Meshfree method for large deformation in dynamic problems

We present a new meshless method, Taylor-SPH, for the numerical analysis of large deformation dynamic problems. This method is based on the previous work developed by the authors to solve solid dynamics problems within the framework of small deformation theory. The governing equations are given in terms of stress and velocity using the updated Lagrangian approach. The Jaumann rate of the Cauchy stress is used to get an objective stress rate tensor. The Taylor-SPH method is based on two sets of particles resulting on avoiding the classical tensile instability. In order to assess the accuracy of the proposed method, numerical examples based on elastic material involving large deformation are solved.

A Comparison of EFGM and FEM for Nonlinear Solid Mechanics Problems

In this paper, element free Galerkin method (EFGM) has been applied to solve nonlinear solid mechanics problems using updated Lagrangian approach. The nonlinear equations have been solved using Newton Raphson method. An associative J2 flow rule and isotropic hardening has been used for the modelling of elasto-plastic material behaviour. Elastic predictor and plastic corrector algorithm has been used for the integration of incremental stress-strain relation. Few test problems involving large deformations have been simulated and the results obtained by EFGM have been compared with those obtained by FEM.

An Adaptive Local Meshfree Updated Lagrangian Approach for Large Deformation Analysis of Metal Forming

The large deformation analysis is one of major challenges in numerical modelling and simulation of metal forming. Because no mesh is used, the meshfree methods show good potential for the large deformation analysis. In this paper, a local meshfree formulation, based on the local weak-forms and the updated Lagrangian (UL) approach, is developed for the large deformation analysis. To fully employ the advantages of meshfree methods, a simple and effective adaptive technique is proposed, and this procedure is much easier than the re-meshing in FEM. Numerical examples of large deformation analysis are presented to demonstrate the effectiveness of the newly developed nonlinear meshfree approach. It has been found that the developed meshfree technique provides a superior performance to the conventional FEM in dealing with large deformation problems for metal forming.

A natural element updated Lagrangian approach for modelling fluid structure interactions

In this paper we present a novel methodology for the numerical simulation of fluid structure interactions in the presence of free surfaces. It is based on the use of the Natural Element Method (NEM) in an updated Lagrangian framework, together with the integration of the Navier-Stokes equations by employing a Galerkin-characteristics formulation. Tracking of the free-surface is made by employing shape constructors, in particular α- shapes. A theoretical description of the method is made and also some examples of the performance of the technique are included.