The strain hardening rotating hollow shaft subject to a positive temperature gradient

Summary The modeling of deformation in flexible multibody systems is still under intensive investigation. While the floating frame of reference formulation has become a standard for the modeling of deformable moving bodies, formulations based on absolute coordinates are comparatively new. The recently developed absolute nodal coordinate formulation uses solely nodal position and slopes as degrees of freedom for structural elements. The numerical treatment is similar to the absolute coordinate formulation, which is investigated in the following. An efficient formulation based on absolute coordinates with a reduced strain tensor (similar to corotational formulations) has been derived recently, and the analogy to the floating frame of reference formulation has been shown. The efficiency of this formulation is based on a co-rotated stiffness matrix which is factorized only once, however, only linear constraints have been treated up to now. The present paper treats the extension of the advantages of the co-rotated formulation with respect to nonlinear constraints, damping and contact. Constraints are discussed for the special cases of linear and nonlinear dependence on the deformation degrees of freedom. The (implicit) Newmark scheme is used to illustrate the time stepping procedure within the present method. In the case of a small number of nonlinear constraints, a single time step can be performed by solving only a small system of nonlinear equations by means of Newton's method. A numerical example shows a method to reduce the number of constraints and illustrates the computational advantages of the proposed method.