A direct method of integrating the equations of two-dimensional problems of elasticity and thermoelasticity for orthotropic materials

For a plane, a half-plane, and a strip, we propose a direct method of integrating the differential equations of equilibrium and continuity with respect to the stresses in the case of two-dimensional problems of elasticity and thermoelasticity for orthotropic materials. We find the relations between the components of the stress tensor, the key integro-differential equation and the equation of continuity equivalent to it for determining one of the components of the normal stresses. Translated fromMatematichni Metodi i Fiziko-Mekhanichni Polya, Vol. 40, No. 1, pp. 24–29.