Equilibrium of an elastic finite cylinder under axisymmetric discontinuous normal loadings

Meleshko, V. V.; Tokovyy, Yu. V.

doi:10.1007/s10665-011-9524-y

Cited by 30 publications

(27 citation statements)

References 21 publications

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“…The term crosswise superposition should not be mistaken with the principle of superposition, which is used in the study of linear BVPs and consists of the superposition of problems obtained by linear decomposition. The term crosswise was used by Meleshko and Tokovyy [18] to reflect the key feature of the method and make a distinction between the name of this method and the principle of superposition.…”

Section: Introductionmentioning

confidence: 99%

“…In his other works, Meleshko has applied the improved reduction method to the plane elasticity problem for a rectangular domain [28] and the equilibrium of a rectangular plate [29]. Meleshko and Tokovyy [18] employed the improved reduction method to study the equilibrium of a finite cylinder under axisymmetric discontinuous normal loading. The method was also used by Meleshko et al [30] to study an axisymmetric thermoelastic problem for a finite cylinder.…”

Section: Introductionmentioning

confidence: 99%

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Axisymmetric equilibrium of an isotropic elastic solid circular finite cylinder

Rahnama

Shokrieh

2018

Mathematics and Mechanics of Solids

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Axisymmetric equilibrium of an elastic solid circular finite cylinder is one of the oldest problems in the theory of linear elasticity. Crosswise superposition is a well-known method that is used to solve this boundary value problem (BVP); however, technical realization of its underlying ideas still seems to be vague and the solution obtained by this method suffers from some convergence issues. In this study, we follow two main objectives via analyzing a benchmark problem where an isotropic elastic solid circular cylinder of finite length is subjected to normal lateral loading. The first goal is to add more insight into the method of crosswise superposition by extending the ideas that are used for solving classical BVPs via the superposition principle. For this purpose, a new unified approach that naturally gives rise to the subtle concept of corner conditions (CCs) in the context of crosswise superposition method is introduced. Another goal is to demonstrate the influence of CCs on the convergence of the solution obtained by the method of crosswise superposition. In this avenue, the Love function approach is used to convert the Navier equations for an isotropic elastic material to a single axisymmetric biharmonic equation. Next, a general solution for the axisymmetric biharmonic equation consisting of separable and non-separable solutions is presented in cylindrical coordinates. These two classes of solutions are used to construct the Love function and associated elastic fields through the unified approach. Numerical results reveal that considering the CCs can significantly affect the convergence rate of the solution on the boundaries of the cylinder. Furthermore, it is observed that the solution does not converge to the boundary data at the rims without considering the CCs. Far enough from the boundaries of the cylinder, the solution does not seem to be much different with or without taking the CCs into account.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Axisymmetric equilibrium of an isotropic elastic solid circular finite cylinder

Rahnama

Shokrieh

2018

Mathematics and Mechanics of Solids

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“…Chau and Wei [27], Meleshko and Tokovyy [28], and Wu et al [29] have implemented such a method for solving practical engineering problems. The simplified models of these problems are all space axisymmetric bending deformations, and the axial stress boundary conditions of axial section is assumed to meet with some certain function distribution, and the shear stress is neglected.…”

Section: Introductionmentioning

confidence: 99%

Theoretical investigation on hub structure design of subsea connectors

Duan

Zhang

Soares³

et al. 2021

Thin-Walled Structures

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“…Then, a finite system is solved by neglecting higher-order terms from the system with infinite conditions [2]. This procedure is often called the Simple Reduction Algorithm (SRA) [3]. As described by Meleshko [2,4], the MCS was applied to the problem of the elastic equilibrium a two-dimensional rectangular prism with symmetric normal loads on opposite sides by Mathieu (1890), Filon (1903), Inglis (1921), Ôkubu (1940), Pickett (1944) and Ling et al (1963).…”

Section: Introductionmentioning

confidence: 99%

A modified Fourier series-based solution with improved rate of convergence for two-dimensional rectangular isotropic linear elastic solids

Barulich

Deutsch

Eisenberger

et al. 2021

Mathematics and Mechanics of Solids

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This paper presents a new displacement solution based on a Modified Fourier Series (MFS) for isotropic linear elastic solids under plane strain or plane stress states subject to continuous displacement and traction boundary conditions in a two-dimensional rectangular domain. In contrast with existing approaches that are restricted to Fourier series with a rate of convergence of second order O(m-2), the MFS allows increasing the rate of convergence of the solution. The governing Partial Differential Equations (PDEs) are satisfied exactly by two displacement solutions while the boundary conditions are approximated after solving a finite system of algebraic equations. Numerical results for a solution with an MFS with rate of convergence O(m-3) are compared with results from existing numerical and analytical methods, showing the enhanced behavior of the present solution.

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Equilibrium of an elastic finite cylinder under axisymmetric discontinuous normal loadings

Cited by 30 publications

References 21 publications

Axisymmetric equilibrium of an isotropic elastic solid circular finite cylinder

Axisymmetric equilibrium of an isotropic elastic solid circular finite cylinder

Theoretical investigation on hub structure design of subsea connectors

A modified Fourier series-based solution with improved rate of convergence for two-dimensional rectangular isotropic linear elastic solids

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