A group-theoretic approach is presented for investigation of large-deformation property of bar-hinge mechanisms with dihedral symmetry in three-dimensional space. The number of the compatibility conditions at bar-ends is reduced by formulating them with respect to the null space of the linear compatibility matrix. It is shown that the system of reduced compatibility equations inherits the group equivariance from the original compatibility equations. This inheritance is used to develop a method to judge whether the frame has a finite mechanism mode. Sufficient conditions for large deformation mechanisms are derived based on the symmetry properties of infinitesimal mechanism modes and generalized self-equilibrium force modes. The detailed procedure of the method is shown through the numerical examples.
Bar-joint mechanism Artibtrarily inclined hinge Group theory Dihedral group
Mathematics Subject Classification
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Zingoni, A.: Group-theoretic exploitations of symmetry in computational solid and structural mechanics. Int. J. Numer. Meth. Eng. 79, 253–289 (2009)MathSciNetCrossRefGoogle Scholar
Ikeda, K., Murota, K.: Imperfect Bifurcation in Structures and Materials, 2nd edn. Applied Mathematical Sciences. Springer, New York (2010)CrossRefGoogle Scholar
Ikeda, K., Ohsaki, M., Kanno, Y.: Imperfection sensitivity of hilltop branching points of systems with dihedral group symmetry. Int. J. Non-Linear Mech. 40, 755–774 (2005)MathSciNetCrossRefGoogle Scholar
Zhang, J.Y., Guest, S.D., Ohsaki, M.: Symmetric prismatic tensegrity structures: Part I. Configuration and stability. Int. J. Solids Struct. 45(1), 1–14 (2009)CrossRefGoogle Scholar
Kanno, Y., Ohsaki, M., Murota, K., Katoh, N.: Group symmetry in interior-point methods for semidefinite program. Optim. Eng. 2, 293–320 (2001)MathSciNetCrossRefGoogle Scholar
Chen, Y., Feng, J.: Generalized eigenvalue analysis of symmetric prestressed structures using group theory. J. Comput. Civil Eng. 26(4), 488–497 (2012)CrossRefGoogle Scholar
Ohsaki, M., Kanno, Y., Tsuda, S.: Linear programming approach to design of spatial link mechanism with partially rigid joints. Struct. Multidisc. Optim. 50, 945–956 (2014)MathSciNetCrossRefGoogle Scholar
Ohsaki, M., Tsuda, S., Miyazu, Y.: Design of linkage mechanisms of partially rigid frames using limit analysis with quadratic yields functions. Int. J. Solids Struct. 88–89, 68–78 (2016)CrossRefGoogle Scholar
Guest, S.D., Fowler, P.W.: Symmetry conditions and finite mechanisms. J. Mech. Mater. Struct. 2(2), 293–301 (2007)CrossRefGoogle Scholar
Schulze, B., Guest, S.D., Fowler, P.W.: When a symmetric body-hinge structure isostatic? Int. J. Solids Struct. 51, 2157–2166 (2014)CrossRefGoogle Scholar
Ikeshita, R.: Bifurcation Analysis of Symmetric Mechanisms by using Group Theory (in Japanese), Graduation thesis, Department of Mathematical Engineering and Information Physics, School of Engineering, The University of Tokyo (2013)Google Scholar