Viscoelastic material design with negative stiffness components using topology optimization

Structural and Multidisciplinary Optimization

Volumn 38, Issue 6, 2009, Pages 583-597

  Prasad, J ^a   Diaz, A R ^a  

^a Michigan State University   (United States)

Author keywords

Inverse homogenization; Material design; Negative stiffness materials; Topology optimization

Indexed keywords

INVERSE HOMOGENIZATION; LUMPED PARAMETER MODELS; MATERIAL DESIGN; NEGATIVE STIFFNESS; NEGATIVE STIFFNESS MATERIALS; ORTHOTROPIC MATERIALS; TOPOLOGY OPTIMIZATION; TWO PHASE COMPOSITES; VISCO-ELASTIC MATERIAL; VISCOELASTIC COMPOSITE MATERIALS;

COMPOSITE MATERIALS; COMPOSITE MICROMECHANICS; DESIGN; ELASTIC MODULI; STIFFNESS; TOPOLOGY;

STRUCTURAL OPTIMIZATION;

EID: 67649556942     PISSN: 1615147X     EISSN: 16151488     Source Type: Journal    
DOI: 10.1007/s00158-008-0308-6     Document Type: Article

References (32)

1. PM Alabuzhev AA Gritchin PT Stepanov VF Khon 1977 Some results of an investigation of a vibration protection system with stiffness correction J Min Sci 13 338 341
2. Alabuzhev PM, Grytchin AA, Kim LI, Migirenko GS, Khon VF, Stepanov PT (1989) Vibration protecting and measuring systems with quasi-zero stiffness. Taylor & Francis, New York
3. TE Bruns DA Tortorelli 2001 Topology optimization of nonlinear elastic structures and compliant mechanisms Comput Method Appl Math 190 3443 3459 (Pubitemid 32379192)
4. AR Diaz A Benard 2003 Designing materials with prescribed elastic properties using polygonal cells Int J Numer Methods Eng 57 301 314 (Pubitemid 36708886)
5. WJ Drugan 2007 Elastic composite materials having a negative-stiffness phase can be stable Phys Rev Lett 98 Article 055502
6. J Falnes 1995 On non-causal impulse response functions related to propagating water waves Appl Ocean Res 17 379 389 (Pubitemid 26417025)
7. J Guest J Prevost T Belytschko 2004 Achieving minimum length scale in topology optimization using nodal design variables and projection functions Int J Numer Methods Eng 61 238 254 (Pubitemid 39174684)
8. YL Hsu MS Hsu CT Chen 2001 Interpreting results from topology optimization using density contours Comput Struct 79 1049 1058
9. T Jaglinski D Kochmann D Stone RS Lakes 2007 Composite materials with viscoelastic stiffness greater than diamond Science 315 620 622 (Pubitemid 46214701)
10. Lakes RS (1999) Viscoelastic solids. CRC, Boca Raton
11. RS Lakes WJ Drugan 2002 Dramatically stiffer elastic composite materials due to a negative stiffness phase? J Mech Phys Solids 50 979 1009 (Pubitemid 34247625)
12. RS Lakes T Lee A Bersie YC Wang 2001 Extreme damping in composite materials with negative stiffness inclusions Nature 1410 565 567 (Pubitemid 32267196)
13. C-M Lee VN Goverdovskiy AI Temnikov 2007 Design of springs with negative stiffness to improve vehicle driver vibration isolation J Sound Vib 302 865 874 (Pubitemid 46435576)
14. C-Y Lin L-S Chao 2000 Automated image interpretation for integrated topology and shape optimization Struct Multidisc Optim 20 125 137 (Pubitemid 30967896)
15. N Makris JA Inaudi JM Kelly 1996 Macroscopic models with complex coefficients and causality J Eng Mech 122 566 573 (Pubitemid 126547562)
16. DL Platus 1991 Negative-stiffness-mechanism vibration isolation systems Proc SPIE 1619 44 54
17. Prasad J (2007) Design of materials with special dynamic properties using negative stiffness components. PhD dissertation, Michigan State University
18. J Prasad AR Diaz 2006 Synthesis of bistable periodic structures using topology optimization and a genetic algorithm J Mech Des 128 1298 1306 (Pubitemid 44970620)
19. Prasad J, Diaz AR (2007a) Conceptual design of materials exhibiting frequency-induced softening. ASME Proceedings of DETC2007, Paper DETC2007-34299
20. Prasad J, Diaz AR (2007b) Material design for frequency-induced softening using topology optimization. Proceedings of WCSMO-7, Seoul, 21-25 May 2007
21. T Pritz 1998 Frequency dependences of complex moduli and complex poisson's ratio of real solid materials J Sound Vib 214 83 104 (Pubitemid 128398447)
22. T Pritz 1999 Verification of local Kramers Kronig relations for complex modulus by means of fractional derivative model J Sound Vib 228 1145 1165 (Pubitemid 129533174)
23. M Sharnoff 1964 Validity conditions for the Kramers-Kronig relations Am J Phys 32 40 44
24. O Sigmund 1994 Materials with prescribed constitutive parameters: an inverse homogenization problem Int J Solids Struct 31 2313 2339
25. O Sigmund 1995 Tailoring materials with prescribed elastic properties Mech Mater 20 351 368
26. O Sigmund 2000 A new class of extremal composites J Mech Phys Solids 48 397 428 (Pubitemid 30541864)
27. O Sigmund 2007 Morphology-based black and white filters for topology optimization Struct Multidisc Optim 33 401 424 (Pubitemid 46362319)
28. K Svanberg 1987 The method of moving asymptotes Int J Numer Methods Eng 24 359 373
29. K Tai J Prasad 2007 Target-matching test problem for multiobjective topology optimization using genetic algorithms Struct Multidisc Optim 34 333 345 (Pubitemid 47325967)
30. YC Wang RS Lakes 2004 Extreme stiffness systems due to negative stiffness elements Am J Phys 72 40 50 (Pubitemid 38143078)
31. YC Wang RS Lakes 2004 Negative stiffness induced extreme viscoelastic mechanical properties: stability and dynamics Philos Mag 35 3785 3801
32. Y-M Yi S-H Park S-K Youn 2000 Design of microstructures of viscoelastic composites for optimal damping characteristics Int J Solids Struct 37 4791 4810 (Pubitemid 30369080)