Abstract
In this paper, two well established Taylor-Galerkin finite element methods and a second-order Godunov-type finite difference scheme are applied to the problem of finite amplitude axisymmetric wave propagation in hyperelastic membranes. The Taylor-Galerkin finite element methods are derived using continuous and discontinuous base functions, respectively. The second-order Godunov-type scheme is an extension of van Leer's method. The governing equations are given in terms of the principal components of Biot stress and stretch tensors, and are expressed as a conservation law with a source term. Ogden's three-term strain energy function is utilized as the constitutive equation. Numerical results are presented for inflation and impact loading cases. A comparison of these results indicates that for the problem considered in this paper, the second-order Godunov-type finite difference scheme provides the best results, whereas the Taylor-Galerkin finite element method using continuous base functions is the most efficient in computation.
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