Correct Solutions of Plane Elastic Problems for a Half-Plane

Analytical solutions to the 2D elasticity and thermoelasticity problems for inhomogeneous planes and half-planes

“…In [37], Vihak showed that the force loadings and stresses would meet certain necessary conditions for existence of continuous and integrable solutions to the elasticity problem for a half-plane. Following this strategy, we assume the stresses satisfying the integral equilibrium conditions and integral conditions for the resultant force and moment of each stress.…”

“…In its turn, the force loadings are assumed to meet the necessary conditions of equilibrium. These conditions, obtained by direct integration [37] of Eq. (1), are presented in Appendix A for the plane D 1 and in Appendix B for the half-plane D 2 .…”

“…In [36,37], Vihak proposed a method for solution of plane elasticity and thermoelasticity problems for isotropic, homogeneous infinite and semi-infinite regions (strips, half-planes, and planes). This method is based upon the direct integration technique which uses essentially the relations between the stress-tensor components as well as the integral equilibrium conditions.…”

Steady-State Heat Transfer and Thermo-Elastic Analysis of Inhomogeneous Semi-Infinite Solids

“…Therefore, when the stress-tensor components are found, then the displacement-vector components are also found automatically. Such relations have been derived for the case of one-dimensional problem for a thermoelastic hollow cylinder (Vigak, 1999a) and plane problems for elastic and thermoelastic semi-plane Vigak, 2004;Rychahivskyy & Tokovyy, 2008). Since application of this method rests upon the direct integration of the equilibrium equations, the proposed solution scheme offers ample opportunities for efficient analysis of inhomogeneous solids.…”

On the solution of plane boundary-value problems of elasticity in a rectangle

“…As an example, we will solve a fairly complicated contact problem for a short prismatic bar of rectangular cross section subject to lateral bending. Note that our method can be used to solve plane problems that are still of interest [9][10][11][12].…”