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A Unified Integral Equation Formulation for Linear and Geometrically Nonlinear Analysis of Thick Plates: Derivation of Equations

In: Integral Methods in Science and Engineering

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  • R. J. Marczak

    (Federal University of Rio Grande do Sul)

Abstract

This chapter presents a compilation of the boundary integral equations for linear and geometrically nonlinear bending analysis of moderately thick plates. The plate models used account for shear influence by using the first-order plate theories of Mindlin and Reissner. An unified integral formulation for the plate models employed is derived for the corresponding Navier’s operator, and higher-order terms of the Green strain tensor are included, so that the membrane-bending coupling is included in order to describe completely large displacement plate bending problems. The analytic derivation of the convective terms for geometrically nonlinear analysis is presented. The existence conditions for the non-null convective terms are clearly stated. An integral equation formulation for linear bending and elastic stability problems can be obtained by linearization of these equations.

Suggested Citation

  • R. J. Marczak, 2022. "A Unified Integral Equation Formulation for Linear and Geometrically Nonlinear Analysis of Thick Plates: Derivation of Equations," Springer Books, in: Christian Constanda & Bardo E.J. Bodmann & Paul J. Harris (ed.), Integral Methods in Science and Engineering, chapter 0, pages 179-195, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-07171-3_13
    DOI: 10.1007/978-3-031-07171-3_13
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