Finite-element analysis of hollow flange beams with web stiffeners

A new cold-formed and resistance-welded section known as the hollow flange beam (HFB) has been developed recently in Australia. In contrast to the common lateral-torsional buckling mode of I-beams, this unique section comprising two stiff triangular flanges and a slender web is susceptible to a lateral-distortional buckling mode of failure involving lateral deflection, twist, and cross-section change due to web distortion. This lateral-distortional buckling behavior has been shown to cause significant reduction of the available flexural capacity of HFBs. An investigation using finite-element analyses and large-scale experiments was carried out into the use of transverse web plate stiffeners to improve the lateral buckling capacity of HFBs. This paper presents the details of the finite-element model and analytical results. The experimental procedure and results are outlined in a companion paper.

Second-order elastic finite element analysis of steel structures using a single element per member

Finite element frame analysis programs targeted for design office application necessitate algorithms which can deliver reliable numerical convergence in a practical timeframe with comparable degrees of accuracy, and a highly desirable attribute is the use of a single element per member to reduce computational storage, as well as data preparation and the interpretation of the results. To this end, a higher-order finite element method including geometric non-linearity is addressed in the paper for the analysis of elastic frames for which a single element is used to model each member. The geometric non-linearity in the structure is handled using an updated Lagrangian formulation, which takes the effects of the large translations and rotations that occur at the joints into consideration by accumulating their nodal coordinates. Rigid body movements are eliminated from the local member load-displacement relationship for which the total secant stiffness is formulated for evaluating the large member deformations of an element. The influences of the axial force on the member stiffness and the changes in the member chord length are taken into account using a modified bowing function which is formulated in the total secant stiffness relationship, for which the coupling of the axial strain and flexural bowing is included. The accuracy and efficiency of the technique is verified by comparisons with a number of plane and spatial structures, whose structural response has been reported in independent studies.

Inelastic finite element analysis of composite beams on the basis of the plastic hinge approach

This paper emphasizes material nonlinear effects on composite beams with recourse to the plastic hinge method. Numerous combinations of steel and concrete sections form arbitrary composite sections. Secondly, the material properties of composite beams vary remarkably across its section from ductile steel to brittle concrete. Thirdly, concrete is weak in tension, so composite section changes are dependent on load distribution. To this end, the plastic zone approach is convenient for inelastic analysis of composite sections that can evaluate member resistance, including material nonlinearities, by routine numerical integration with respect to every fiber across the composite section. As a result, many researchers usually adopt the plastic zone approach for numerical inelastic analyses of composite structures. On the other hand, the plastic hinge method describes nonlinear material behaviour of an overall composite section integrally. Consequently, proper section properties for use in plastic hinge spring stiffness are required to represent the material behaviour across the arbitrary whole composite section. In view of numerical efficiency and convergence, the plastic hinge method is superior to the plastic zone method. Therefore, based on the plastic hinge approach, how to incorporate the material nonlinearities of the arbitrary composite section into the plastic hinge stiffness formulation becomes a prime objective of the present paper. The partial shear connection in this paper is by virtue of the effective flexural rigidity as AISC 1993 [American Institute of Steel Construction (AISC). Load and resistance factor design specifications. 2nd ed., Chicago; 1993]. Nonlinear behaviour of different kinds of composite beam is investigated in this paper, including two simply supported composite beams, a cantilever and a two span continuous composite beam.

