Free vibration analysis of membranes using the h–p version of the finite element method

The h–p version of the finite element method is applied to the vibration of membranes. This is accomplished using a polynomially enriched triangular element. New simple expressions of hierarchical C 0 shape functions for triangles are given in terms of the shifted Legendre orthogonal polynomials. The h–p version of the finite element method marries both the concepts of the conventional h-version and the p-version. The accuracy of the solution is sought by simultaneously refining the mesh and increasing the polynomial order in each element. Results of frequency calculations are found for triangular and L-shaped membranes using a number of meshes and polynomial orders. It is shown that the h–p version of the finite element method is always convergent from above and produces a high accuracy with few degrees of freedom.