Finite rotation analysis and consistent linearization using projectors
A systematic procedure is presented for extending the capabilities of an existing linear finite element of accomodate finite rotation analysis. The approach is based on the element -- independent co-rational algorithm, where the element rigid body motion is separated from the deformational part of its total motion by attaching a local frame to the element, such that the motion of the element with respect to this local frame fully describes the deformation. The independence of the internal strain energy of an element on the rigid body part of the motion is used to obtain invariance conditions for the element internal force vector and the tangent stiffness matrix. The consistent linearization of the co- rotational formulation results in a projector matrix, whose action has no effect on consistent internal forces and moments. The anti-symmetric part of the tangent stiffness matrix is shown to depend on the out-of-balance force vector. It is proved that using the symmetric part of the tangent matrix, the Newton iteration retains its quadratic rate of convergence. Three large rotation test examples are solved. The results demonstrate that it is possible to analyze structures displaying highly nonlinear behaviour involving very large rotations within a general co-rotational framework, using simple and economical finite elements.
scientific article; zbMATH DE number 63170
scientific article