Geometric sensitivity of patient-specific finite element models of the spine to variability in user-selected anatomical landmarks

Software to create individualised finite element (FE) models of the osseoligamentous spine using pre-operative computed tomography (CT) data-sets for spinal surgery patients has recently been developed. This study presents a geometric sensitivity analysis of this software to assess the effect of intra-observer variability in user-selected anatomical landmarks. User-selected landmarks on the osseous anatomy were defined from CT data-sets for three scoliosis patients and these landmarks were used to reconstruct patient-specific anatomy of the spine and ribcage using parametric descriptions. The intra-observer errors in landmark co-ordinates for these anatomical landmarks were calculated. FE models of the spine and ribcage were created using the reconstructed anatomy for each patient and these models were analysed for a loadcase simulating clinical flexibility assessment. The intra-observer error in the anatomical measurements was low in comparison to the initial dimensions, with the exception of the angular measurements for disc wedge and zygapophyseal joint (z-joint) orientation and disc height. This variability suggested that CT resolution may influence such angular measurements, particularly for small anatomical features, such as the z-joints, and may also affect disc height. The results of the FE analysis showed low variation in the model predictions for spinal curvature with the mean intra-observer variability substantially less than the accepted error in clinical measurement. These findings demonstrate that intra-observer variability in landmark point selection has minimal effect on the subsequent FE predictions for a clinical loadcase.

Second-order elastic finite element analysis of structures using a single element per member

Finite element frame analysis programs targeted for design office application necessitate algorithms which can deliver reliable numerical convergence in a practical timeframe with comparable degrees of accuracy, and a highly desirable attribute is the use of a single element per member to reduce computational storage, as well as data preparation and the interpretation of the results. To this end, a higher-order finite element method including geometric non-linearity is addressed in the paper for the analysis of elastic frames for which a single element is used to model each member. The geometric non-linearity in the structure is handled using an updated Lagrangian formulation, which takes the effects of the large translations and rotations that occur at the joints into consideration by accumulating their nodal coordinates. Rigid body movements are eliminated from the local member load-displacement relationship for which the total secant stiffness is formulated for evaluating the large member deformations of an element. The influences of the axial force on the member stiffness and the changes in the member chord length are taken into account using a modified bowing function which is formulated in the total secant stiffness relationship, for which the coupling of the axial strain and flexural bowing is included.

Experimental and finite element analysis to identify the source of vibration of a coach

This paper presents an investigation on the cause of severe vibration problem of a coach with four-cylinder engine running at an idle state using vibration and impact hammer modal experiments to obtain the main vibration frequency components and the natural characteristics of the coach. The vibration results indicate that the main vibration component comes from the vibration transmitted from the engine to the chassis frame, which is closely related with the engine idle speed. Based on structural simulation analysis of the coach’s chassis frame and comparison with modal testing, the coach severe vibration problem was due to coupling resonance between the engine idle frequency and the fourth natural frequency of the chassis frame. The solution to eliminate the vibration problem is provided by changing the local structure stiffness of the chassis frame. The contribution of this paper lies in providing a solution to solve similar problems.

Finite element analysis of the in-plane shear behaviour of masonry panels confined with reinforced grouted cores

A combined experimental and numerical program was conducted to study the in-plane shear behaviour of hollow concrete masonry panels containing reinforced grout cores. This paper is focused on the numerical program. A two dimensional macromodelling strategy was used to simulate the behaviour of the confined masonry (CM) shear panels. Both the unreinforced masonry and the confining element were modelled using macromasonry properties and the steel reinforcement was modelled as an embedded truss element located within the grout using perfectly bonded constraint. The FE model reproduced key behaviours observed in the experiments, including the shear strength, the deformation and the crack patterns of the unconfined and confined masonry panels. The predictions of the validated model were used to evaluate the existing in-plane shear expressions available in the national masonry standards and research publications.

Numerical modelling and analysis of the blast performance of laminated glass panels and the influence of material parameters

This paper presents a comprehensive numerical procedure to treat the blast response of laminated glass (LG) panels and studies the influence of important material parameters. Post-crack behaviour of the LG panel and the contribution of the interlayer towards blast resistance are treated. Modelling techniques are validated by comparing with existing experimental results. Findings indicate that the tensile strength of glass considerably influences the blast response of LG panels while the interlayer material properties have a major impact on the response under higher blast loads. Initially, glass panes absorb most of the blast energy, but after the glass breaks, interlayer deforms further and absorbs most of the blast energy. LG panels should be designed to fail by tearing of the interlayer rather than failure at the supports to achieve a desired level of protection. From this aspect, material properties of glass, interlayer and sealant joints play important roles, but unfortunately they are not accounted for in the current design standards. The new information generated in this paper will enhance the capabilities of engineers to better design LG panels under blast loads and use better materials to improve the blast response of LG panels.

