A finite element interior-point implementation of tension field theory

This paper presents an interior-point implementation method of the relaxed strain energy function to model the stress distribution in membranes in the presence of wrinkles. The relaxed strain energy function is reformulated using the interior-point method. This formulation is proven to be quasi-convex with respect to the deformation gradient. A set of governing equations for the membrane is developed in the standard finite element format. The solution to this set of equations is obtained using the interior-point method, and several numerical examples are presented for validation. The proposed method is shown to converge and to be robust and efficient.