Uniform Domain Equilibrium Equation with Finite Deformations

In corner areas of structures, high stress values and gradients occur, and lead to stress concentrations. Infinite stress and deformations are determined by a solution of the linear elasticity theory problem in the area with a wedge-shape boundary notch. Infinite solutions of the elasticity problem occur under impact of forced deformations, when a surge of the deformation value reaches beyond the area boundary. Relative values of stress concentrations for corner area zones make no more sense. At finite displacements, high deformation and stress values occur in the corner zones of the area. For a linear statement of the elasticity theory problem, at minor deflections, not only first-order, but also second-order derivatives of the displacements function are significant. To account for finite deformations of such corner zones of the area, correct formulations of elasticity problems are required. Study objective: influence determination of the infinitesimal order of the deformation on the appearance of equilibrium equations of an area with induced (temperature) deformations. This allows for the analysis of the influence of linear, shear deformations, and of the swing on the solution of the elasticity problem with induced deformations.