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 C0 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.