Effect of out-of-plane dimension on simplified geometric models in stress analysis

Abstract

Without exception, every physical object is three-dimensional. However, in many stress analysis situations the analyst is justified in using simplified two-dimensional idealizations of plane stress and plane strain, reducing the complexity of the problem. By obviating the need to mesh in the third dimension, this advantage also extends to numerical studies, helping economize significantly on time and computational power requirements. In plane stress idealization the out-of-plane stresses are zero, whereas in plane strain the out-of-plane strains are zero. These idealizations have variously been linked with the out-of-plane dimension, as well as the end conditions of the object under consideration. However, the exact correlation of the out-of-plane dimension with these idealizations remains ambiguous. Unlike the case of plane stress, there is much disagreement found in literature regarding the necessary conditions for the realization of plane strain, which needs to be addressed. In this article, finite element analysis was employed to study the effect of various out-of-plane dimensions and end constraints. The results show that there is no correlation between the out-of-plane dimension and plane strain, which depends only on the end constraints. However, the out-of-plane dimension does result in the transition from plane stress to generalized plane strain.