Calculation of stresses in a spherical shell with internal surface defects
Keywords:finite element method, pressure vessels, stress state, spherical shell, surface defect
Pressure vessels, in particular cylindrical and spherical thin-walled vessels, are widely used in the industry. The aggressive impact of the environment during operation, as well as workloads, lead to the gradual accumulation of defects in structures. Since local defects act as stress concentrators, to ensure the strength and reliability of a structure, it is necessary to take into account the stress concentration near the defects. The paper considers a thin-walled sphere under pressure with the damages on its inner surface. The author modeled the defects as spherical notches immersed to the depth equal to half of their radius. Defects are evenly spaced along one of the circumferences of a large sphere. To estimate the stress state, the author built 3-D models of a spherical vessel with defects. The study considers the different number of defects and various sizes of defects; each parameter value corresponds to its geometry model. With the ANSYS Workbench package of finite element analysis, for each model, the author carried out the application of loads (pressure acts on the inner surface of a vessel), model decomposition into finite elements, and builds the field of maximum normal stresses distribution in a body. Calculations are made in the framework of the linear theory of elasticity. The author carried out a numerical experiment to study the influence of the number of surface defects on the stress state within their neighborhood. The paper studies the dependence of calculated stresses in the body on the depth of defects. The study showed that with an increase in the number of defects, as well as with an increase in their depth, the maximum normal stress increases.
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