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Efficient approximate solutions for postbuckling of axially compressed orthotropic plates with rotationally restrained and free longitudinal edges

Beerhorst, M. and Seibel, M. and Mittelstedt, C. (2018):
Efficient approximate solutions for postbuckling of axially compressed orthotropic plates with rotationally restrained and free longitudinal edges.
88, In: Archive of Applied Mechanics, (3), Springer, pp. 461-476, ISSN 0939-1533 (Print) 1432-0681 (Online), DOI: 10.1007/s00419-017-1319-9,
[Online-Edition: https://doi.org/10.1007/s00419-017-1319-9],
[Article]

Abstract

This paper presents approximate solutions for the postbuckling behavior of a plate consisting of laminated composites with symmetrical, balanced lay-up loaded in longitudinal compression. The transversal edges of the plate are simply supported, one longitudinal edge is free and the opposite one is rotationally restrained. Key to obtain an explicit and thus highly computational efficient solution is the use of a shape function with only few variables. First, the shape function is inserted into the compatibility condition of in-plane strains to derive a closed-form solution of Airy's stress function. Then, the equilibrium condition is approximated with the Galerkin procedure yielding a load--deflection relationship. Subsequently, other state variables such as in-plane displacements and stresses can be obtained. Overall, results for displacements and strains show very good agreement with detailed nonlinear finite element analyses.

Item Type: Article
Erschienen: 2018
Creators: Beerhorst, M. and Seibel, M. and Mittelstedt, C.
Title: Efficient approximate solutions for postbuckling of axially compressed orthotropic plates with rotationally restrained and free longitudinal edges
Language: English
Abstract:

This paper presents approximate solutions for the postbuckling behavior of a plate consisting of laminated composites with symmetrical, balanced lay-up loaded in longitudinal compression. The transversal edges of the plate are simply supported, one longitudinal edge is free and the opposite one is rotationally restrained. Key to obtain an explicit and thus highly computational efficient solution is the use of a shape function with only few variables. First, the shape function is inserted into the compatibility condition of in-plane strains to derive a closed-form solution of Airy's stress function. Then, the equilibrium condition is approximated with the Galerkin procedure yielding a load--deflection relationship. Subsequently, other state variables such as in-plane displacements and stresses can be obtained. Overall, results for displacements and strains show very good agreement with detailed nonlinear finite element analyses.

Journal or Publication Title: Archive of Applied Mechanics
Volume: 88
Number: 3
Publisher: Springer
Divisions: 16 Department of Mechanical Engineering
16 Department of Mechanical Engineering > Institute for Lightweight Construction and Design (KluB)
Date Deposited: 08 Apr 2019 09:36
DOI: 10.1007/s00419-017-1319-9
Official URL: https://doi.org/10.1007/s00419-017-1319-9
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