The Torsion of Elastic Medium with Internal Cylindrical Crack

Abstract

A class of mixed boundary problems on equilibrium of three-dimensional bodies weakened by nonflat cracks on parts of the second-degree surfaces is examined. The general approach to these problems is developed. The solution of Lame vector equation of equilibrium is presented in the form of eigenfunction expansions. The unknown coefficients are found from boundary conditions transferred to a crack surface according to the superposition principle. Thev principle of displacements and stresses fields continuity is used out of the crack. The result is a coupled system of dual series equations or integral equations. Data obtained are applicable to the study of material damage.