Fast Stiffness Matrix Calculation for Nonlinear Finite Element Method

We propose a fast stiffness matrix calculation technique for nonlinear finite element method (FEM). Nonlinear stiffness matrices are constructed usingGreen-Lagrange strains, which are derived from infinitesimal strains by adding the nonlinear terms discarded from small deformations. We implemented a linear and a nonlinear finite element method with the same material properties to examine the differences between them.We verified our nonlinear formulationwith different applications and achieved considerable speedups in solving the system of equations using our nonlinear FEM compared to a state-of-the-art nonlinear FEM.