Abstract: In this paper,the improved r and h adaptive finite element method based on matrix perturbation theory and element energy ratio is proposed.In structure vibration analysis,through r convergence adaptive finite element process,mesh optimization can be realized.In the light of the judgement on the changes in the magnitude of element energy ratio,a local optimal refinement can be achieved in the process of h convergence adaptive finite element method so that more accurate finite element solutions can be obtained with as least grids as possible.A lot of numerical examples are given and the proposed approach is shown to be feasible and effective.

Key words: iterative perturbation, element energy ratio, r and h adaptive FEM, mesh optimization, natural frequency