Abstract
Kinematics in structural optimisation and configurational mechanics coincide as long as sufficiently smooth design variations of the material bodies are considered. Thus, variational techniques from design sensitivity analysis can be used to derive the well-known Eshelby tensor. The impact on numerical techniques including computer aided design (cad) and the finite element method (fern) is outlined.
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References
Arora, J. (1993). An exposition of the material derivative approach for structural shape sensitivity analysis. Computer Methods in Applied Mechanics and Engineering, 105:41–62.
Barthold, F.-J. (2002). Zur Kontinuumsmechanik inverser Geometrieprobleme. Habilitationsschrift, Braunschweiger Schriften zur Mechanik 44-2002, TU Braunschweig.
Barthold, F.-J. and Stein, E. (1996). A continuum mechanical based formulation of the variational sensitivity analysis in structural optimization. Part I: analysis. Structural Optimization, 11(1/2):29–42.
Bertram, A. (1989). Axiomatische Einfiihrung in die Kontinuumsmechanik. Bl-Wissenschaftsverlag, Mannheim.
Epstein, M. and Maugin, G. (2000). Thermomechanics of volumetric growth in uniform bodies. Int. J. Plasticity, 16:1–28.
Gurtin, M. (2000). Configurational Forces as Basic Concepts of Continuum Physics. Springer-Verlag, New York.
Kamat, M., editor (1993). Structural Optimization: Status and Promise. Number 150 in Progress in Astronautics and Aeronautics. AIAA, Washington, DC.
Kienzler, R. and Hermann, G. (2000). Mechanics in Material Space. Springer-Verlag, Berlin.
Kienzler, R. and Maugin, G., editors (2001). Configurational Mechanics of Materials, Wien, New York. Springer-Verlag.
Krawietz, A. (1986). Materialtheorie. Mathematische Beschreibung des phänomenologischen thermomechanischen Verhaltens. Springer-Verlag, Berlin.
Noll, W. (1972). A new mathematical theory of simple materials. Archives of Rational Mechanics, 48(1):l–50.
Tortorelli, D. and Wang, Z. (1993). A systematic approach to shape sensitivity analysis. International Journal of Solids & Structures, 30(9):1181–1212.
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Barthold, FJ. (2005). On Structural Optimisation and Configurational Mechanics. In: Steinmann, P., Maugin, G.A. (eds) Mechanics of Material Forces. Advances in Mechanics and Mathematics, vol 11. Springer, Boston, MA. https://doi.org/10.1007/0-387-26261-X_22
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DOI: https://doi.org/10.1007/0-387-26261-X_22
Publisher Name: Springer, Boston, MA
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