Method of direct integration of equations of plane problems of elasticity and thermoelasticity for infinite domains (Q2753509)

A method of direct integration of differential equations of plane problems of elasticity and thermoelasticity in stresses for infinite domains, plane, half-plane and strip, is proposed. Significant attention is paid to integration of equilibrium equations. Here, relationships between components of the stress tensor and integral equilibrium conditions for individual components are obtained. Limiting relations for stress components at infinity are analyzed. Key integro-differential continuity equations in stresses are derived. For infinite domain these equations are reduced to equivalent differential equations. It is demonstrated that such reduction for a rectangular domain with corner points is impossible. General solutions of equilibrium equations are found by Fourier transform.