Numerical solution of hyperelastic membranes by energy minimization

In this work, a numerical approach is presented for solving problems of finitely deformed membrane structures made of compressible hyperelastic material and subjected to external pressure loadings. Instead of following the usual finite element procedure that requires computing the material tangent stiffness and the geometric stiffness, here we solve the membrane structures by directly minimizing the total potential energy, which proves to be an attractive alternative for inflatable structures. The numerical computations are performed over two simple geometries––the circular and the rectangular membranes––and over a more complex structure––a parabolic antenna––using the Saint-Venant Kirchhoff and neo-Hookean models. Whenever available, analytical or semi-analytic solutions are used to validate the finite element results.