Shell Finite Element Model Research Articles

Avaliação dos métodos da tensão estrutural e curva mestre para determinação da vida em fadiga de junta soldada

This paper presents a study on the structural hot spot stress method and the master curve method (Battelle) for evaluating the fatigue life of a T‐shaped welded joint. Both methods are based on the concept of structural stress, which is usually determined using finite element models. Using different types of shell finite element models, the results obtained by the two methods were compared to experimental data, verifying significant differences between the studied methods. The loading level had a great deal of influence over the accuracy of both methodologies, but on the other hand the hot spot method revealed to be more precise for the analyzed joint. The main differential for the Batelle method was the correction of the stress amplitude into an equivalent structural stress parameter, since, without this correction, the stresses on the weld toe were very similar between the Battelle and the hot spot methods. Comparing the master curve for the fatigue behavior of the Battelle method to the fatigue curve of hot spot method, with both curves expressed in terms of the nominal stress applied in the experiment, it was verified that the hot spot method is conservative. Among the different modeling techniques used, only one provided results that are not in agreement with the others. Using the Battelle method, the behavior of the bending stress component varied considerably according to the employed numerical model, indicating that can be a greater variability in the expected fatigue life for joints under more complex loading configuration.

Inelastic Test and Design Method of Cold-formed Steel Lipped Channel Members in Bending

The aim of this paper is to investigate the inelastic bending capacity and design method of cold-formed steel lipped channel bending members. The bending tests were conducted on 30 cold-formed steel lipped channel members. The nominal yield stress and the nominal thickness of the bending members were 235 MPa and 2mm. The theoretical global buckling stress was higher three times than the yield stress which can make sure the failure of members were in inelastic stage. For each specimen, an analytical analysis using Finite Element Method (FEM) was also conducted considering the influence of the boundary, the ultimate bending capacity, and the failure mode could also be captured. The test results show that the Chinese cold-formed steel specification Technical code of cold-formed thin-walled steel structures (GB50018-2002) is conservative for lipped channel bending sections in inelastic stage. The test results are used to put forward to a revised design method based on effective width method for the current Chinese cold-formed steel specification. The comparison on the bending capacity between the test results and the calculated results by using the proposed method, effective width method and direct strength method in North American cold-formed steel specification (AISI-S120-2016(draft)) shows that the proposed method can consider the inelastic reserve capacity of bending members well. The failure modes and bending capacity of bending members obtained using the idealized shell finite element model, which are close to the experimental results, shows that the idealized model is very well to model the buckling behavior and calculate capacity of bending members.

Computational model for supporting SHM systems design: Damage identification via numerical analyses

This work presents a computational model to simulate thin structures monitored by piezoelectric sensors in order to support the design of SHM systems, which use vibration based methods. Thus, a new shell finite element model was proposed and implemented via a User ELement subroutine (UEL) into the commercial package ABAQUS™. This model was based on a modified First Order Shear Theory (FOST) for piezoelectric composite laminates. After that, damaged cantilever beams with two piezoelectric sensors in different positions were investigated by using experimental analyses and the proposed computational model. A maximum difference in the magnitude of the FRFs between numerical and experimental analyses of 7.45% was found near the resonance regions. For damage identification, different levels of damage severity were evaluated by seven damage metrics, including one proposed by the present authors. Numerical and experimental damage metrics values were compared, showing a good correlation in terms of tendency. Finally, based on comparisons of numerical and experimental results, it is shown a discussion about the potentials and limitations of the proposed computational model to be used for supporting SHM systems design.

Generalised Beam Theory for composite beams with longitudinal and transverse partial interaction

This paper presents a Generalised Beam Theory formulation to study the partial interaction behaviour of two-layered prismatic steel–concrete composite beams. The novelty of the proposed approach is in its capacity to handle the deformability of the shear connections at the interface between the slab and steel beam in both the longitudinal and transverse directions in the evaluation of the deformation modes. This method falls within a category of cross-sectional analyses available in the literature for which a suitable set of deformation modes, including conventional, extension and shear, is determined from dynamic analyses of discrete planar frame models representing the cross-section. In this context, the shear connections are modelled using shear deformable spring elements. As a result, the in-plane partial shear interaction behaviour is accounted for in the planar dynamic analysis during the evaluation of the conventional and extension modes, while the longitudinal partial interaction behaviour associated with the shear modes is included in the out-of-plane dynamic analyses. In the case of the conventional modes, the longitudinal slip is accounted for in the post-processing stage where the warping displacements are determined. A numerical example of a composite box girder beam is presented and its structural response investigated for different levels of shear connection stiffness in both the longitudinal and transverse directions. The accuracy of the numerical results is validated against those obtained with a shell finite element model implemented in ABAQUS/Standard software.

