A structural optimisation viewpoint on growth phenomena

• Autorzy: Barthold F.
• Języki publikacji: EN

Abstrakty

EN

Evolutionary solid bodies undergoing changes of mass, of properties, and of shapes are considered in models of growth and adaptation and similarily in structural optimisation. A fundamental separation of different growth phenomena and a subsequent parametrisation using independent design variables for the amount of substance as well as for molar mass and molar volume facilitates an efficient formulation of the design space. Thus, the effects of design variations, i.e. change of amount of substance, on the variations of the structural response, i.e. the deformation in physical space, can be clearly described. Overall, a novel treatment of growth processes based on an evolution of the amount of substance is outlined. The parallelism of variations in physical and design space are highlighted and compared with the multiplicative decomposition of the deformation gradient into a growth and an elastic part incorporating an incompatible intermediate configuration. This drawback is overcome by a compatible manifold based on material points modelling the amount of substance outside of any geometrical space.

Słowa kluczowe

EN

computational mechanics; structural optimisation; sensitivity analysis; configurational mechanics; growth

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2012
• Tom: Vol. 60, nr 2
• Strony: 247--252
• Opis fizyczny: Bibliogr. 16 poz., rys.

Twórcy

autor

Barthold F.

• Department of Architecture and Civil Engineering, Technische Universit¨at Dortmund, 8 August-Schmidt-Str., D-44227 Dortmund, Germany,

Bibliografia

• [1] L.A. Taber, “Biomechanics of growth, remodeling, and morphogenesis”, Appl. Mech. Rev. 48 (8), 487–545 (1995).
• [2] E.K. Rodrigues, A. Hoger, and A.D. McCulloch, “Stressdependent finite growth in soft elastic tissues”, J. Biomech. 27, 455–467 (1994).
• [3] V.A. Lubarda, “Constitutive theories based on the multiplicative decomposistion of deformation gradient: Thermoelasticity, elastoplasticity, and biomechanics”, Appl. Mech. Rev. 57 (2), 95–108 (2004).
• [4] M. Epstein and M. Elzanowski, Material Inhomogeneities and their Evolution, Springer, Berlin, 2007.
• [5] R. Segev and M. Epstein, “On theories of growing bodies”, Contemporary Research in the Mechanics and Mathematics of Materials 1, 119–130 (1996).
• [6] K.K. Choi and N. Kim, Structural Sensitivity Analysis and Optimisation 1 – Linear Systems, Springer, Berlin, 2005.
• [7] K. Choi and N.H. Kim, Structural Sensitivity Analysis and Optimization 2 – Nonlinear Systems and applications, Springer, Berlin, 2005.
• [8] J.F. Ganghoffer and B. Haussy, “Mechanical modeling of growth considering domain variation. Part I: Constitutive framework”, Int. J. Solids Struct. 42, 4311–4337 (2005).
• [9] J.F. Ganghoffer, “Mechanical modeling of growth considering domain variation. Part II: volumetric and surface growth involving Eshelby tensors”, J. Mech. Phys. Solids 58, 1434–1459 (2010).
• [10] A. Klarbring and B. Torstenfelt, “Dynamical systems and topology optimization”, Structural and Multidisciplinary Optimization 42 (2), 179–192 (2010).
• [11] F.-J. Barthold, “Zur Kontinuumsmechanik inverser Geometrieprobleme”, Braunschweiger Schriften zur Mechanik 44- 2002, http://hdl.handle.net/2003/23095 (2002).
• [12] F.-J. Barthold, “Remarks on variational shape sensitivity analysis based on local coordinates”, Eng. Analysis with Boundary Elements 32 (11), 971–985 (2008).
• [13] C.A. Truesdell and W. Noll, “The nonlinear field theories of mechanics”, in: Handbuch der Physik III/3, ed. S. Fl ¨ugge, Springer, Berlin, 1965.
• [14] D. Materna and F.-J. Barthold, “On variational sensitivity analysis and configurational mechanics”, Comput. Mechanics 41 (5), 661–681 (2008).
• [15] W. Noll, “A new mathematical theory of simple materials”, Arch Ration Mech Anal 48 (1), 1–50 (1972).
• [16] W. Noll, “A frame-free formulation of elasticity”, J. Elasticity 83, 291–307 (2006).