Green's matrix of the plane problem of elasticity theory for an orthotropic strip

Abstract

Green's matrix for a homogeneous and orthotropic half-strip clamped between two absolutely rigid half-planes is constructed. The boundary conditions on all sides correspond to frictionless contact. The equations of equilibrium in displacements formulated for the case with mass forces are solved by Fourier transform methods. The final results are represented by relatively simple formulas. The Green's matrix elements, which in physical terms represent the displacements of the half-strip points under the action of a concentrated force, are expressed in terms of elementary functions. Numerical results are given for the case with a transverse concentrated force. Hence it is shown that the algorithm for constructing Green's functions and matrices for a mixed boundary-value problem of elasticity theory with an isotropic strip /1/ can be extended to some plane problems of elasticity theory for orthotropic materials.