TORSION OF AN ANISOTROPIC CYLINDER WITH LONGITUDINAL CAVITIES AND PLANAR CRACKS

The elasticity theory problem of torsion of a cylinder with arbitrary cavities and planar cracks is solved using the complex potential of the torsion theory of anisotropic body. That said, the original problem is reduced to a redefined system of linear algebraic equations by means of conformal mappings, decompositions of holomorphic functions into Laurent series and Faber polynomials and satisfaction of boundary conditions by the generalized least squares method. This redefined system is solved by the singular value decomposition method. Numerical results are described for a circular cylinder with a circular cavity or a planar crack, including those extending to the outer edge of the cylinder, a circular cylinder with a central circular cavity and a crack between the contours, including those passing into a cut. The regularities of influence of physical and mechanical properties of the cylinder material and geometrical characteristics of holes and cracks on the stress values, their distribution and concentration were investigated. Keywords: torsion of a cylinder; cavities and planar cracks; complex potentials; generalized least squares method; stress intensity factors.