Some Investigations of Condensation Methods for Elasto-impact Contact Stress Analysis by Finite Element Method

Abstract

To calculate efficiently elasto-impact contact stresses and their distributions by the finite element method (FEM), the static, dynamic and mixed condensation methods are investigated. These methods are introduced in the formulation of the FEM and applied to a two-dimensional analysis of longitudinal impact of two prismatic rods with a uniform section and equal cross section. The following results are mainly obtained in this paper : (1) The contact-impact time and contact stresses by the FEM for two elasto-impact bodies with the static condensation method agree well with the normal results by the FEM without the condensation methods. (2) The contact-impact time by the FEM with the dynamic condensation method becomes shorter than that by the FEM without the condensation methods, because of the decrease in the element values of the mass matrix and the increase in those of the stiffness matrix. From the results described above, the static condensation method is found the best one of them. Moreover, by selecting any condensed points among the nodes apart from the contact surface between two rods, the accurate elasto- impact contact stresses can be calculated efficiently by the FEM with the static condensation method.