General sliding-beam formulation: A non-material description for analysis of sliding structures and axially moving beams. (18th August 2020) - Humer, Alexander; Steinbrecher, Ivo; Vu-Quoc, Loc
Abstract: We present a general formulation for problems of sliding structures and axially moving beams that undergo large deformations. The formulation relies on a coordinate transformation that facilitates the analysis of beams characterized by a large sliding motion, for which conventional approaches typically become inefficient. The transformation maps variable domains in the material coordinate, which result, e.g., from the beam's sliding motion relative to its supports and external loads, onto fixed domains with respect to the new stretched coordinate. We do not only consider supports and loads prescribed at variable points and domains, but their current position relative to the material points of the structure may additionally depend on the current state of deformation. Hamilton's principle and the geometrically exact theory for shear-deformable beams serve as basis for the derivation of the equations of motion in the stretched coordinate. We introduce a generalized notion of variation that includes the boundaries of variable domains as unknowns and we discuss the implications on the governing equations. Upon a spatial semi-discretization, symmetric mass and tangent stiffness matrices are obtained from the variational formulation of the equations of motion along with non-linear velocity and stiffness-convection terms. Several numerical examples demonstrate both the range of applications and the advantages of the proposed formulation in problems of sliding structures and axially moving beams.