2-D frictionless dynamic contact analysis of large deformable bodies by Petrov–Galerkin natural element method

This paper presents a Petrov–Galerkin natural element method for the nonlinear analysis of 2-D dynamic contact problems without friction. The frictionless dynamic contact problem is formulated according to the linearized total Lagrangian method incorporated with the linearized penalty method. The displacement increment is approximated with Laplace interpolation functions defined with the help of Voronoi polygons, while the admissible virtual displacement is expanded with constant strain functions which are supported on Delaunay triangles. The spatial numerical integration is carried out by applying the conventional Gauss quadrature rule to Delaunay triangles and the temporal time integration is performed by the implicit Newmark method. The validity of the proposed method is examined through the illustrating numerical experiments.