Torsion problem for elastic multilayered finite cylinder with circular crack  

作　　者：Y.PROTSEROV N.VAYSFELD 

机构地区：[1]Institute of Mathematics, Economics and Mechanics, Odessa Mechnikov University, Dvoryanskaya str. 2, Odessa 65082, Ukraine

出　　处：《Applied Mathematics and Mechanics(English Edition)》2017年第3期423-438,共16页应用数学和力学（英文版）

基　　金：Project supported by the Ukrainian Department of Science and Education(No.0115U003211)

摘　　要：An axisymmetric tangent stress is applied to a lateral surface of a multilayered elastic finite cylinder with a fixed bottom face. The problem is solved for an arbitrary number of layers. The layers are coaxial, and the conditions of an ideal mechanical contact are fulfilled between them. A circular crack is situated parallel to the cylinder’s faces in the internal layer with branches free from stress. The upper face of the cylinder is also free from stress. Concretization of the problem is done on examples of two-and three-layered cylinders. An analysis of cylinders’ stress state is conducted and the stress intensity factor is evaluated depending on the crack’s geometry, its location and ratio of the shear modulus. Advantages of the proposed method include reduction of the solution constants’ number regardless of the number of layers, and presentation of the mechanical characteristics in a form of uniformly convergent series.An axisymmetric tangent stress is applied to a lateral surface of a multilayered elastic finite cylinder with a fixed bottom face. The problem is solved for an arbitrary number of layers. The layers are coaxial, and the conditions of an ideal mechanical contact are fulfilled between them. A circular crack is situated parallel to the cylinder's faces in the internal layer with branches free from stress. The upper face of the cylinder is also free from stress. Concretization of the problem is done on examples of two-and three-layered cylinders. An analysis of cylinders' stress state is conducted and the stress intensity factor is evaluated depending on the crack's geometry, its location and ratio of the shear modulus. Advantages of the proposed method include reduction of the solution constants' number regardless of the number of layers, and presentation of the mechanical characteristics in a form of uniformly convergent series.

关 键 词：multilayered cylinder circular crack integral transformation singular integral equation 

分 类 号：O343.4[理学—固体力学]