Skip to main content
SpringerLink
Log in

Three-Dimensional Solids

  • Chapter
  • First Online:
Partial Differential Equations of Classical Structural Members

Part of the book series: SpringerBriefs in Applied Sciences and Technology ((BRIEFSCONTINU))

  • 608 Accesses

Abstract

This chapter covers the continuum mechanical description of solid or three-dimensional 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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 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. 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. 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, [2].

References

  1. Chen WF, Saleeb AF (1982) Constitutive equations for engineering materials. Volume 1: Elasticity and modelling. Wiley, New York

    MATH  Google Scholar 

  2. Chen WF, Han DJ (1988) Plasticity for structural engineers. Springer, New York

    Book  Google Scholar 

  3. Eschenauer H, Olhoff N, Schnell W (1997) Applied structural mechanics: Fundamentals of elasticity, load-bearing structures, structural optimization. Springer, Berlin

    Book  Google Scholar 

  4. Öchsner A (2014) Elasto-plasticity of frame structure elements: modeling and simulation of rods and beams. Springer, Berlin

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Mechanical Engineering, Esslingen University of Applied Sciences, Esslingen, Baden-Württemberg, Germany

    Andreas Öchsner

Authors
  1. Andreas Öchsner
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Andreas Öchsner .

Rights and permissions

Reprints and permissions

Copyright information

© 2020 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Öchsner, A. (2020). Three-Dimensional Solids. In: Partial Differential Equations of Classical Structural Members. SpringerBriefs in Applied Sciences and Technology(). Springer, Cham. https://doi.org/10.1007/978-3-030-35311-7_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-35311-7_8

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-35310-0

  • Online ISBN: 978-3-030-35311-7

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation