Abstract
This contribution is concerned with duality techniques in the physical and material spaces. Variational formulations for the primal physical and primal material problem are derived and we introduce the corresponding dual problems. The dual solutions in the physical and material spaces can be used to compute the changes in a certain quantity of interest for arbitrary given changes in the physical and material residual, respectively.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Hartmann, F., The Mathematical Foundation of Structural Mechanics. Springer-Verlag, Berlin/Heidelberg, 1985.
Herrmann, G., Kienzler, R., Reciprocity relations in Eshelbian mechanics. Mech. Res. Commun. 34, 2007, 338–343.
Kienzler, R., Herrmann, G., Mechanics in Material Space. Springer-Verlag, Berlin/Heidelberg/New York, 2000.
Lions, J.L., Optimal Control of Systems Governed by Partial Differential Equations. SpringerVerlag, Berlin/Heidelberg/New York, 1971.
Materna, D., Barthold, F.J., Variational design sensitivity analysis in the context of structural optimization and configurational mechanics. Int. J. Fract. 147(1–4), 2007, 133–155.
Materna, D., Barthold, F.J., Goal-oriented r-adaptivity based on variational arguments in the physical and material spaces. Comput. Methods Appl. Mech. Engrg., 2008, submitted.
Materna, D., Barthold, F.J., Configurational variations for the primal and dual problem in elasticity. Z. Angew. Math. Mech., 2009, DOI 10.1002/zamm.200800144, accepted for publication.
Maugin, G.A., Material Inhomogeneities in Elasticity. Chapman & Hall, London, 1993.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer Science + Business Media B.V.
About this paper
Cite this paper
Materna, D., Barthold, FJ. (2009). A Variational Framework for Dual Solutions in the Physical and Material Space. In: Steinmann, P. (eds) IUTAM Symposium on Progress in the Theory and Numerics of Configurational Mechanics. IUTAM Bookseries, vol 17. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3447-2_9
Download citation
DOI: https://doi.org/10.1007/978-90-481-3447-2_9
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-3446-5
Online ISBN: 978-90-481-3447-2
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)