The application of a complex 3-dimensional elasticity solution representation for the analysis of a thick rectangular plate
type: Item
instance of: scholarly article
title: The application of a complex 3-dimensional elasticity solution representation for the analysis of a thick rectangular plate
zbMATH Open document ID: 0668.73046
DOI: 10.1007/BF01174629
published in: Acta Mechanica
publication date: 1988-01-01T00:00:00Z
review text: Recently a complex representation of the stresses and displacements for the three-dimensional field equations of elasticity was developed such that the complex formulas of Muskhelishvili for plane strain are included as special cases [the author, e.g.: J. Elasticity 18, 191-225 (1987; Zbl 0619.73004)]. The solution is given in terms of six arbitrary complex valued functions. The complex variables in the formulation contain parameters, which can be considered as discrete parameter values or parameter functions. In this paper the use of the complex formulation for the case of discrete parameter values is illustrated within the example of a thick rectangular plate, where the boundary conditions on the side faces are chosen to be the vanishing deflection, normal stress and tangential displacements. Assuming these three-dimensional boundary conditions for the evaluation of the according conditions of a two- dimensional Reissner-model gives a set of boundary conditions which was treated by \textit{V. L. Salerno} and \textit{M. A. Goldberg} [J. Appl. Mech. 27, 54-58 (1960; Zbl 0097.186)]. The Reissner-results are used for the sake of comparison with the three-dimensional solution.
Mathematics Subject Classification ID: 74K20
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 74B10
zbMATH DE Number: 4094956
zbMATH Keywords: discrete parameter values
zbMATH Keywords: vanishing deflection
zbMATH Keywords: normal stress
zbMATH Keywords: tangential displacements
zbMATH Keywords: three-dimensional boundary conditions
zbMATH Keywords: two- dimensional Reissner-model
author: Reinhard Piltner
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4094956