A problem of elasticity theory for a space containing an inclusion of any stiffness in shear
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A PROBLEM OF ELASTICITY THEORY FOR A SPACE CONTAINING AN INCLUSION OF ANY STIFFNESS IN SHEAR M. M. Stadnyk
UDC 539.3
We deduce the formulas for the evaluation of stresses in thin inclusions and their concentration in the matrix near its contour convenient for engineering applications. The influence of stiffness of the inclusion and its geometric parameters on the levels of stresses in the matrix and in the inclusion is investigated. Partial cases of the problem for an ellipsoidal cavity and an absolutely rigid ellipsoidal inclusion are analyzed. The formulas for the evaluation of the corresponding stress intensity factors are obtained. Keywords: singular integrodifferential equations, inclusion, jumps of stresses and displacements.
The solutions of the problems of elasticity theory for bodies with inclusions are necessary for the investigation of the strength of materials with various defects. The problem of elasticity theory for a body with compliant thin inclusion under the conditions of shear was studied in [1]. In what follows, we study the case of an elastic inclusion of any stiffness placed in a body under the conditions of pure shear.
Statement and Solution of the Problem Consider a three-dimensional body containing an elastic ( 0 G1 /G < , G1 and G are the shear moduli of the inclusion and the matrix, respectively) thin inclusion bounded by a smooth surface z = ±h(x, y) ( max h
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