Quasi-Mechanism Method of Structural Morphogenesis Based on Self-Adapting Function of Net System
Publication: Journal of Structural Engineering
Volume 144, Issue 11
Abstract
This study explores a geometric method of structural morphogenesis, referred to here as the quasi-mechanism (QM) method because it is based on the self-adapting function of mechanism systems. First, a net-shaped mechanism system is modeled by adopting B-spline curves. Subsequently, an equation of shape is established to determine the tendency of shape transformation under the condition of constraining the length of each cable. This equation is solved using the generalized inverse matrix theory and the gradient of potential energy increment with shape transformation. Next, an iterative process is formed to determine the final shape of the system, which corresponds to an optimized structural shape featuring a predominant axial force and small bending moment under a specific loading case. Finally, the new structural shapes generated by the QM method illustrate its validity and characteristics.
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References
Adriaenssens, S., P. Block, D. Veenendaal, and C. Williams. 2014. Shell structures for architecture: Form finding and optimization. New York: Routledge.
Adriaenssens, S. M. L., and M. R. Barnes. 2001. “Tensegrity spline beam and grid shell structures.” Eng. Struct. 23 (1): 29–36. https://doi.org/10.1016/S0141-0296(00)00019-5.
Ali, N. B. H., L. Rhode-Barbarigos, and I. F. C. Smith. 2011. “Analysis of clustered tensegrity structures using a modified dynamic relaxation algorithm.” Int. J. Solids Struct. 48 (5): 637–647. https://doi.org/10.1016/j.ijsolstr.2010.10.029.
Alic, V., and K. Persson. 2016. “Form finding with dynamic relaxation and isogeometric membrane elements.” Comput. Methods Appl. Mech. Eng. 300: 734–747. https://doi.org/10.1016/j.cma.2015.12.009.
Aufaure, M. 1993. “A finite element of cable passing through a pulley.” Comput. Struct. 46 (5): 807–812. https://doi.org/10.1016/0045-7949(93)90143-2.
Barnes, M. R. 1977. “Form finding and analysis of tension structures by dynamic relaxation.” Ph.D. thesis, City Univ.
Barnes, M. R. 1999. “Form finding and analysis of tension structures by dynamic relaxation.” Int. J. Space Struct. 14 (2): 89–104. https://doi.org/10.1260/0266351991494722.
Barnes, M. R., S. Adriaenssens, and M. Krupka. 2013. “A novel torsion/bending element for dynamic relaxation modeling.” Comput. Struct. 119: 60–67. https://doi.org/10.1016/j.compstruc.2012.12.027.
Bletzinger, K. U., R. Wüchner, F. Daoud, and N. Camprubí. 2005. “Computational methods for form finding and optimization of shells and membranes.” Comput. Methods Appl. Mech. Eng. 194 (30–33): 3438–3452. https://doi.org/10.1016/j.cma.2004.12.026.
Block, P., and J. Ochsendorf. 2007. “Thrust network analysis: A new methodology for three-dimensional equilibrium.” J. Int. Assoc. Shell Spatial Struct. 48 (3): 167–173.
Cui, C. Y., and B. S. Jiang. 2014. “A morphogenesis method for shape optimization of framed structures subject to spatial constraints.” Eng. Struct. 77: 109–118. https://doi.org/10.1016/j.engstruct.2014.07.032.
Day, A. S. 1965. “An introduction to dynamic relaxation.” Engineer 219: 218–221.
Eschenauer, H. A., V. V. Kobelev, and A. Schumacher. 1994. “Bubble method for topology and shape optimization of structures.” Struct. Optim. 8 (1): 42–51. https://doi.org/10.1007/BF01742933.
Ghaboussi, J., and S. M. Shrestha. 1998. “Evolution of optimum structural shapes using genetic algorithm.” J. Struct. Eng. 124 (11): 1331–1338. https://doi.org/10.1061/(ASCE)0733-9445(1998)124:11(1331).
