Dynamic analysis of composite members with interlayer slip

Girhammar, Ulf Arne; Pan, Danhua

doi:10.1016/0020-7683(93)90041-5

Cited by 125 publications

(50 citation statements)

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“…Figure 3 illustrates this behaviour, where the normalized slip freedom k s /k s1 on the diagonal of the stiffness matrix (corresponding to k(3, 3) of Equation (41)) is plotted as a function of the dimensionless L stiffness defined by Girhammar and Pan [16] as…”

Section: Numerical Instabilitymentioning

confidence: 99%

A direct stiffness analysis of a composite beam with partial interaction

Ranzi

Bradford

2004

Numerical Meth Engineering

120

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SUMMARYThe use of the conventional semi-analytical stiffness method in finite element analysis, in which interpolation polynomials are used to develop the stiffness relationships, leads to problems of curvature locking when beam-type elements are developed for composite members with partial interaction between the materials of which it is comprised. The curvature locking phenomenon that occurs for composite steel-concrete members is quite well reported, and the general approach to minimizing the undesirable ramifications of curvature locking has been to use higher-order polynomials with increasing numbers of internal nodes. This paper presents an alternate formulation based on a direct stiffness approach rather than starting from pre-defined interpolation polynomials, and which does not possess the undesirable locking characteristics. The formulation is based on a more general approach for a bi-material composite flexural member, whose constituent materials are joined by elastic shear connection so as to provide partial interaction. The stiffness relationships are derived, and these are applied to a simply supported and a continuous steel-concrete composite beam to demonstrate the efficacy of the method, and in particular its ability to model accurately both very flexible and very stiff shear connection that causes difficulties when implemented in competitive semi-analytical algorithms.

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Section: Numerical Instabilitymentioning

confidence: 99%

A direct stiffness analysis of a composite beam with partial interaction

Ranzi

Bradford

2004

Numerical Meth Engineering

120

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“…The expression utilized in Equation (10) to illustrate the weak formulation of the partial interaction problem can be re-arranged into the following compact form:…”

Section: Global Balance Conditionsmentioning

confidence: 99%

“…Since then, the longitudinal partial nature of composite beams has been studied extensively in the last decades in the linear-elastic range [5][6][7][8][9][10], in the non-linear range [11][12][13][14][15][16][17][18][19][20], accounting for time effects [21][22][23][24][25] and including shear-lag effects [26]. For this purpose, various modelling techniques have been utilized, among the others the finite difference method, the finite element method and exact analytical solutions, while it is beyond the scope of this paper to provide an extensive list of references.…”

Section: Introductionmentioning

confidence: 99%

Displacement-based formulations for composite beams with longitudinal slip and vertical uplift

Gara¹,

Ranzi²,

Leoni³

2006

Int. J. Numer. Meth. Engng

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This paper describes three novel displacement-based formulations for the analysis of composite beams with a flexible connection which is capable of deforming along the longitudinal axis of the member as well as vertically, i.e. transverse to the interface connection. For completeness, the analytical model which forms the basis of the proposed modelling technique is presented in both its weak and strong forms. The three novel finite element formulations are derived and tested using different structural systems; their nodal freedoms include the vertical and axial displacements as well as the rotations at each element end of both layers. Curvature locking problems are observed to occur for one of these elements and the origin of this behaviour is demonstrated analytically. Two applications are then proposed adopting a bi-linear constitutive relationship for the vertical interface connection to, reflect the more realistic case in which, already in the linear-elastic range of the materials forming the cross-section and of the longitudinal interface connection, two vertical connection stiffnesses are required, i.e. one to model the event of separation between the layers and one when one bears against the other one. Copyright (c) 2005 John Wiley & Sons, Ltd

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“…In the following section the governing homogenized equation (21) given above for symmetric three-layer sandwich beams is modified for asymmetric two-layer elastic beams exhibiting the important defect of viscoelastic interlayer slip. Such a model refers to the practically very important case of a single-span compound bridge consisting, for example, of a steel girder connected (elastically) to the concrete deck; for details see, for example, [Girhammar and Pan 1993]. Figure 2 shows the free body diagram of such a two-layer beam with marked centroids, S 1 and S 2 , of the individual Figure 2.…”

Section: Linear Viscoelastic Layered Beamsmentioning

confidence: 99%

“…where k is the elastic slip modulus [Hoischen 1954;Girhammar and Pan 1993]. Differentiating (33) with respect to the axial coordinate x and substituting (29), (30), and (32) 2 lead to…”

Section: Linear Viscoelastic Layered Beamsmentioning

confidence: 99%