Study of stress concentrations in a shell under local forces by the transition matrix method
Authors: Vinogradov Yu.I. | Published: 07.05.2014 |
Published in issue: #5(650)/2014 | |
Category: Calculation and Design of Machinery | |
Keywords: shell, stress concentration, boundary value problem, initial problem |
Spacecraft structures like shells connected by frames are inevitably loaded by local forces that may cause dangerous stress concentrations. Universal numerical techniques like finite difference and finite element methods provide results with unpredictable errors in these areas. In this paper, an analytical method for studying stress concentrations in shells is first proposed. Differential equations of the mechanics of shells are solved analytically in terms of Cauchy-Krylov special functions. The property of these functions to satisfy arbitrary initial conditions is used to construct an algorithm that reduces a boundary value problem to an initial problem. Another property of Cauchy-Krylov functions, that is, to represent a solution multiplicatively also forms the basis of this algorithm. By way of example, the critical parameters of a cylindrical shell, which determine the upper bound for stable calculations without orthogonalization and normalization of the solution, are computed. The results of studies will be useful when designing spacecrafts to decrease their weight.
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