Large deformation analysis of elastic bodies by nonlinear Petrov–Galerkin natural element method

Abstract

A two-dimensional nonlinear Petrov–Galerkin natural element method is presented for the large deformation analysis of elastic structures. The large deformation problem is formulated according to the linearized total Lagrangian method based on Taylor series expansion. The displacement increment is approximated with the Voronoi polygon-based Laplace interpolation functions, while the admissible virtual displacement is expanded by the constant strain basis functions that are supported on Delaunay triangles. The iterative computation is performed by Newton–Raphson method, and the numerical integration is carried out by applying the conventional Gauss quadrature rule to Delaunay triangles. The proposed nonlinear Petrov–Galerkin natural element method is illustrated through the numerical experiments, and its numerical accuracy is compared with MSC/Marc, constant strain finite element method, and Bubnov–Galerkin natural element method and the symmetry preservation in the very large strain is presented.