Axial Vibration Of Bar Using Material Point Method (MPM)

Abstract

This paper evaluates the performance of material point model for the validation of vibration of the one- dimensional elastic bar. Validation is carried out against the exact solution for different cases.In modern engineering applications, material point method (MPM) has emerged as a promising alternative to FEM for simulating large deformations between different material phases. For academia and industry people, FEM is used in all disciplines, but its shortcomings make it less suitable for specific application in structural engineering. An educational tool in MATLAB is needed to promote educational and integrated research activities. MPM has been utilized to solve complex problems in the literature, but due to lack of validation, many are still giving unsatisfactory results. Theory and algorithm of MPM are documented. To validate the educational tool one-dimensional problems are solved using linear elastic model. The approximate results were found using material point method are compared and verified against exact solutions. The approximate solutions are determined from one- dimensional MPM code. Single material point vibration of 1- dimensional rectangular, circular steel and aluminum bar, composite bar, cross- ply laminate, symmetric and antisymmetric laminate is presented and verified against the exact solution. Kinetic energy and strain energy is calculated to verify whether energy is conserved or not. Velocity vs Time and displacement vs. time graph is plotted. Dominating frequency can be calculated from velocity time history response.