Analytical Buckling Loads for Rectangular Orthotropic and Symmetrically Laminated Plates

Tenenbaum, Joseph; Deutsch, Aharon; Eisenberger, Moshe

doi:10.2514/1.j058536

Cited by 6 publications

(1 citation statement)

References 13 publications

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“…Similar methods using exact solutions for the governing PDE and Fourier series to approximate the boundary conditions has been recently developed to study out-of-plane free vibrations [11–16], in-plane free vibrations [17], and buckling [18–22] of rectangular plates or assemblies of them. In these papers, the coefficients for the Fourier series have been obtained by integrating over a domain spanning the dimensions of the plate.…”

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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