Abstract
An algorithm is proposed to optimize the performance of a two-phase composite under dynamic loading. The goal is to determine a series of different layouts of the two base materials in a three-dimensional region such that the time-averaged stress energy is minimized. Four cases with different boundary conditions and ratios of mass density are considered and solved numerically. The resulting optimal designs are compared to the static case to illustrate the effect of the dynamic loading. Furthermore, a qualitative comparison is done to indicate the difference between the optimization of eigenfrequencies and the present formulation.
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References
Allaire-etal:2001 Allaire G, Aubry S, Jouve F (2001) Eigenfrequency optimization in optimal design. Comput Method Appl Mech Eng 190(28):3565–3579
Bendsoe-Sigmund:2002 Bendsøe MP, Sigmund O (2002) Topology optimization: theory, methods, and applications. Springer, Berlin Heidelberg New York
Bruck:2000 Bruck HA (2000) A one-dimensional model for designing functionally graded materials to attenuate stress waves. Int J Solids Struct 37(44):6383–6395
Dems-Mroz:1998 Dems K, Mróz Z (1998) Methods of sensitivity analysis. In: Kleiber K (ed.), Handbook of computational solid mechanics: survey and comparison of contemporary methods, pp. 673–755. Springer, Berlin Heidelberg New York
Diaz-Kikuchi:1992 Díaz AR, Kikuchi N (1992) Solutions to shape and topology eigenvalue optimization problems using a homogenization method. Int J Numer Method Eng 35(7):1487–1502
Hashin-Shtrikman:1963 Hashin Z, Shtrikman S (1963) A variational approach to the theory of the elastic behaviour of multiphase materials. J Mech Phys Solids 11:127–140
Kleiber-etal:1997 Kleiber M, Antúnez H, Hien TD, Kowalczyk P (1997) Parameter sensitivity in nonlinear mechanics: theory and finite element computations. Wiley, NJ
Krog-Olhoff:1999 Krog LA, Olhoff N (1999) Optimum topology and reinforcement design of disk and plate structures with multiple stiffness and eigenfrequency objectives. Comput Struct 72(4–5):535–563
Lipton:1994 Lipton R (1994) A saddle-point theorem with application to structural optimization. J Optim Theory Appl 81(3):549–568
Sigmund-Petersson:1998 Sigmund O, Petersson J (1998) Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Struct Optim 16(1):68–75
Suresh-Mortensen:1998 Suresh S, Mortensen A (1998) Fundamentals of functionally graded materials: processing and thermomechanical behaviour of graded metals and metal-ceramic composites. IOM Communications
Turteltaub:2002a Turteltaub S (2002a) Functionally graded materials for prescribed field evolution. Comput Method Appl Mech Eng 191(21–22):2283–2296
Turteltaub:2002b Turteltaub S (2002b) Optimal control and optimization of functionally graded materials for thermomechanical processes. Int J Solids Struct 39(12):3175–3197
Velo-etal:2002 Velo AP, Gazonas GA, Scheidler MJ (2002) Homogeneous optimal design of a finite elastic strip subjected to transient loading. 15th ASCE Engineering Mechanics Conference Proceedings. Columbia University, New York
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Turteltaub, S. Optimal non-homogeneous composites for dynamic loading. Struct Multidisc Optim 30, 101–112 (2005). https://doi.org/10.1007/s00158-004-0502-0
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DOI: https://doi.org/10.1007/s00158-004-0502-0