A fundamental solution of equations of thermoelasticity for shallow orthotropic shells (Q2754707)

A fundamental solution for shells of arbitrary Gaussian curvature in the presence of heat exchange with the surrounding medium is constructed. Thermoelastic deformation of shallow orthotropic shells is described by a system of partial differential equations of the eighth order with constant coefficients. Application to this system of integral Fourier transform gives explicit expressions for transformed displacements and integral characteristics of temperature. Inversion of the Fourier transform is constructed in polar coordinates. Asymptotic analysis of the obtained solution is performed and comparison with the case of orthotropic plates is done. A numerical example is considered, and plots of displacements are presented.