高阶等参元在薄膜结构自由振动中的应用

The membrane is one of the most widely used structures in engineering. Because the theoretical solution of the structure’s natural vibration characteristics is related to the trigonometric function family, the accuracy of the finite element solution is not very high by the conventional low-order element analysis. Although the h-type finite element method can improve the accuracy of the finite element solution with refined meshing of the structure, the corresponding pre-processing is relatively difficult, and the accuracy of the finite element solution may be reduced if the refined mesh is distorted. Based on the p-type finite element method, 2 quadrilateral high order isoparametric elements, i.e., isoparametric element Q16 with 16 nodes and isoparametric element Q13 with 13 nodes, were constructed to study the free vibration characteristics of membranes. Examples of membranes with different shapes and different boundary conditions show that, the proposed elements have fas- ter convergence rates, higher computational accuracies and efficiencies than conventional low-order isoparametric elements.