Khapko B. Stressed-strained state of local heated plates and shallow shells with breaks

Basic system of differential equations of heat conductivity and thermoelasticity for shallow shells with median surface breaks that are under discontinuous heat loading is obtained in the thesis. The method to solve such problems is developed. It is based on the finite integral transforms method and generalized functions theory. The thermoelasticity of circular and rectangular plates, freely beared around their perimeter, and of spherical and finite cylindrical shells is investigated for different heat transfer coefficients. Analytical solutions to boundary problems of heat conductivity and thermoelasticity for finite cylindrical shells with breaks, spherical and prismatic shells assembled from plane elements were obtained in the case of breaks located along coordinate lines. Numerical analysis of both stress resultant and stress couple distributions was performed in the vicinities of the shell breaks. It was discovered that the break substantially redistributes stresses in the shell causing high stress concentration along the breaks.