Numerical and Experimental Analyses of Vibrations of Annular Plates with Multiple Eccentric Holes

This paper deals with the free transverse vibrations of annular plates with geometrical discontinuities in form of eccentric holes and rims. The finite element method and experimental studies are used. Solid and shell finite element models are employed in the numerical analysis using the commercial ANSYS software. The calculated results are verified by the original experimental data via innovative laser measurement techniques. Numerical and experimental results of this study adequately describe the phenomenon of dividing natural frequency values corresponding to the mode shapes, where the number of nodal diameters is a factor of the number of through holes. The proposed procedure of analysis of transverse vibrations of annular plates with eccentric through holes arranged over the specified radius is recommended for engineering applications.

Analysis and Control of the Coupled Vibration Between the Ship Lift and Ship Chamber

Coupled vibrations may occur between ship lift structure and the ship chamber during seismic process due to the ship chamber being hung at the roof of the ship lift. An investigation is carried out to explore the possibility of using different devices to connect the ship lift towers and the ship chamber to prevent the coupled vibrations. A three-dimensional shell finite element model is established, and then simplified into a three-dimensional truss finite element model through dynamic equivalent principle. And the numerical model of coupled vibration analysis is formed through static condensation, calculating the coupled vibration response between the ship lift structure and the ship chamber under five connection conditions: no connection, rigid connection, spring, viscous liquid damper and magneto-rheological fluid damper. The result shows that no connection and rigid connection between them are both inadvisable; the magneto-rheological fluid damper provides better vibration damping effect if suitable semi-active control strategy is applied, in comparison with passive control devices.

Fastener Demands for Sheathing-Braced Cold-Formed Steel Stud Gravity Walls

We explore, in this paper, the demands and behavior on fasteners supplying sheathing-based bracing of gravity loaded cold-formed studs and wall assemblies. The studies are carried out by shell finite element (FE) models, which are compared to analytical solutions and previously completed laboratory tests conducted by the authors. The connection between the sheathing and the stud should be able to develop enough resistance to restrain global buckling of the studs; therefore, special attention has to be given to the demands on these connections for design. Local buckling and stress concentrations may damage some connections and redistribution of forces should be ensured. Classical practice for determining fastener demand - i.e., the 2% rule - may be deficient. An analytical method developed for determining fastener demand is compared to the FE models presented in this paper; the analytical method results in a reasonable prediction of the fastener forces in wall studs.

On the strength and DSM design of cold-formed steel web/flange-stiffened lipped channel columns buckling and failing in distortional modes

Results recently reported by Kumar and Kalyanaraman [1] suggest that the presence of web and flange V-shaped intermediate stiffeners in cold-formed steel lipped channel columns may alter considerably their distortional buckling, post-buckling and collapse behaviours. The objective of this work is to assess the validity of this assertion, constituting a significant break from the existing knowledge, which is widely accepted by the technical/scientific community working with cold-formed steel structures. In particular, it may even imply that the application of the Direct Strength Method (DSM) to web/flange-stiffened lipped channel columns requires the consideration of a different (higher) distortional strength curve. In order to carry out the above assessment, this work reports a thorough numerical investigation aimed at studying the peculiarities of the distortional buckling, post-buckling and collapse behaviours of (web/flange) stiffened cold-formed steel lipped channel columns. The first step consists of selecting column geometries associated with “pure” distortional buckling and failure modes, which is ensured by having local and global critical buckling loads much higher than their distortional counterparts – this task is carried out by means of sequences of “trial-and-error” buckling analyses, performed with the GBTul code. Then, it is necessary to address the mechanical characterisation of the distortional critical buckling modes in the stiffened columns, a task much more involved than in plain lipped channel columns (and by no means trivial). This is done through the in-depth inspection of the results provided by the aforementioned GBT buckling analyses. Next, an Ansys shell finite element model is employed to perform geometrically and materially non-linear analyses of the selected stiffened lipped channel columns. The numerical results obtained (equilibrium paths, failure loads and deformed configurations) are presented and discussed, in order to assess the influence of the V-shaped intermediate stiffeners. Finally, on the basis of the ultimate strength data obtained and also the experimental and numerical failure loads reported in [1], the paper presents some considerations concerning the application of the current DSM strength curve to the design of (web/flange) stiffened lipped channel columns failing in distortional modes – in particular, some conclusions are drawn concerning the need to develop a new DSM distortional design curve to handle columns with this cross-section shape.

