Shell Element Model Research Articles

Nonlinear seismic modeling of reinforced concrete cores including torsion

Reinforced concrete (RC) cores are used in many residential multi-story buildings as the primary seismic force resisting system (SFRS). Due to architectural limitations, these buildings are often torsionally flexible. To assess the effect of torsion on the nonlinear seismic response of RC cores, a wide-column model (WCM) with fiber elements is used. The nonlinear warping and the nonlinear biaxial (P-Mx-My) cyclic behaviors of the WCM are validated against experimental results and exhibit excellent agreement. According to modal and linear time history analyses, the model can adequately capture the dynamic characteristics and seismic response of core structures, including torsion. The WCM is then extended to the nonlinear range to perform three-dimensional (3D) time history analyses of a typical RC building structure located in Eastern North America (ENA) that is subjected to high-frequency ground motions. Three different building configurations with increasing torsional flexibility (B=1.7, B=2.1 and B=2.5, according to the current National Building Code of Canada) are studied to investigate the effect of torsion on the seismic behavior. The nonlinear envelopes of key response parameters are similar to the design envelopes obtained from the linear response spectrum analysis of a shell elements model (B=1.7) with proper inelastic force modification factors. Aside from the story torque, the shear and moment demands remain relatively constant, regardless of the torsional flexibility value. The effective shear stiffness must be carefully selected in the WCM to avoid large questionable rotations.

Numerical Simulation and Experimental Validation of the Vibration Modes for a Processing Reciprocating Compressor

The low-order vibration modes of a reciprocating compressor were studied by means of numerical simulation and experimental validation. A shell element model, a beam element model, and two solid element models were established to investigate the effects of bolted joints and element types on low-order vibration modes of the compressor. Three typical cases were compared to check the effect of locations of moving parts on the vibration modes of the compressor. A forced modal test with the MRIT (Multiple References Impact Test) technique was conducted to validate the simulation results. Among four numerical models, the solid element model with the bolt-pretension method showed the best accuracy compared with experimental data but the worst computational efficiency. The shell element model is recommended to predict the low-order vibration modes of the compressor with regard to effectiveness and usefulness. The sparsely distributed bolted joints with a small bonded region on the contact surface were key bolted joints that had greater impacts on the low-order vibration modes of the compressor than the densely distributed bolted joints. The positions of the moving parts had little effect on the low-order vibration modes of the compressor.

Analysis of gusset plate of contemporary bridge truss girder

Trussed structures in modern bridge building usually have “W” bracing. Structural joints are often based on application of gusset plates. Experimental tests of stress distribution in such gusset plates are rather sparse. Lab testing of scaled bridge truss girder was carried out in Poznań University of Technology in Poznań. Investigation into stress distribution in gusseted joint was carried out. Test results were put against results obtained from analyses of two finite element models: beam-element model and shell-element model. Normal stress and Huber-Mises equivalent stress distributions within gusseted joint were analysed. General conclusions are: a) normal stress distribution in gusseted joint cross-section, perpendicular to truss flange axis, is nonlinear and extreme stresses occur near cross-section edges, b) Huber-Mises equivalent stress distribution in the cross-section of gusset plate near its connection to truss flange is nonlinear and extreme stresses occur near centre of the cross-section, c) assessment of normal stresses in gusseted joints should not be carried out with an aid of beam-element modelling, d) it is possible to assess Huber-Mises equivalent stresses in gusset plate near its welded connection to rigid flange with an aid of beam-element modelling if non-uniform distribution of shear stress is taken into account, e) shell-element modelling of gusseted joint provides satisfactory accuracy of normal and equivalent stress assessment, f) beam-element modelling of friction grip bolts is sufficiently accurate for shell-element models of steel joints analysed within elastic range of behaviour.

