A Stabilized Particle Method for Large Deformation Dynamic Analysis of Structures

The property of free movement of particles allows for most meshless particle methods to be efficiently used for simulation of solid problems involving large deformation as it removes the necessity of remeshing, which is one of the time-consuming parts of the traditional finite element method based on an updated Lagrangian formulation. One of the main sources of instabilities in meshfree particle methods, which approximate the strong form of partial differential equations, is the existence of extra high frequency vibrations. They are induced into the solution due to the use of truncated Taylor series expansions. The cumulative effect of the extra vibrations makes the solution to be polluted by zero energy modes and tensile instabilities. In this paper, the CSPM particle method is used to solve elastodynamic large deformation problems based on an updated Lagrangian procedure. A field smoothing approach, recently proposed for reduction of instabilities that rise from excessive high frequency vibrations, is further extended to large deformation problems. Also, the phenomenon of particles penetration can be prevented without the requirement of any additional artificial damping forces. Another major advantage of the new approach is its generality which allows for its implementation into other particle methods and its application for solving other physical problems. A variety of large deformation problems are solved by the proposed approach and the results are compared with other available results.