A method of analyzing the near-edge stress state in mixed problems of the deformation of an isotropic cylindrical body is proposed. The method is based on the expansion of the solution of three-dimensional problems of elasticity into a series of Lurie-Vorovich homogeneous basis functions. An asymptotic analysis is performed to find the principal part of the solution of the infinite systems of linear algebraic systems to which the problems are reduced. The type of the stress singularity at the edge of the cylinder is the same as in the mixed problems for a quarter plane. Kummer's convergence acceleration method is used. The obtained results are validated by testing the boundary conditions and by comparing with results obtained by other authors
The mixed problem of bending of a transtropic thick plate and a short cylinder is solved using the Lur'e-Vorovich homogeneous solutions. The most typical results from numerical experiments for a wide range of physical and geometrical parameters are presented Keywords: cylindrical thick transtropic plate, short cylinder, pure bending, Lur'e-Vorovich homogeneous solutions, numerical experiments Solving mixed problems of elasticity for finite cylindrical bodies is a challenge because of the integrable singularities of the stress components at the corner points [1]. The elastic-equilibrium problem for an isotropic finite-length cylinder was solved in [2, 3] by the method of homogeneous solutions and in [4,5] by the superposition method. As to a transtropic body, only an approximate formulation with weakened boundary conditions on the lateral surface and restrained ends was used [6]. Problems for noncircular hollow cylinders were analyzed in [12,13,15].We will discuss results from stress-strain analysis of a short transtropic cylindrical body based on the use of Lur'e-Vorovich homogeneous solutions [7]. These solutions allow obtaining a solution close to the exact one with the help of modern computers. We will also analyze the influence of the type of material and the relative thickness of the elastic body on the stress-strain state (SSS) and estimate the accuracy and applicability limits of the theory of thin plates. The accuracy of the obtained solution will also be determined.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.