Numerical Solution by Energy Minimization of Hyperelastic Membrane in Large Displacements and Finite Strains

摘要

In this work, a numerical approach is presented for solving problems of u0002nitely deformedrnmembrane structures made of quasi-incompressible hyperelastic material andrnsubjected to external pressure loadings. Instead of following the usual u0002nite elementrnprocedure that requires computing the geometric stiffness and large displacement matrices,rnhere we solve the membrane structures by directly minimizing the total potentialrnenergy, which proves to be a more robust and efu0002cient technique.rnThe numerical computations are performed over two geometries - the circular andrnthe rectangular membranes - with different material behaviors - isotropic linear or orthotropicrnlinear or nonlinear elasticity. Whenever available, analytical or semi-analyticrnsolutions are used to validate the u0002nite element results.