Hangai, Y., and K. I. Kawaguchi. 1987. “Shape-finding analysis of unstable link structures.” [In Japanese.] J. Struct. Constr. Eng. 381: 56–60. https://doi.org/10.3130/aijsx.381.0_56.
Hassani, B., and E. Hinton. 1999. Homogenization and structural topology optimization. London: Springer.
Heyman, J. 2007. Structural analysis: A historical approach. Cambridge, UK: Cambridge University Press.
Huerta, S. 2008. “The analysis of masonry architecture: A historical approach.” Archit. Sci. Rev. 51 (4): 297–328. https://doi.org/10.3763/asre.2008.5136.
Isler, H. 1994. “Concrete shells derived from experimental shapes.” Struct. Eng. Int. 4 (3): 142–147. https://doi.org/10.2749/101686694780601935.
Kawamura, H., H. Ohmori, and N. Kito. 2002. “Truss topology optimization by a modified genetic algorithm.” Struct. Multidiscip. Optim. 23 (6): 467–473. https://doi.org/10.1007/s00158-002-0208-0.
Kilian, A., and J. Ochsendorf. 2005. “Particle-spring systems for structural form finding.” J. Int. Assoc. Shell Spatial Struct. 46 (2): 77–84.
Moored, K. W., and H. Bart-Smith. 2009. “Investigation of clustered actuation in tensegrity structures.” Int. J. Solids Struct. 46 (17): 3272–3281. https://doi.org/10.1016/j.ijsolstr.2009.04.026.
Pauletti, R. M. O., and P. M. Pimenta. 2008. “The natural force density method for the shape finding of taut structures.” Comput. Methods Appl. Mech. Eng. 197 (49–50): 4419–4428. https://doi.org/10.1016/j.cma.2008.05.017.
Philipp, B., M. Breitenbergera, I. D’Auriab, R. Wuchner, and K. U. Bletzingera. 2016. “Integrated design and analysis of structural membranes using the Isogeometric B-Rep Analysis.” Comput. Methods Appl. Mech. Eng. 303: 312–340. https://doi.org/10.1016/j.cma.2016.02.003.
Piegl, L., and W. Tiller. 2010. Non-uniform rational B-spline. [In Chinese.] Beijing: Tsinghua University Press.
Schek, H. J. 1974. “The force density method for form finding and computation of general networks.” Comput. Methods Appl. Mech. Eng. 3 (1): 115–134. https://doi.org/10.1016/0045-7825(74)90045-0.
Tomlow, J. 2011. “Gaudí’s reluctant attitude towards the inverted catenary.” Proc. Inst. Civ. Eng.-Eng. Hist. Heritage 164 (4): 219–233. https://doi.org/10.1680/ehah.2011.164.4.219.
Tramontin, M. L. 2006. “Textile tectonics: An interview with Lars Spueybroek.” Archit. Des. 76 (6): 52–59. https://doi.org/10.1002/ad.357.
Wang, S., and Z. Yang. 1996. Generalized inverse matrix and its application. [In Chinese.] Beijing: Beijing University Technology Press.
Xie, Y. M., and G. P. Steven. 1997. Evolutionary structural optimization. Berlin: Springer.
Zhang, L., M. K. Lu, H. W. Zhang, and B. Yan. 2015. “Geometrically nonlinear elasto-plastic analysis of clustered tensegrity based on the co-rotational approach.” Int. J. Mech. Sci. 93: 154–165. https://doi.org/10.1016/j.ijmecsci.2015.01.015.
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Published In
Journal of Structural Engineering
Volume 144 • Issue 11 • November 2018
Copyright
©2018 American Society of Civil Engineers.
History
Received: Jan 5, 2017
Accepted: May 8, 2018
Published online: Aug 30, 2018
Published in print: Nov 1, 2018
Discussion open until: Jan 30, 2019
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