Plane mixed thermoelasticity problem for a semi-strip (Q2831366)

The authors study the stress state of a semi-strip. Smooth contact conditions are given on one lateral side of the semi-strip while coupling conditions are given on the other side, and the external normal loading and temperature are applied to its end. By means of the method of integral transforms, the initial problem is reduced to a one-dimensional vector boundary value problem. The apparatus of matrix differential calculus and Green's matrix function are applied to reduce the obtained problem to a singular integral equation with respect to the derivative of displacements at the semi-strip end. The equation is solved by the method of orthogonal polynomials. Stress and displacement fields in the semi-strip are analyzed numerically. Zones of tensile stresses on the lateral side of the semi-strip are determined and conditions of their occurrence are established.