Solving equations of 3D elasticity for orthotropic bodies

Abstract

Abstract A mathematical model of the three-dimensional orthotropic body was used. A technique has been developed for integrating equilibrium equations in displacements that describe the stress state of orthotropic materials. We find the solution of equilibrium equations in displacements for orthotropic bodies. The expression of displacements, strains and stresses is obtained through the introduced displacement function, which satisfies the sixth-order equation for partial derivatives. We develop the algorithm of the analytical and numerical solutions of boundary value problem for orthotropic rectangular prism. Solution of boundary value problems is reduced to minimize a generalized quadratic form.