Measuring, modelling and understanding the mechanical behavior of bagasse

In the Australian sugar industry, sugar cane is smashed into a straw like material by hammers before being squeezed between large rollers to extract the sugar juice. The straw like material is initially called prepared cane and then bagasse as it passes through successive roller milling units. The sugar cane materials are highly compressible, have high moisture content, are fibrous, and they resemble some peat soils in both appearance and mechanical behaviour. A promising avenue to improve the performance of milling units for increased throughput and juice extraction, and to reduce costs is by modelling of the crushing process. To achieve this, it is believed necessary that milling models should be able to reproduce measured bagasse behaviour. This investigation sought to measure the mechanical (compression, shear, and volume) behaviour of prepared cane and bagasse, to identify limitations in currently used material models, and to progress towards a material model that can predict bagasse behaviour adequately. Tests were carried out using a modified direct shear test equipment and procedure at most of the large range of pressures occurring in the crushing process. The investigation included an assessment of the performance of the direct shear test for measuring bagasse behaviour. The assessment was carried out using finite element modelling. It was shown that prepared cane and bagasse exhibited critical state behavior similar to that of soils and the magnitudes of material parameters were determined. The measurements were used to identify desirable features for a bagasse material model. It was shown that currently used material models had major limitations for reproducing bagasse behaviour. A model from the soil mechanics literature was modified and shown to achieve improved reproduction while using magnitudes of material parameters that better reflected the measured values. Finally, a typical three roller mill pressure feeder configuration was modelled. The predictions and limitations were assessed by comparison to measured data from a sugar factory.

Computational strategies for surface fitting using thin plate spline finite element methods

Thin plate spline finite element methods are used to fit a surface to an irregularly scattered dataset [S. Roberts, M. Hegland, and I. Altas. Approximation of a Thin Plate Spline Smoother using Continuous Piecewise Polynomial Functions. SIAM, 1:208--234, 2003]. The computational bottleneck for this algorithm is the solution of large, ill-conditioned systems of linear equations at each step of a generalised cross validation algorithm. Preconditioning techniques are investigated to accelerate the convergence of the solution of these systems using Krylov subspace methods. The preconditioners under consideration are block diagonal, block triangular and constraint preconditioners [M. Benzi, G. H. Golub, and J. Liesen. Numerical solution of saddle point problems. Acta Numer., 14:1--137, 2005]. The effectiveness of each of these preconditioners is examined on a sample dataset taken from a known surface. From our numerical investigation, constraint preconditioners appear to provide improved convergence for this surface fitting problem compared to block preconditioners.

Comparison of eight published static finite element models of the intact lumbar spine : predictive power of models improves when combined together

Finite element (FE) model studies have made important contributions to our understanding of functional biomechanics of the lumbar spine. However, if a model is used to answer clinical and biomechanical questions over a certain population, their inherently large inter-subject variability has to be considered. Current FE model studies, however, generally account only for a single distinct spinal geometry with one set of material properties. This raises questions concerning their predictive power, their range of results and on their agreement with in vitro and in vivo values. Eight well-established FE models of the lumbar spine (L1-5) of different research centres around the globe were subjected to pure and combined loading modes and compared to in vitro and in vivo measurements for intervertebral rotations, disc pressures and facet joint forces. Under pure moment loading, the predicted L1-5 rotations of almost all models fell within the reported in vitro ranges, and their median values differed on average by only 2° for flexion-extension, 1° for lateral bending and 5° for axial rotation. Predicted median facet joint forces and disc pressures were also in good agreement with published median in vitro values. However, the ranges of predictions were larger and exceeded those reported in vitro, especially for the facet joint forces. For all combined loading modes, except for flexion, predicted median segmental intervertebral rotations and disc pressures were in good agreement with measured in vivo values. In light of high inter-subject variability, the generalization of results of a single model to a population remains a concern. This study demonstrated that the pooled median of individual model results, similar to a probabilistic approach, can be used as an improved predictive tool in order to estimate the response of the lumbar spine.

