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1 - Introduction

Published online by Cambridge University Press:  05 June 2012

Steen Krenk
Affiliation:
Technical University of Denmark, Lyngby
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Summary

Many problems of practical interest involve non-linear behavior of solids and structures. In the present context a solid means a body with a firm shape, as opposed to a fluid, while a structure refers to a solid composed of slender elements such as beams, plates and shells. Typical problems are the motion of robots, collapse scenarios of structures, metal forming processes in industrial production, and material deformation and failure in geotechnical engineering. These problems typically involve a considerable change of shape, often accompanied by non-linear material behavior.

The finite element method is an important tool for the analysis of nonlinear problems, such as geometrical and material non-linear behavior of solids and structures. The solution of non-linear problems by the finite element method involves modeling, leading to the formulation of an appropriate set of non-linear equations describing the problem, followed by an appropriate strategy for the numerical solution of these equations. In contrast to linear problems, where the solution strategy reduces to the solution of a system of linear equations, the solution phase in a non-linear problem typically involves an iterative procedure.

Non-linear modeling and analysis is a very active research area with many engineering applications. The many different aspects involved are not covered in any single text. However, some central references to general texts should be given here. A brief introduction to some of the basic problems of non-linear finite element analysis of solids and structures is included in the book by Cook et al. (1989).

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Publisher: Cambridge University Press
Print publication year: 2009

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  • Introduction
  • Steen Krenk, Technical University of Denmark, Lyngby
  • Book: Non-linear Modeling and Analysis of Solids and Structures
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511812163.002
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  • Introduction
  • Steen Krenk, Technical University of Denmark, Lyngby
  • Book: Non-linear Modeling and Analysis of Solids and Structures
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511812163.002
Available formats
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Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Introduction
  • Steen Krenk, Technical University of Denmark, Lyngby
  • Book: Non-linear Modeling and Analysis of Solids and Structures
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511812163.002
Available formats
×