Jeppe Jönsson

Fatigue analysis and testing of adhesive joints

Abstract The fatigue resistance of a single-lap aluminium adhesive joint to cyclic loading in combined shear and bending mode is investigated by nonlinear finite element analysis and crack propagation experiments. The epoxy adhesive is modelled by an elasto-plastic overlay material model. The initial cycles build up a residual stress state, leading to nearly linear material behaviour in the following cycles. Fatigue crack propagation is modelled by removing adhesive elements. Two series of experiments with one-sided cyclic load were carried out. The crack length was monitored by measuring the bending compliance around the end of the overlap with clip-gauges. The crack length is determined as a simple linear function of the measured compliance. The experiments show nearly constant rate crack growth until failure, with no appreciable crack initiation period. The rate of crack growth is proportional to the stress level to the power m = 6.2. Fatigue life results are given in the form of SN curves for adhesive thickness of 0.1 and 0.3 mm. There is no systematic influence of the thickness of the adhesive on the fatigue life. This supports the use of a crack propagation and fatigue life criterion formulated in terms of the energy release rate.

Distortional warping functions and shear distributions in thin-walled beams

In the analysis of thin-walled beams it is often necessary to consider the effects of distortion of the cross-section. The distortion in the plane of the cross-section generates axial warping displacements. On the basis of a known in-plane distortional displacement mode it is possible to derive a unique warping function and the related shear stress distributions. Local axial equilibrium is used to derive the main differential equation for determination of the distortional warping function and shear distributions. In closed single- or multi-celled cross-sections it is necessary to introduce circulation shear force flows around the cells to achieve compatibility of the axial displacement. Methods for analysis of open and closed cross-sections are generalized to include distortional displacement modes. It is shown that axial extension, flexure and torsional warping are included as special cases of distortion. A generalization of the conventional orthogonalization procedure and a normalization technique for distortional modes are also presented. A triple cell cross-section is used to illustrate the generalized calculation procedure and computed results are presented.

Distortional theory of thin-walled beams

Abstract The classic thin-walled beam theory for open and closed cross-sections is generalized to include one distortional mode of deformation. Distortional cross-section parameters are introduced and the new orthogonality conditions for uncoupling of the axial displacement modes are given. A normalization technique for the distortional modes leads to unique distortional cross-section properties. The theoretical formulations for torsion and distortion are nearly similar and result in nearly identical equilibrium equations. However, for closed single- or multi-cell cross-sections the torsional and distortional shear flows may couple. A study of the order of magnitude of the governing torsional and distortional parameters shows the difference between open and closed cross-sections and the related solution types. The difference in the order of magnitude of the governing cross-section parameters also leads to approximate solution techniques. In the examples, section three cross-sections are used to illustrate variations of the theoretical parameters.

Determination of shear stresses, warping functions and section properties of thin-walled beams using finite elements

Abstract Simple, one dimensional finite elements in the plane of the cross section are used to model the axial displacement modes of thin-walled beams. Based on the weak formulation of axial equilibrium of an infinitesimal section cut-out, the axial shear displacement modes, and the torsional and distortional warping functions are determined. The axial displacement functions are then used to determine the shear stress distributions and the section properties. The method makes no distinction between open and closed single or multi celled cross sections. The transverse distortional displacement modes are found by the use of a frame model in the plane of the cross section. The paper also presents a very efficient recursive formulation of super-elements.

Recursive Substructuring of Finite Elements

Abstract Recursive substructuring takes advantage of the simple repetition of substructures of identical geometry. In each recursive step the problem is transformed into a new problem involving half the number of identical substructures. The computational work involved in factorization only grows logarithmically with an increasing number of substructures as opposed to conventional methods which grow linearly. For some vector problems the efficiency of recursive substructuring may be further improved by use of symmetry relations. In the present paper the technique is applied in linear buckling analysis of thin-walled beams.

Random fields of initial out of straightness leading to column buckling

AbstractThe elastic load-carrying capacity and buckling trajectory of steel columns under compression with open and hollow cross-sections, whose axis is curved by spatial random fields, are studied in the article. As a result of the spatial curvature of the axis the cross-sections are subjected to compression, bending and torsion from the onset of loading. Numerical simulations are performed using the geometrically non-linear model created using the ANSYS software package. Each simulation run has input random realizations of yield strength and the random field generated using the Latin Hypercube Sampling method. In the plane perpendicular to a perfectly straight column axis, the random observations of deformation trajectories of a node in the middle of the column height are studied. The increasing compression load moves the node along the curve path (open sections) or along the linear path (hollow sections). Large discrepancies in the deformation trajectories of open sections (curvilinear paths) and hollo...

Strain gauge measurement of wheel-rail interaction forces

Abstract A theoretical basis for quasi static determination of wheel—rail interaction forces using strain measures in the foot of the rail is given. Vlasovs theory for thin-walled beams is used in combination with continuous translational and rotational elastic supports based on smoothing out the stiffness of the rail sleepers. The smoothing out of the rotational elastic support has traditionally not been done. The use of this model is validated by the decay lengths of the problem and through finite element analysis. The finite element analysis is performed using discrete sleeper stiffness and Vlasov beam elements. The sensitivity of the measuring technique to parameter variations is illustrated and an example shows the simplicity of the proposed direct measuring technique.

A hybrid displacement plate element for bending and stability analysis

Abstract A hybrid displacement plate element is derived from a modified energy functional based on a variational principle. The higher order curvature terms which generate high energy densities are filtered out by using independent interpolation of curvatures and moments. The inter-element compatibility requirements are relaxed by including element discontinuities in the variational formulation. The accuracy of the element is shown to be excellent in both plate bending and buckling analysis.

Mechanical interaction between concrete and structural reinforcement in the tension stiffening process

The interaction between structural reinforcement and the surrounding concrete matrix in tension is a governing mechanism in the structural response of reinforced concrete members. The tension stiffening process, defined as the concrete´s contribution to tensile response of the composite, has been investigated using an image-based deformation measurement and analysis system. This allowed for detailed view of surface deformations and the implications on the resulting response of the member in tension. In this study, conventional concrete and a ductile, strain hardening cement composite, known as Engineered Cementitious Composite (ECC), have been combined with steel and glass fiber reinforced polymer (GFRP) reinforcement to contrast the effects of brittle and ductile cement matrices as well as elastic/plastic and elastic reinforcement on the tension stiffening process. Particular focus was on the deformation process and transverse crack formation in the cementitious matrix at increasing tensile strain.

Pedestrian-induced lateral forces on footbridges

This paper investigates the phenomenon of excessive pedestrian-induced lateral vibrations as observed on several high-profile footbridges. The vibrations are a consequence of human-structure interaction, in which the forces generated by the pedestrians depend strongly on the vibration of the underlying pavement. An extensive experimental analysis has been carried out to determine the lateral forces generated by pedestrians when walking on a laterally moving treadmill. Two different conditions are investigated; initially the treadmill is fixed and then it is laterally driven in a sinusoidal motion at varying combinations of frequencies (0.33–1.07 Hz) and amplitudes (4.5–48 mm). The component of the pedestrian-induced force which is caused by the laterally moving surface is herewith quantified through equivalent velocity and acceleration proportional coefficients. It is shown that large amplitude lateral vibrations are the results of correlated pedestrian forces in the form of negative damping, with amplitudes that depend on the relationship between the step frequency and the frequency of the lateral movement.