The application of the direct integration method for finding the solutions of 2D elasticity and thermoelasticity problems for the radially inhomogeneous ring and for the strip inhomogeneous with respect to width is presented. The main feature of this approach is the integration of the equilibrium equations, which do not depend on material properties. This gives the possibility to express all the stresses in terms of a governing one, as well as to deduce the integral equilibrium conditions for all of the stress tensor components. In such way, the original problem can be reduced to finding the governing stress from compatibility equation. The governing equation is reduced to the Volterra type integral equation and it can be solved by simple iterations.
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