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The transient analysis of sliding beams represents a challenging problem of structural mechanics. Typically, the sliding motion superimposed by large flexible deformation requires numerical methods as, e.g., finite elements, to obtain approximate solutions. By means of the classical sliding spaghetti problem, the present paper provides a guideline to the numerical modeling with conventional finite element codes. For this purpose, two approaches, one using solid elements and one using beam elements, respectively, are employed in the analysis, and the characteristics of each approach are addressed. The contact formulation realizing the interaction of the beam with its support demands particular attention in the context of sliding structures. Additionally, the paper employs the sliding-beam formulation as a third approach, which avoids the numerical difficulties caused by the large sliding motion through a suitable coordinate transformation. The present paper briefly outlines the theoretical fundamentals of the respective approaches for the modeling of sliding structures and gives a detailed comparison by means of the sliding spaghetti serving as a representative example. The specific advantages and limitations of the different approaches with regard to accuracy and computational efficiency are discussed in detail. Through the comparison, the sliding-beam formulation, which proves as an effective approach for the modeling, can be validated for the general problem of a sliding structure subjected to large deformation. [ABSTRACT FROM AUTHOR]

Abstract: In conventional problems of structural mechanics, both kinematic boundary conditions and external forces are prescribed at fixed material points that are known in advance. If, however, a structure may move relative to its supports, the position of the imposed constraint relations generally changes in the course of motion. A class of problems which inherently exhibits this particular type of non-material boundary conditions is that of axially moving continua. Despite varying in time, the positions of the supports relative to the material points of the body have usually assumed to be known a priori throughout the deformation process in previous investigations. This requirement is abandoned in the present paper, where the dynamic behavior of a structure is studied, which may move freely relative to one of its supports. As a consequence, the position of such a non-material boundary relative to the structure does not only change in time but also depends on the current state of deformation of the body. The variational formulation of the equilibrium relations of a slender beam that may undergo large deformations is presented. To this end, a theory based on Reissner''s geometrically exact relations for the plane deformation of beams is adopted, in which shear deformation is neglected for the sake of brevity. Before a finite element scheme is developed, a deformation-dependent transformation of the beam''s material coordinate is introduced, by which the varying positions of the constraint relations are mapped onto fixed points with respect to the new non-material coordinate. By means of this transformation, additional convective terms emerge from the virtual work of the inertia forces, whose symmetry properties turn out to be different from what has previously been presented in the literature. In order to obtain approximate solutions, a finite element discretization utilizing absolute nodal displacements as coordinates is subsequently used in characteristic numerical examples, which give an insight into the complex dynamic behavior of problems of this type. On the one hand, the free vibrations of a statically pre-deformed beam are investigated, on the other hand, an extended version of the sliding beam problem is studied. [Copyright &y& Elsevier]

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. [ABSTRACT FROM AUTHOR]