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2023 | OriginalPaper | Chapter

4. Non-linear Boundary Value Problems

Author : Uwe Mühlich

Published in: Enhanced Introduction to Finite Elements for Engineers

Publisher: Springer International Publishing

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Abstract

After discussing possible sources of non-linearities, the subject is discussed for the case of non-linear constitutive equations and spatially one-dimensional problems. Developing FEM for non-linear boundary value problems leads eventually to systems of non-linear algebraic equations and the use of Newton’s method for solving such systems is demonstrated. The commonly applied approach for controlling convergence of Newton’s method by employing a time or pseudo time incrementation procedure, respectively, with nested iteration loop is laid out. Numerical integration employing Gauss integration is discussed together with its benefits regarding the separation of spatial discretisation and material routines.

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previous chapter Linear Initial Boundary Value Problems
next chapter A Primer on Non-linear Dynamics and Multiphysics
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Metadata
Title
Non-linear Boundary Value Problems
Author
Uwe Mühlich
Copyright Year
2023
Book
Enhanced Introduction to Finite Elements for Engineers

Print ISBN: 978-3-031-30421-7

Electronic ISBN: 978-3-031-30422-4

Copyright Year: 2023

DOI
https://doi.org/10.1007/978-3-031-30422-4_4

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