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

2020 | OriginalPaper | Chapter

5. Plane Members

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 plane elasticity members. Based on the three basic equations of continuum mechanics, i.e., the kinematics relationship, the constitutive law and the equilibrium equation, the partial differential equation, which describes the physical problem, is derived.

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previous chapter Timoshenko Beams
next chapter Classical Plates
Footnotes
1
In the case of a shear force \(\sigma _{ij}\), the first index i indicates that the stress acts on a plane normal to the i-axis and the second index j denotes the direction in which the stress acts.
 
2
If gravity is acting, the body force f results as the product of density times standard gravity: \(f=\tfrac{F}{V}=\tfrac{mg}{V}=\tfrac{m}{V}g=\varrho g\). The units can be checked by consideration of \(1\,\text {N}=1\tfrac{\text {m}\text {kg}}{\text {s}^2}\).
 
3
A differentiation is there indicated by the use of a comma: The first index refers to the component and the comma indicates the partial derivative with respect to the second subscript corresponding to the relevant coordinate axis, [1].
 
Literature
1.
Chen WF, Han DJ (1988) Plasticity for structural engineers. Springer, New YorkCrossRef
2.
Eschenauer H, Olhoff N, Schnell W (1997) Applied structural mechanics: fundamentals of elasticity, load-bearing structures, structural optimization. Springer, BerlinCrossRef
3.
Öchsner A (2016) Continuum damage and fracture mechanics. Springer, Singapore
Metadata
Title
Plane Members
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_5

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