Abstract
In previous chapters, equations for various thermomechanical problems derived within the FEM approximation methodology have been presented. Here, methods of their solution are going to be briefly described.
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Notes
- 1.
The rank of a matrix \(\mathbf {A}\) is the maximum number of linearly independent rows or columns it contains.
- 2.
In this subsection equations, the summation convention is not used, i.e. there is no summation over \(\alpha \) in Eq. (13.29), for instance.
- 3.
Note: the term “line search” refers in fact to nonlinear problems—here, instead of performing the search, one needs to only determine the value of \(\eta ^i\) from Eq. (13.57).
- 4.
Discrete equations of dynamics derived in Chap. 11 had a simple form which did not include the term with \(\dot{\mathbf {q}}\). In computational practice, this term is frequently added for physical reasons (the matrix \(\mathbf {C}\) describes damping in the system) as well as for numerical reasons—to assure a better stability of solution algorithms.
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© 2016 Springer International Publishing Switzerland
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Kleiber, M., Kowalczyk, P. (2016). Solution of FEM Equation Systems. In: Introduction to Nonlinear Thermomechanics of Solids. Lecture Notes on Numerical Methods in Engineering and Sciences. Springer, Cham. https://doi.org/10.1007/978-3-319-33455-4_13
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DOI: https://doi.org/10.1007/978-3-319-33455-4_13
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