though illustrated by the plane beam analytical model of FEM, the method can be applied to other analytical models of FEM for optimal design of engineering structures.