Methods for the determination of static and dynamic stresses in bodies with subsurface cracks

We study the analytic and numerical methods for the solution of problems of the theory of cracks located near the surfaces of three-dimensional and thin-walled bodies under thermal and force static and dynamic loads. We describe the influence of the surfaces of the body or the interfaces between its materials on the static and dynamic stress intensity factors in the vicinity of the defects.     

Application of an analog of the δc-model to the analysis of strength of elastoplastic cracked shellsto the analysis of strength of elastoplastic cracked shells

We propose a method for the investigation of the limiting equilibrium of elastoplastic shells with systems of interacting cracks. It can be described as follows: By using an analog of the δ_c-model, the elastoplastic problem is reduced to an elastic problem of the limiting equilibrium of a shell with cracks of unknown length whose lips are subjected to the action of unknown forces and moments satisfying the conditions of plasticity for thin shells. By using equations of the general moment theory of shells and the theory of generalized functions, we reduce the problem to the solution of a system of singular integral equations with unknown limits of integration and singular right-hand sides. We construct an algorithm for the numerical solution of systems of this sort supplemented by the conditions of boundedness of stresses and conditions of plasticity. We investigate crack tip opening displacements in a closed cylindrical shell with a regular system of longitudinal cracks or two transverse cracks. For a cylindrical shell with a single crack, we present an approximate relation for the determination of the critical load or crack length. Pidstryhach Institute of Applied Problems of Mechanics and Mathematics, Ukrainian Academy of Sciences, L'viv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 32, No. 3, pp. 5–15, May–June, 1996.     

Application of the δc-Model to the Strength Analysis of Orthotropic Cylindrical Shells with Cracks

We propose a method for the investigation of the limiting equilibrium of an elastoplastic orthotropic cylindrical shell with cracks. The idea of this method is to reduce the elastoplastic problem, by using an analog of the _c -model, to the problem of elastic equilibrium of an orthotropic shell with cracks of unknown length whose lips are subjected to the action of unknown forces and moments satisfying the conditions of plasticity of thin shells. The equations of the Timoshenko-type theory of shells and the methods of generalized functions are used to reduce the elastic problem to the system of singular integral equations with unknown limits of integration and discontinuous right-hand parts. We construct a numerical solution of this system and study the dependence of the crack-tip opening displacement and the sizes of the plastic zones on the geometric and mechanical parameters of the orthotropic and transversely isotropic shell.     

Limiting equilibrium of a welded joint of gas main

We study the dependence of the crack-tip opening displacement for a surface crack in a welded joint of gas main on the geometric and physicomechanical parameters of pipe. It is assumed that the strength characteristics of the material in the zone of thermal influence and the base material are different. We propose a simplified formula for the evaluation of the opening displacements of surface cracks. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 36, No. 2, pp. 113–117, March-April. 2000.     

Thermoelastic vibrations of inhomogeneous anisotropic cylindrical shells

For inhomogeneous anisotropic circular cylindrical shells, we deduce a coupled system of differential equations of thermoelasticity with regard for the anisotropy of physicomechanical properties of materials in the transverse direction. On the basis of these equations, we solve the dynamic problem of thermoelasticity for axisymmetric shells of finite length and study their natural thermoelastic vibrations. We analyze the cases of cross-and angle-ply laminated shells. The results of evaluation of the eigenfrequencies and decrement of damping for graphite-epoxy composites are presented in the form of plots. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 44, No. 2, pp. 33–40, March–April, 2008.     

Limiting equilibrium of a spherical shell nonuniform across the thickness and containing a surface crack

The problem of limiting equilibrium of an elastoplastic spherical shell nonuniform across the thickness and containing a surface crack is reduced to a system of singular integral equations. The algorithm of numerical solution of this system takes into account the conditions of plasticity of thin shells and the conditions of boundedness of stresses in the vicinity of the crack. The influence of internal pressure and the mechanical parameters of functionally inhomogeneous material on the opening displacement of the surface crack and the length of plastic strips on its continuation is investigated. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 43, No. 3, pp. 5–11, May–June, 2007.