The applications of Meshless Local Petrov-Galerkin (MLPG) approaches in high-speed impact, penetration and perforation problems

This paper presents the implementation of a three-dimensional dynamic code, for contact, impact, and penetration mechanics, based on the Meshless Local Petrov-Galerkin (MLPG) approach. In the current implementation, both velocities and velocity-gradients are interpolated independently, and their compatibility is enforced only at nodal points. As a result, the time consuming differentiations of the shape functions at all integration points is avoided, and therefore, the numerical process becomes more stable and efficient. The ability of the MLPG code for solving high-speed contact, impact and penetration problems with large deformations and rotations is demonstrated through several computational simulations, including the Taylor impact problem, and some ballistic impact and perforation problems. The computational times for the above simulations are recorded, and are compared with those of the popular finite element code (Dyna3D), to demonstrate the efficiency of the present MLPG approach.