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Published in:
Introduction to Structural Modeling Read chapter Read first chapter

2020 | OriginalPaper | Chapter

7. Shear Deformable Plates

Author : Andreas Öchsner

Published in: Partial Differential Equations of Classical Structural Members

Publisher: Springer International Publishing

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Abstract

This chapter covers the continuum mechanical description of thick plate members. Thick plates are plates where the contribution of the shear force on the deformations is considered. Based on the three basic equations of continuum mechanics, i.e., the kinematics relationship, the constitutive law, and the equilibrium equation, the partial differential equations, which describes the physical problem, is derived.

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previous chapter Classical Plates
next chapter Three-Dimensional Solids
Footnotes
1
Strictly speaking, there is a small difference between the plate theory according to Reissner [4] and Mindlin [2] and only for zero Poisson’s ratio both derivations are the same.
 
2
This plate elasticity matrix should not be confused with the compliance matrix which is represented by the same symbol.
 
Literature
1.
Blaauwendraad J (2010) Plates and FEM: surprises and pitfalls. Springer, DordrechtCrossRef
2.
Mindlin RD (1951) Influence of rotary inertia and shear on flexural motions isotropic, elastic plates. J Appl Mech-T ASME 18:1031–1036
3.
Reddy JN (2006) An introduction to the finite element method. McGraw Hill, Singapore
4.
Reissner E (1945) The effect of transverse shear deformation on the bending of elastic plates. J Appl Mech-T ASME 12:A68–A77MathSciNet
5.
Ventsel E, Krauthammer T (2001) Thin plates and shells: theory, analysis, and applications. Marcel Dekker, New YorkCrossRef
6.
Wang CM, Reddy JN, Lee KH (2000) Shear deformable beams and plates: relationships with classical solution. Elsevier, OxfordMATH
Metadata
Title
Shear Deformable Plates
Author
Andreas Öchsner
Copyright Year
2020
Book
Partial Differential Equations of Classical Structural Members

Print ISBN: 978-3-030-35310-0

Electronic ISBN: 978-3-030-35311-7

Copyright Year: 2020

DOI
https://doi.org/10.1007/978-3-030-35311-7_7

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