Displacement Analysis on Plane Stress Problems

Abstract

Abstract The vertical z direction displacement component and its effect are not considered in the displacement analysis of the plane stress problems currently, and it may cause misunderstanding of the problems. The plane stress problems are three-dimensional problems actually because the strains are three-dimensional. The relationships among stress, strain and displacement of plane stress problems were analyzed in three-dimensional space based on the basic theory of elasticity in this paper. According to the characteristic constraints of the plane stress problems, the displacement expressions in three directions were derived. The displacement in the plane consists of the integral of the plane strain in the x-y plane and the independent function of the z-direction. Under the condition that the plane stress problem is strictly satisfied, the first stress invariant should be linearly distributed in the plane, and the displacement in the z direction is the product of the x, y related linear function and z.