Separation of variables in integro-differential equations of axisymmetric problems of thermoelasticity for cylindrical domains (Q2754693)

A technique of separation of variables is proposed for solving equations of elasticity and thermoelasticity in stresses for hollow and solid cylinders of finite length. For representation of solutions as a superposition of expansions in radial and axial coordinates, a complete system of eigenfunctions and associated eigenfunctions (in Saint-Venant sense) is constructed. Instead of classic stress equilibrium equations, a formulation of elastostatics problems using different equations of integro-differential type is suggested. In deriving the solution, the integral Laplace transform is used.