Options for Dynamic Similarity of Interacting Fluids, Elastic Solids and Rigid Bodies Undergoing Large Motions
Source abstract
Abstract
Abstract Motivated by a design of a vertical axis wind turbine, we present a theory of dynamical similarity for mechanical systems consisting of interacting elastic solids, rigid bodies and incompress-ible fluids. Throughout, we focus on the geometrically nonlinear case. We approach the analysis by analyzing the equations of motion: we ask that a change of variables take these equations and mutual boundary conditions to themselves, while allowing a rescaling of space and time. While the disparity between the Eulerian and Lagrangian descriptions might seem to limit the possibilities, we find numerous cases that apparently have not been identified, especially for stiff nonlinear elastic materials (defined below). The results appear to be particularly adapted to structures made with origami design methods, where the tiles are allowed to deform isometrically. We collect the results in tables and discuss some particular numerical examples.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Advanced Materials and Mechanics · Structural Analysis and Optimization · Dynamics and Control of Mechanical Systems
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (25)
Show source-provided references
1. Little Heath, T., et al.: The Works of Archimedes. Courier Corporation, Chelmsford (2002)
2. Timoshenko, S.: History of Strength of Materials: With a Brief Account of the History of Theory of Elasticity and Theory of Structures. Courier Corporation, Chelmsford (1983)
3. Euler, L.: Scientia naualis seu tractatus de construendis ac dirigendis pars prior [-pars posterior] complectens theoriam vniuersam de situ ac motu corporum aquae innatantium. Typis Academiae Scientiarum, vol. 2 (1749)
4. Euler, L.: Opera Omnia vol. 18. Birkhäuser, Bäsel (1967)
5. Euler, L.: Opera Omnia vol. 19. Birkhäuser, Bäsel (1972)
6. Coutinho, C.P., Baptista, A.J., Rodrigues, J.D.: Reduced scale models based on similitude theory: a review up to 2015. Eng. Struct. 119, 81–94 (2016)10.1016/j.engstruct.2016.04.016 ↗
7. Kline, S.J.: Similitude and Approximation Theory. Springer, Berlin (2012)
8. Casaburo, A., Petrone, G., Franco, F., De Rosa, S.: A review of similitude methods for structural engineering. Appl. Mech. Rev. 71(3), 030802 (2019)10.1115/1.4043787 ↗
9. Birkhoff, G.: Hydrodynamics. Princeton University Press, Princeton (1960)
10. Truesdell, C., Noll, W.: The Non-linear Field Theories of Mechanics. Springer, Berlin (2004)10.1007/978-3-662-10388-3 ↗
11. Olver, P.J.: Applications of Lie Groups to Differential Equations, vol. 107. Springer, Berlin (1993)10.1007/978-1-4612-4350-2 ↗
12. Choma, J.: In: Morphing: A Guide to Mathematical Transformations for Architects, Designers, Hachette, UK (2015)
13. Liu, H., Plucinsky, P., Feng, F., Soor, A., James, R.D.: Origami and the structure of materials. SIAM News 55(01) (2022)
14. Velvaluri, P., Soor, A., Plucinsky, P., Lima de Miranda, R., James, R.D., Quandt, E.: Origami-inspired thin-film shape memory alloy devices. Sci. Rep. 11(1), 1–10 (2021)10.1038/s41598-021-90217-3 ↗
15. Dafermos, C.M.: Hyperbolic Conservation Laws in Continuum Physics. Springer, Berlin (2016)10.1007/978-3-662-49451-6 ↗
16. Coleman, B.D., Noll, W.: The thermodynamics of elastic materials with heat conduction and viscosity. In: The Foundations of Mechanics and Thermodynamics, pp. 145–156. Springer, Berlin (1974)10.1007/978-3-642-65817-4_9 ↗
17. Raoult, A.: Non-polyconvexity of the stored energy function of a Saint Venant-Kirchhoff material. Apl. Mat. 31(6), 417–419 (1986)10.21136/AM.1986.104220 ↗
18. Friesecke, G., James, R.D., Müller, S.: A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity. Commun. Pure Appl. Math. 55(11), 1461–1506 (2002)10.1002/cpa.10048 ↗
19. Mooney, M.: A theory of large elastic deformation. J. Appl. Phys. 11(9), 582–592 (1940)10.1063/1.1712836 ↗
20. Gent, A.N., Thomas, A.G.: Forms for the stored (strain) energy function for vulcanized rubber. J. Polym. Sci. 28(118), 625–628 (1958)10.1002/pol.1958.1202811814 ↗
21. Ogden, R.W.: Large deformation isotropic elasticity–on the correlation of theory and experiment for incompressible rubberlike solids. Proc. R. Soc. Lond. Ser. A, Math. Phys. Sci. 326(1567), 565–584 (1972)
22. Miller, M.A., Kiefer, J., Westergaard, C., Hansen, M.O.L., Hultmark, M.: Horizontal axis wind turbine testing at high Reynolds numbers. Phys. Rev. Fluids 4(11), 110504 (2019)10.1103/PhysRevFluids.4.110504 ↗
23. Ashby, M.F.: Materials Selection in Mechanical Design. Elsevier, Amsterdam (2011)
24. Dean, B., Bhushan, B.: Shark-skin surfaces for fluid-drag reduction in turbulent flow: a review. Philos. Trans. - Royal Soc., Math. Phys. Eng. Sci. 368(1929), 4775–4806 (2010)
25. Wen, L., Weaver, J.C., Lauder, G.V.: Biomimetic shark skin: design, fabrication and hydrodynamic function. J. Exp. Biol. 217(10), 1656–1666 (2014)10.1242/jeb.097097 ↗