A Comparative Study of the Shell Element and Strip Model Methods for Analysis of Steel Plate Shear Wall Structures

Shell element and strip model are the two available numerical methods in the analysis of steel plate shear wall (SPSW) structures. The shell element model provides excellent prediction of the behavior of SPSWs. However, when the number of elements increases, especially in high-rise frames, the method becomes time consuming and produces convergence complications. In such cases, the strip model is commonly used as an alternative method. In the literature, the evaluation of the strip model has only been carried out for up to four-story SPSW structures. In the present study, fourteen low- to high-rise SPSW frames having 4, 7, 10 and 13 stories with different bay widths of 2, 3, 6 and 9m are designed and modeled using shell element and strip methods. The pushover analysis results show that the accuracy of strip model is affected by the number of story levels as well as the bay width. The use of beam element in modeling frame members is shown to have considerable effects on the results of the strip model. The panel zones should be modeled as effectively rigid regions in the strip model; and the slenderness ratio of frame members should be considered. It is also found that the distribution of story shear between infill plates and frame members are quite different in the two modeling methods. Furthermore, modifications to improve the accuracy of the strip model are recommended in this paper.

Seismic Performance Assessment of Multitiered Steel Concentrically Braced Frames Designed in Accordance with the 2010 AISC Seismic Provisions

AbstractMultitiered steel concentrically braced frames (CBFs) are commonly used to provide lateral resistance for tall single-story commercial, performing arts, sports, and industrial buildings. The seismic response of these frames is studied in this paper. A set of seven special concentrically braced frames (SCBFs), ranging from 9 to 30 m tall with two to six tiers, located in a high seismic area was designed according to the 2010 AISC Seismic Provisions. Fundamental behavior of the two- and four-tiered frames was investigated using three-dimensional (3D) finite element models with shell elements, with particular focus on the buckling response of the columns. The seismic frame response and column stability were then studied more broadly for all frames using more computationally efficient 3D finite element models with fiber-based beam-column elements, which were validated against the shell element models. Multitiered CBFs designed according to current multistory CBF procedures are shown to develop drift c...

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.

Modal Analysis of Bridge Structure Using Finite Element Analysis

The objective of the research study is to model a bridge with four different material using ANSYS software and to perform a modal analysis of bridge problem. For all four materials eight node solid element is selected and meshing is done individually for each modal. The material property of each material is selected as per literature database in ANSYS software. The modal analysis in ANSYS is performed to obtain the natural frequency and mode shapes of bridge to avoid the resonance of the bridge. Broquet et al. (2004) describe in a paper the dynamic behavior of deck slabs of concrete road bridge. This research interesting in dynamic analyses of bridges. The finite element method was used to study the local dynamic effects of traffic actions on the deck slabs. Advanced numerical models were described and the results of a parametric study presented. The bridge was represented by a shell element model and the vehicle by lumped masses, assembled in a nonlinear damped system. Important parameters that influence bridge vehicle interaction were taken into account, to investigate characteristic properties of the dynamic behavior of the bridge deck slabs of concrete bridges and to deduce the distribution of dynamic amplification factors throughout the deck slab. The vehicle was excited by irregularities of the road surface, generated by using power spectral density function. Experimental studies (Wolek 1992) have indicated that present methods of analysis underestimate impact and, thus, the dynamic effect for many structures. Since so many variables play a significant role in the generation and control of the total response, it is essential that bridge designers develop a better understanding of the dynamic behavior of bridge structures and the physical characteristics and parameters that affect response. II. Material Properties The dynamic material properties for the road-bridge as well as for the adjacent ground are vital information for the study of the road-bridge. Parameters concerning the soil characteristics are taken from the database that was formed during previous studies which were aimed of ensuring adequate vibration levels. By choosing the parameters according to that database it was easier to equate the results with research made previously. The database enclosing material data for the studies also contains information about suitable parameters for concrete and other materials such as asphalt.In Table 2.1 the material parameters which are used in the modelling are displayed. The quantities displayed in Table 2.1 are the materials density ρ (kg/m3), Young's modulus E (MPa), Poisson's ratio v (−).

Contrastive Study on Finite Element Models of High-Strength Pipelines Crossing Active Faults

There is a potential for major damage to the pipelines crossing faults, therefore the strain-based design method is essential for the design of buried pipelines. Finite element models based on soil springs which are able to accurately predict pipelines’ responses to such faulting are recommended by some international guidelines. In this paper, a comparative analysis was carried out among four widely used models (beam element model; shell element model with fixed boundary; shell element model with beam coupled; shell element model with equivalent boundary) in two aspects: differences of results and the efficiency of calculation. The results show that the maximum and minimum strains of models coincided with each other under allowable strain and the calculation efficiency of beam element model was the highest. Besides, the shell element model with beam coupled or equivalent boundary provided the reasonable results and the calculation efficiency of them were higher than the one with fixed boundary. In addition, shell element model with beam coupled had a broader applicability.

