An exact conserving algorithm for nonlinear dynamics with rotational DOFs and general hyperelasticity. Part 2: shells |
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Authors: | E M B Campello P M Pimenta P Wriggers |
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Affiliation: | 1.Polytechnic School at the University of S?o Paulo,S?o Paulo,Brazil;2.Institute for Continuum Mechanics,Leibniz Universit?t Hannover,Hanover,Germany |
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Abstract: | Following the approach developed for rods in Part 1 of this paper (Pimenta et al. in Comput. Mech. 42:715–732, 2008), this work presents a fully conserving algorithm for the integration of the equations of motion in nonlinear shell dynamics.
We begin with a re-parameterization of the rotation field in terms of the so-called Rodrigues rotation vector, allowing for
an extremely simple update of the rotational variables within the scheme. The weak form is constructed via non-orthogonal
projection, the time-collocation of which ensures exact conservation of momentum and total energy in the absence of external
forces. Appealing is the fact that general hyperelastic materials (and not only materials with quadratic potentials) are permitted
in a totally consistent way. Spatial discretization is performed using the finite element method and the robust performance
of the scheme is demonstrated by means of numerical examples. |
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