Meshfree smooth contact formulation and boundary condition treatments in multi-body contact

A meshfree formulation based on the reproducing kernel approximation is developed by integrating the enhanced boundary condition treatments and a smooth contact formulation for analysis of multi-body contact problems. The proposed boundary condition treatments significantly improve the computational efficiency. The smooth contact formulation in meshfree discretization offers advantages over the classical piecewise contact formulation in iteration convergence.; The imposition of essential boundary conditions is first addressed by developing an explicit relation between a full transformation method and a collocation Lagrange multiplier method. Their advantages and disadvantages are identified. A mixed transformation method (MTM) is then proposed by introducing a particle partitioning and a mixed coordinate to the coordinate transformation so that matrix inversion and multiplication involve only the degrees of freedom associated with the essential boundary points. In addition, a boundary singular kernel (BSK) method is proposed by introducing singularity to the kernel functions associated with essential boundary points so that the coefficients associated with the newly constructed shape functions become nodal values. Consequently, the essential boundary conditions can be imposed directly with standard procedures. The convergent rates, computation efficiency and solution accuracy of both MTM and BSK methods are evaluated using several benchmark problems.; The continuum-based contact formulation provides a precise statement of the contact minimization problem, where a C2 continuity in the approximation of geometry and displacement variables is required. The C2 requirement is difficult to meet under the finite element framework since smooth finite element shape functions are difficult to construct. On the other hand, meshfree method allows any degree of smoothness to be introduced to the approximation of contact surface geometry and displacement variables (isoparamentric). In corporation with the continuum-based contact formulation, the resulting meshfree contact force vector is continuous when a material point slides between segments of contact surface. This property provides substantial advantage in the Newton iteration of contact analysis.; The proposed smooth contact formulation is applied to the simulation of metal forming processes. An improvement on iteration convergence is achieved in comparison with the analysis using piecewise linear contact formulation.