Nous étendons le principe dʼexclusion des treillis de Michell énoncé dans Figueraoa et al. (2012) [2], à des structures obtenues par supperposition dʼun nombre dénombrable de barres. De plus, notre principle dʼexclusion sʼapplique en tout point de la structure à analyser.
The exclusion optimality principle for Michell trusses established in Figueraoa et al. (2012) [2] is extended to frames which consist of countably many bars or rods. Furthermore, our extended exclusion principle can be applied to any point of the support of the frame under analysis.
@article{CRMATH_2012__350_21-22_991_0, author = {Ross Granowski}, title = {An elementary exclusion principle for {Michell} trusses}, journal = {Comptes Rendus. Math\'ematique}, pages = {991--995}, publisher = {Elsevier}, volume = {350}, number = {21-22}, year = {2012}, doi = {10.1016/j.crma.2012.10.030}, language = {en}, }
Ross Granowski. An elementary exclusion principle for Michell trusses. Comptes Rendus. Mathématique, Volume 350 (2012) no. 21-22, pp. 991-995. doi : 10.1016/j.crma.2012.10.030. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.10.030/
[1] Michell trusses and lines of principal action, Mathematical Models and Methods in Applied Sciences, Volume 18 (2008) no. 9, pp. 1571-1603
[2] Cutting corners in Michell trusses, Portugalie Mathematica, Volume 69 (2012) no. 2, pp. 95-112
[3] Discrete decomposition of discrete forces, 2011 www.math.gatech.edu/~gangbo/ (unpublished lecture notes, cf.)
[4] The limits of economy of material in framed-structures, Philosophical Magazine Ser. 6, Volume 8 (1904), pp. 589-597
[5] Optimal tensegrity structures in bending: The discrete Michell truss, Journal of Franklin Institute, Volume 347 (2010), pp. 257-283
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