Buckling of rolled thin sheets under residual stresses by ANM and Arlequin method

We present a numerical technique to model the buckling of a rolled thin sheet. It consists in coupling, within the Arlequin framework, a three dimensional model based on 8-nodes tri-linear hexahedron, used in the sheet part located upstream the roll bite, and a well-suited finite element shell model, in the roll bite downstream sheet part, in order to cope with buckling phenomena. The resulting nonlinear problem is solved by the Asymptotic Numerical Method (ANM) that is efficient to capture buckling instabilities. The originalities of the paper ly, first in an Arlequin procedure with moving meshes, second in an efficient application to a thin sheet rolling process. The suggested algorithm is applied to very thin sheet rolling scenarios involving “edges-waves” and “center-waves” defects. The obtained results show the effectiveness of our global approach.

Buckling of thin-walled structures through a higher order beam model

A higher order beam model for the buckling analysis of thin-walled structures is presented in this paper.The model considers an enrichment of the displacement field so as to accurately represent the three-dimensional behaviour of thin-walled structures. The definition of an uncoupled set of deformation modes allows a meaningful definition of hierarchical higher order solutions, which are useful for the linear buckling analysis of thin-walled structures. A criterion for the definition of local and global buckling modes, as well as possible interaction between modes is put forward. A comparison between the results obtained with the higher order beam model and results obtained from a shell finite element model implemented in Abaqus allows to conclude not only the efficiency of the beam model but also its simplicity of use.

Second-order effects in locally and/or distortionally buckled frames and design based on beam element analysis

In the design of steel portal frames, second order effects are usually accounted for by using a second order elastic analysis to calculate the deformations and internal actions of the frame. In this analysis, one-dimensional beam elements are employed irrespective of whether the cross-sections of members are slender or non-slender. However, frames composed of members with slender cross-sections may buckle in local and/or distortional modes before reaching the ultimate limit state. In this case, the flexural rigidity of the frame is reduced when local/distortional buckling occurs, and as a result it undergoes larger sway deflections than had local/distortional buckling not occurred. The additional second order moments thus caused by local/distortional bucking are not accounted for in current design provisions.In this paper, the additional second-order effects caused by the development of local/distortional buckling are studied by comparing numerically determined ultimate capacities with design capacities. The numerical ultimate strengths are based on previously calibrated geometric and material nonlinear shell finite element models, and the design capacities are determined using the Australian Standard for Cold-formed Steel Structures AS/NZS 4600. A simplified approach to account for local/distortional buckling in beam-element-based design is also proposed. The focus is on portal frames subject to in-plane sway failure.

A rod model with thin-walled flexible cross-section: Extension to 3D motions and application to 3D foldings of tape springs

A planar rod model with flexible cross-section has been proposed and discussed recently in literature (Guinot et al., 2012; Picault et al., 2014). This 1D model is especially suitable for the modeling of tape springs, which develop localized folds through the flattening of the cross-section, and represents a good alternative to 2D shell models which are numerically hard to perform. However, due to its planar nature, it does not account for the coupling between bending and twisting that is noticed experimentally. In this context, we propose an extension of this rod model to 3D motions that includes torsional warping of the cross-section, based on postulated assumptions that are approximations. Starting from a complete non-linear elastic shell model, we introduce an original kinematics inspired from the elastica model and from Vlassov’s theory (Vlassov, 1962) in order to describe in-plane and out-of-plane changes of the cross-section shape with few parameters. In the specific case of shallow tape springs, approximate expressions of the strain and kinetic energies are derived by performing an analytical integration over the cross-section. The 1D tape spring rod model eventually involves only eight kinematic variables: seven to describe the translation and the rotation of the cross-section (parameterized by a unit quaternion) and one for the shape of the cross-section which is assumed to remain circular. Expressions of the potential and kinetic energies are then introduced in a suitable finite element software that can perform an automatic differentiation to solve the problem. Two static cases are treated. The first one, a tape spring clamped at one end and submitted at the other end to a follower twisting moment, shows that the model account for the bending-twisting couplings in large displacements and large rotations. The second one, a novel test named the transverse bending test, illustrates the ability of the model to account for complex scenarios of 3D foldings, involving bending and twisting as well as the creation of folds, their migration along the tape and their duplication. Quantitative comparisons to numerical results obtained with a shell finite element model are shown.

