Structural analysis of prestressed Saint Venant–Kirchhoff hyperelastic membranes subjected to moderate strains

This paper presents a complete numerical formulation for the nonlinear structural analysis of prestressed membranes with immediate applications in Civil Engineering. The membranes will be considered to undergo large deformations but moderate strains. Therefore, Nonlinear Continuum Mechanics principles dealing with large deformations on prestressed bodies will be accounted for. The constitutive model adopted for the material will be a prestressed Saint Venant–Kirchhoff hyperelastic one. To carry out the computational resolution of the structural problem, the Finite Element Method (FEM) will be implemented according to a Total Lagrangian Formulation (TLF), by means of the Direct Core Congruential Formulation (DCCF). Different numerical schemes—first and second-order unconstrained optimization techniques—will be presented to solve the resulting geometrically nonlinear problem, which involves the minimization of the total potential energy system functional. These ones will be improved by a parametric line search algorithm according to a polynomial interpolation. Eventually, numerical examples will be introduced to verify the robustness of the aforementioned formulation.