DYNAMIC ANALIZES OF ELASTIC STRUCTURES BY USING MOVING PARTICLE SEMI-IMPLICIT METHOD (MPS)

This paper presents the theory and hypotheses used in the development of a particle method for dynamic structural analysis. The method was implemented by the authors and the validation of the code was carried out through comparison with analytical results. This method is based on the Moving Particle Semi-implicit Method (MPS) that was first developed to simulate the behavior of incompressible fluids. The main strategy of the MPS is to replace the differential operators in the governing equations by a model of interaction between particles. As a meshless method, it is very effective in the simulation of the hydrodynamic problems that involve large deformation and fragmentation of free-surfaces, complex shaped bodies or moving boundaries. In the recent years, the developments of the method extended its application to the analysis of elastic structures, making possible the analysis of dynamic systems and the coupling of hydrodynamics and structural analysis to investigate hydro-elasticity problems. For dynamic analysis of elastic structures, the elastic structures are discretized as particles and the theory of small displacements is considered. By using the particles interactions model, the governing equations of the dynamic of the elastic bodies are solved by the gradient and laplacian operators originally developed for fluids, with some adaptations, and a newly defined rotation operator. As a result, the dynamic interaction between two particles can be related to the behavior of normal and tangential springs between the particles, and the rotation of the particles is taken into account. The qualitative and quantitative validations of the method are carried out herein considering dynamic systems present in numerous engineering problems, such as mass-spring systems, forced or not, and vibrations. Simulation of 2D models were analyzed and compared to analytical models, which showed consistent results.