Reproducing kernel particle method for large deformations

The Reproducing Kernel Particle Method (RKPM) is presented and applied to the simulations of large deformation problems. RKPM is a meshless method which does not need a mesh- (or grid-) structure in its formulation. Because of this mesh-free property, RKPM is able to simulate large deformation problems without remeshing which is often required for the mesh-based methods such as the finite element method. The RKPM shape function and its derivatives are constructed by imposing the consistency conditions. An efficient treatment of essential boundary conditions is also proposed for explicit time integration.; The Lagrangian method referred to the reference configuration is employed for RKPM simulation of large deformation problems. It is also compared with the formulation referred to the current configuration from the viewpoint of meshless method. Several examples of nonlinear elastic materials and compressible fluid are solved to demonstrate the performance of the method. The numerical experiment for the problem of underwater bubble explosion is also performed using the Lagrangian RKPM formulation.; The multiple scale RKPM is a method that combines the multiresoultion analysis with meshless methods. In this dissertation, it is developed for nonlinear large deformation problems for the first time. Several measures which are associated with primitive variables are suggested and examined in order to capture the high scale component of complex responses. Finally, a simple adaptive algorithm based on the multiple scale RKPM is presented to obtain the refined solution for large deformation problems.