Thermoelasticity problem for half-space completely adhered to an infinite beam with a point of change of elastic constants (Q2753472)

An elastic half-plane \(-\infty<x<\infty\), \(y>0\) is adhered to an elastic beam. The beam has different Young moduli and Poisson ratios for \(x>0\) and \(x<0\). There is a heat source of intensity \(w_0\) at the point \((x_0, y_0)\) of the half-plane. Temperature at the half-plane boundary is equal to zero. Stresses in beam and contact stresses between the beam and the half-space are to be found. The system of integro-differential equations with respect to unknown normal force \(N_x\) and bending couple \(M_x\) is derived and by means of Fourier transform is reduced to the Riemann problem for two pairs of analytic functions. An exact solution of the problem is obtained.