Finite elastic deformations and finite rotations of 3d continuum with independent rotation field
Keywords:
3d continuum, finite rotation, elastic deformation, regularized variational principle, 8-node solid element, incompatible modesAbstract
Several variational principles for finite elastic deformations of a continuum with independent (finite) rotation field are constructed based on the polar decomposition theorem. Their regularized forms are then discussed and reduced to the one which is the most suitable for finite element implementation. A three-dimensional 8-node solid element with 6 degrees of freedom per node (three translational and three rotational) is developed based on the preferred variational formulation and the modified method of incompatible modes. A special care is dedicated to enhancing the computational efficimcy, by considering on one hand an alternative parametrization of the finite rotation field, and on the other hand by using the operator split method in dealing with the incompatible modes. The proposed approach is evaluated on a set of challenging large displacement/large rotation problems in nonlinear elastostatics.
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