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Simo-Vu Quoc rods using Clifford algebra. (English) Zbl 0940.74081
Summary: We present an alternative derivation of Simo and Vu Quoc’s numerical algorithm [J. C. Simo and L. Vu-Quoc, Comput. Methods Appl. Mech. Eng. 66, No. 2, 125-161 (1988; Zbl 0618.73100)] for modelling the nonlinear dynamic behaviour of rods. The original derivation uses differential topology, describing large rotations using the Lie group SO(3) and Lie algebra so(3), but resorting to quaternions for the numerical implementation. The new derivation uses Clifford or geometric algebra for both the formulation and implementation. We show that the new approach is considerably simpler to follow, and thereby allows to investigate alternative modelling strategies. The new description is also novel in that all formulae for rotational kinematics are applicable in a Euclidean space of any dimension.
MSC:
74S99Numerical methods in solid mechanics
74K10Rods (beams, columns, shafts, arches, rings, etc.) in solid mechanics
15A66Clifford algebras, spinors