Analytical Approach to the Derivation of the Stress Field of a Cylindrical Shell with a Circular Hole Under Axial Tension

Abstract

AbstractA new analytical approach to the stress field problem of the cylindrical shell with a circular cutout under axial tension is proposed. Classical models because of an expansion into small parameter have narrow range of applicability and almost do not differ from Kirsch case for plate. The new approach opens up opportunities for the analytical study of the stress field. The idea is to decompose each basis function into a Fourier series by separating the variables, which allows us to obtain an infinite system of algebraic equations for finding coefficients. One of the important steps of the study is that the authors were able to prove which of the equations of the system is a linear combination of several others. Excluding it made it possible to create a reduced system for finding unknown coefficients. The proposed approach does not impose mathematical restrictions on the values of the main parameter that characterizes the cylindrical shell.KeywordsCylindrical shellCircular cutoutElasticity theory