Parametric study on static and dynamic characteristics of bump-type gas foil thrust bearing for oil-free turbomachinery

Gas foil bearings have bright application prospects in oil-free turbomachinery such as aircraft air cycle machines, compressors and gas turbines. To extend the applicability of foil bearings to high-speed and heavy-load systems, the axial force produced primarily by the pressure difference between the turbine and compressor sides must be taken into consideration. The thrust disc of the rotor is typically used to sustain the axial force and maintain the attitude of the rotor in a rotor-bearing system. In an analytical model used to predict the performance of gas foil thrust bearings (GFTBs), fluid–structure interaction must be considered because of the coupling effects of hydrodynamic lubrication and the compliance of bearing surface. In this study, a link-spring structural model was employed to calculate the equivalent vertical stiffness of the bump foil. This model exhaustively considered the effect of three factors: flexibility of the bump foil, interactions between bumps, and frictional forces at the contact surfaces. In addition, top foil deflection that directly affects film thickness is calculated using a finite-element shell model. The static and dynamic characteristics of GFTBs were predicted after solving the steady-state Reynolds equation and two linearized dynamic coefficient equations which were obtained with perturbation method by using finite-difference method. The structural deformation equation was substituted into the Reynolds equations in the calculation process. The calculated static load was compared with the published experimental data, and the results validated the theoretical analysis. Thereafter, the static and dynamic characteristics including impact of rotational speed, initial minimum film thickness and the ratio of the inlet to outlet film thicknesses were analyzed. Parametric studies were also conducted to evaluate the effect of different structural parameters of the bump foil and journal tilting on the static characteristics of GFTBs. Because the proposed analytical model is completely algebraic, it can be easily programmed for accurately and effectively investigating the performance of GFTBs.

Torsion of cold-formed steel lipped channels dominated by warping response

The objective of this paper is to provide benchmark test results, explanatory shell finite element models, and preliminary Direct Strength Method prediction for cold-formed steel lipped channels undergoing torsion dominated by warping response. Although the elastic theory for the torsional response of a thin-walled cold-formed steel lipped channel member is well-developed, the extent to which warping torsion dominates the response of cold-formed steel members is not widely appreciated. Further, for cold-formed steel members in torsion little exists in terms of experimental benchmarks and even less on situations beyond the classic elastic theory, including geometric nonlinearity and post-buckling, and/or material nonlinearity from partial to full plastification of the section. Here, a typical cold-formed steel lipped channel member loaded experimentally in torsion exhibits significant strength beyond first yield. Shell finite element models of the testing correlate well with the experiments and indicate the extent of plastification as the thin-walled member undergoes torsion dominated by warping response. Idealized end boundary conditions are developed for the shell finite element model that is conservative with respect to the response, and in agreement with classical expressions in the elastic regime. The shell finite element model with idealized end boundary conditions is used to develop a parametric study on ultimate torsional capacity for members dominated by warping torsion. The results indicate that torsional slenderness may be used to predict torsional capacity and indicate that Direct Strength Method predictions for torsion for members dominated by warping torsion are possible. Preliminary design expressions for warping torsion strength prediction are provided.

Structural modeling of cold-formed steel portal frames

The paper describes the modeling of pitched roof cold-formed steel portal frames with slender cross-sections. Two types of finite element models are introduced: a shell finite element model and a modified beam finite element model. The shell element model involves explicit modeling of each structural member and accounts for the semi-rigid behavior of apex and eave joints by incorporating spring-like elements. The beam element model utilizes a reduced tangent rigidity method to account for cross-sectional instability. Both models are compared with results of experimentally tested portal frames, and good agreement is demonstrated.

Post-buckling modeling for strips under tension and residual stresses using asymptotic numerical method

In many industrial processes, geometric strip defects may be generated by buckling due to excessive residual stresses and these defects are difficult to control. Usually residual stresses have complex distributions so that defects with complex shapes appear. In strip rolling, strips are fabricated under tension, which has an impact on the shape and the amplitude of the defects. This tension can hide completely or partially the defects that increase and evolve during tension release. In this work we calculate flatness defects of strips generated by residual stresses, with and without tension, by using a shell finite element model based on the asymptotic numerical method (ANM).

