Solutions of one-dimensional problems of elasticity and thermoelasticity for cylindrical piecewise-homogeneous bodies

We propose a method of direct integration of the equilibrium and continuity equations in stresses for one-dimensional problems of elasticity and thermoelasticity for piecewise-homogeneous cylinders and disks with an arbitrary number of layers. The solutions are reduced to finding the constants of systems of algebraic equations with nearly triangular matrices of coefficients, making it possible to find the unknown constants in a closed form that is functionally dependent on the bulk forces and temperature field.Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 4, 1997, pp. 139–148.     

Correct Solutions of Plane Elastic Problems for a Half-Plane

Continuous and integrable solutions and one-to-one relationships between boundary forces and displacements are found through the direct integration of the differential equations of the plane elastic problem for a half-plane with boundary conditions for either forces or displacements or with mixed boundary conditions. The necessary equilibrium conditions for forces and the compatibility conditions for displacements that ensure the correctness of the solutions are formulated     

Optimization of zonal thermal treatment of cylindrical component parts by moving concentrated heat sources

We propose a numerical-analytic method of determining the optimal heating regimes and stress-strain state of steplike cylindrical shells to guarantee the maximally admissible length of the annealing zones in the cirumferential direction and the number of these zones in the absence of residual strains and stresses.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 33, 1991, pp. 65–69.     

On the unsolvability of the boundary inverse problem of heat conduction

It is shown that the boundary inverse nonstationary problem of heat conduction with given heat flux and temperature on one of the boundary surfaces is essentially ill-posed, since it has no solution in the class of continuous functions.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 35, 1992, pp. 114–118.     

Method for direct integration of the equations of an axisymmetric problem on thermoelasticity in stresses for unbounded regions

We consider a method for direct integration of equilibrium and consistency equations for axisymmetric quasistatic thermoelasticity problems in regions with unbounded radial coordinates. Relations between stress tensor components are obtained. We derive a system of two integro-differential equations in stresses and an equivalent system of differential equations. We present solutions for the thermoelasticity problem and integral equilibrium conditions for the first stress invariant for a space, half-space, and unbounded layer. Ya. S. Podstrigach Institute for Applied Problems in Mechanics and Mathematics, National Academy of Sciences of Ukraine, L'vov, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 3, pp. 49–56, March, 1999.     

The Method of Direct Integration of the Equations of Three-Dimensional Elastic and Thermoelastic Problems for Space and a Halfspace

The method of direct integration of differential equilibrium and compatibility equations in stresses is proposed for three-dimensional quasistatic elastic and thermoelastic problems for space and a halfspace. A closed system of equations is formulated to determine six components of the stress tensor. These problems are solved with the help of the integral Fourier transformation     

Optimal control of two-dimensional nonaxisymmetric temperature field in a hollow cylinder with thermoelastic stress restrictions

Institute of Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine, Lvov. Translated from Prikladnaya Mekhanika, Vol. 31, No. 6, pp. 42–49, June, 1995.