Photoelastic and numerical stress analysis of a 2D contact problem and 3D numerical solution for the case of a rigid body on a deformable one

Abstract

A finite element analysis and a photoelastic stress analysis are conducted in order to determine the stress field developed in the pin on plan contact problem. Although this problem is relatively easy to study experimentally, the purpose here is to show the possibilities of the finite element method; after validation of the numerical procedure, problems with complicated geometry and boundary conditions can then be solved numerically. Isochromatic and isoclinic fringes, similar to the ones obtained experimentally by the photoelastic method, are obtained numerically over the whole model. The details of the finite element solution are fully given in the paper. Many studies have been achieved in order to separate the principal stresses and obtain their orientations (integration of the equilibrium equations...) in order to compare them with the simulated results. However, this requires a high precision of measurement. Here, a whole field comparison of the experimental and numerical photoelastic fringes and a local analysis using the principal stresses difference, allowed us to validate the numerical approach. Relatively good agreements were obtained. A numerical solution for a three dimensional contact problem is also developed for a rigid parallelepiped on a deformable cylinder. The mesh was refined in the neighborhood of the contact zone in order to achieve better approximation of stresses. The loading is given by the limit conditions that are simply the imposed displacement. The calculated photoelastic fringes are obtained for various sections inside the model. These simulated fringes can be compared to the experimental ones which can be obtained by slicing the model and analyzing it in a plan polariscope. The program developed allows us to calculate stresses on any given section inside the model, particularly in the neighborhood of the contact zone. © 2011 WIT Press.