Yuzvyak M. Development of the direct integration method towards the elasticity and thermoelasticity problems for solids with the plane and cylindrical surfaces

This work addresses the development of the direct integration method with concern to the two- and three-dimensional elasticity and thermoelasticity problems for finite domains with corner points bounded with plane and cylindrical surfaces: i.e., the plane problems for rectangular domains, axisymmetric problems for solid and hollow cylinders of finite length, and spatial problems for rectangular parallelepipeds. Making use of the equilibrium equations allows for deriving integral-form expressions for the stress-tensor components through the key functions which have been introduced by a special procedure and named herein to be the Vihak functions (after the inventor and developer of the direct integration method Prof. Vasyl M. Vihak). These expressions were efficiently used for reducing the original sets of the local boundary conditions imposed on all the edges of the considered domains to the equivalent sets of the integral conditions for the Vihak functions. In such manner, the original problems are managed to be reduced to the auxiliary boundary value problems for the governing integro-differential equations with the accompanying integral conditions for the Vihak functions. Special semi-analytical algorithms are suggested for constructing the key function and, consequently, the stress-tensor components in the form of explicit analytical dependences of on the applied force and thermal loadings. The derived solution form is beneficial for solving the inverse and identification problems as well as the optimization ones for the further applications in both academia and industry.