Finite element analysis of CFRP strengthened steel hollow sections under tension

This paper presents a nonlinear finite element (FE) model for the analysis of very high strength (VHS) steel hollow sections wrapped by high modulus carbon fibre rein forced polymer (CFRP) sheets. The bond strength of CFRP wrapped VHS circular steel hollow section under tension is investigated using the FE model. The three dimensional FE model by Nonlinear static analysis has been carried out by Strand 7 finite element software. The model is validated by the experimental data obtained from Fawzia et al [1]. A detail parametric study has been performed to examine the effect of number of CFRP layers, different diameters of VHS steel tube and different bond lengths of CFRP sheet. The analytical model developed by Fawzia et al. [1] has been used to determine the load carrying capacity of different diameters of CFRP strengthened VHS steel tube by using the capacity from each layer of CFRP sheet. The results from FE model have found in reasonable agreement with the analytical model developed by Fawzia et al [1]. This validation was necessary because the analytical model by Fawzia et al [1] was developed by using only one diameter of VHS steel tube and fixed (five) number of CFRP layers. It can be concluded that the developed analytical model is valid for CFRP strengthened VHS steel tubes with diameter range of 38mm to 100mm and CFRP layer range of 3 to 5 layers. Based on the results it can also be concluded that the effective bond length is consistent for different diameters of steel tubes and different layers of CFRP. Three layers of CFRP is considered most effective wrapping scheme due to the cost effectiveness. Finally the distribution of longitudinal and hoop stress has been determined by the finite element model for different diameters of CFRP strengthened VHS steel tube.

Comparison of eight published lumbar spine finite element models

Due to its ability to represent intricate systems with material nonlinearities as well as irregular loading, boundary, geometrical and material domains, the finite element (FE) method has been recognized as an important computational tool in spinal biomechanics. Current FE models generally account for a single distinct spinal geometry with one set of material properties despite inherently large inter-subject variability. The uncertainty and high variability in tissue material properties, geometry, loading and boundary conditions has cast doubt on the reliability of their predictions and comparability with reported in vitro and in vivo values. A multicenter study was undertaken to compare the results of eight well-established models of the lumbar spine that have been developed, validated and applied for many years. Models were subjected to pure and combined loading modes and their predictions were compared to in vitro and in vivo measurements for intervertebral rotations, disc pressures and facet joint forces. Under pure moment loading, the predicted L1-5 rotations of almost all models fell within the reported in vitro ranges; their median values differed on average by only 2° for flexion-extension, 1° for lateral bending and 5° for axial rotation. Predicted median facet joint forces and disc pressures were also in good agreement with previously published median in vitro values. However, the ranges of predictions were larger and exceeded the in vitro ranges, especially for facet joint forces. For all combined loading modes, except for flexion, predicted median segmental intervertebral rotations and disc pressures were in good agreement with in vivo values. The simulations yielded median facet joint forces of 0 N in flexion, 38 N in extension, 14 N in lateral bending and 60 N in axial rotation that could not be validated due to the paucity of in vivo facet joint forces. In light of high inter-subject variability, one must be cautious when generalizing predictions obtained from one deterministic model. This study demonstrates however that the predictive power increases when FE models are combined together. The median of individual numerical results can hence be used as an improved tool in order to estimate the response of the lumbar spine.