Truss models for inelastic stability analysis and design of steel plate girders

The capacity of a truss model introduced in the past to represent steel and steel–concrete composite I-girders is examined to non-linear stability problems that include various stability modes. Linear buckling and geometrically and material non-linear analyses including equivalent geometrical imperfections are performed applying the truss model and a detailed shell finite element model. The results indicate that the truss model correctly determines the critical buckling modes and accurately describes the structural response up to and after the limit load. Its big advantage compared to a detailed shell element model is the easier implementation, the smaller computation time and the easier interpretation and exploitation of results. The truss model constitutes accordingly a viable alternative to Codes’ prescribed simplified methods for buckling design of specific topologies, like for plate girder bridges, both in the construction and the service phase.

A GBT Model for the Analysis of Composite Steel–Concrete Beams with Partial Shear Interaction

Composite steel–concrete beams represent an efficient form of construction for building and bridge applications. In this structural arrangement, the composite action is provided by means of a shear connection placed at the interface between the steel beam and the concrete slab, and this is commonly specified in the form of shear connectors. In this system, the structural rigidity is dependent on the deformability of the shear connection and this kinematic condition is usually referred to as partial shear interaction. In this context, this paper presents a theoretical model to study the partial shear interaction behaviour of composite steel–concrete beams in the framework of GBT. The effects of longitudinal slip between the concrete slab and steel beam are accounted for by taking into account the deformability of shear connectors during the evaluation of the warping components of the deformation modes. The proposed approach falls within a category of cross-sectional analyses available in the literature for which a suitable set of deformation modes, including conventional, extension and shear modes, is chosen from dynamic analyses. This method is applicable to open, closed and partially-closed cross-sections with one or more shear connections. A numerical example of a composite bridge is presented, with the results validated against those obtained from a shell finite element model developed in ABAQUS/Standard. The effect of different finite elements used in the GBT cross-sectional analysis is considered, in particularly highlighting how they influence the stress distributions induced in the composite section.

Accuracy of an efficient framework for structural analysis of wind turbine blades

AbstractThis paper presents a novel framework for the structural design and analysis of wind turbine blades and establishes its accuracy. The framework is based on a beam model composed of two parts—a 2D finite element‐based cross‐section analysis tool and a 3D beam finite element model. The cross‐section analysis tool is able to capture the effects stemming from material anisotropy and inhomogeneity for sections of arbitrary geometry. The proposed framework is very efficient and therefore ideally suited for integration within wind turbine aeroelastic design and analysis tools. A number of benchmark examples are presented comparing the results from the proposed beam model to 3D shell and solid finite element models. The examples considered include a square prismatic beam, an entire wind turbine rotor blade and a detailed wind turbine blade cross section. Phenomena at both the blade length scale—deformation and eigenfrequencies—and cross section scale—3D material strain and stress fields—are analyzed. Furthermore, the effect of the different assumptions regarding the boundary conditions is discussed in detail. The benchmark examples show excellent agreement suggesting that the proposed framework is a highly efficient alternative to 3D finite element models for structural analysis of wind turbine blades. Copyright © 2015 John Wiley & Sons, Ltd.

Generalised Beam Theory (GBT) for composite beams with partial shear interaction

This paper presents a theoretical model for the partial interaction analysis of composite steel–concrete beams within the framework of Generalised Beam Theory (GBT). The main contribution of this work relies on its ability to account for the deformability of the longitudinal shear connection between the slab and the steel beam, commonly known as partial shear interaction, in the evaluation of the cross-sectional deformation modes. This approach can handle arbitrary composite cross-sections, in which more than one shear connection can exist between the concrete and steel components, and for which the steel beam can be formed by open, closed or partially closed cross-sections. The proposed GBT approach falls within a category of cross-sectional analyses available in the literature for which a suitable set of deformation modes, including conventional, extension and shear, is determined from dynamic analyses. In particular, the deformation modes are selected as the dynamic eigenmodes of an unrestrained planar frame representing the cross-section. Warping is then evaluated for the conventional modes in a post-processing stage taking account of the kinematic discontinuity at the interface, while in the evaluation of the shear modes the partial interaction behaviour is included in the out-of-plane dynamic analysis. Two numerical composite examples, one where the bottom component consists of an open steel section and one based on a partially closed one, are presented to highlight the ease of use of the proposed partial interaction formulation for different levels of shear connection stiffness. The accuracy of the numerical results is validated against those calculated with a shell finite element model developed in ABAQUS.