Lateral buckling of C-section purlins with one anti-sag bar at middle span section

Anti-sag bar is frequently adopted to enhance the lateral stiffness of cold-formed steel purlins. In existing studies, the anti-sag bar is normally treated as the rigid lateral restraint of cold-formed steel purlins, while according to the previous study of the authors', the local deformation of purlin web near the location connecting the anti-sag bar may significantly reduce the efficiency of anti-sag bar for providing the lateral restraint to cold-formed steel purlins. The lateral buckling of C-section purlins with one anti-sag bar at their middle span section is investigated in this paper, where the effective stiffness of the anti-sag bar taking into account the local deformation of purlin web is adopted. Two representative total potentials for the lateral buckling of C-section purlins are discussed with the differences between highlighted. Based on the proposed total potential, a hand-calculation solution for the lateral buckling load of C-section purlins is developed. The total potential and the solution for buckling load proposed in this study are verified by comparing their results with those from the finite element (FE) analysis using the shell element modeling of ANSYS or the FE program developed. The influences of the key parameters on the lateral buckling load of the C-section purlins are discussed in the parametric study.

Aerodynamic Optimization Based on Continuous Adjoint Method for a Flexible Wing

Aerodynamic optimization based on continuous adjoint method for a flexible wing is developed using FORTRAN 90 in the present work. Aerostructural analysis is performed on the basis of high-fidelity models with Euler equations on the aerodynamic side and a linear quadrilateral shell element model on the structure side. This shell element can deal with both thin and thick shell problems with intersections, so this shell element is suitable for the wing structural model which consists of two spars, 20 ribs, and skin. The continuous adjoint formulations based on Euler equations and unstructured mesh are derived and used in the work. Sequential quadratic programming method is adopted to search for the optimal solution using the gradients from continuous adjoint method. The flow charts of rigid and flexible optimization are presented and compared. The objective is to minimize drag coefficient meanwhile maintaining lift coefficient for a rigid and flexible wing. A comparison between the results from aerostructural analysis of rigid optimization and flexible optimization is shown here to demonstrate that it is necessary to include the effect of aeroelasticity in the optimization design of a wing.

Lateral buckling of simply supported C- and Z-section purlins with top flange horizontally restrained

Lateral buckling is a main failure mode controlling the strength of C- and Z-section purlins under wind suction, as the compressive flange of cross-section is laterally free in this case. The lateral buckling of roof purlins is different from the normally considered simply supported beams, because the top flange of cross-section of these purlins is laterally restrained due to the bracing of the above roof sheeting. To reveal the lateral buckling of C- and Z-section purlins with their top flanges horizontally restrained, two representative buckling theories for the lateral buckling of thin-walled beams, the traditional buckling theory and a new theory recently proposed by the authors of this paper, are adopted in this study. Comparisons made in this study indicate that the total potentials derived from these two theories have different expressions for the considered purlins. Subsequently, the finite element (FE) analysis using the shell element modeling is adopted to examine the buckling loads of purlins based on these two buckling theories, which indicates that the buckling theory proposed by the authors of this paper is more reasonable for this problem. Simple solutions are also proposed for buckling loads of C- and Z-section purlins with their top flange horizontally restrained, and very good agreements are achieved in the comparisons between the predictions of the proposed solutions and FE results.

Application of steel equivalent constitutive model for predicting seismic behavior of steel frame

In order to investigate the accuracy and applicability of steel equivalent constitutive model, the calculated results were compared with typical tests of steel frames under static and dynamic loading patterns firstly. Secondly, four widely used models for time history analysis of steel frames were compared to discuss the applicability and efficiency of different methods, including shell element model, multi-scale model, equivalent constitutive model (ECM) and traditional beam element model (especially bilinear model). Four-story steel frame models of above-mentioned finite element methods were established. The structural deformation, failure modes and the computational efficiency of different models were compared. Finally, the equivalent constitutive model was applied in seismic incremental dynamic analysis of a ten-floor steel frame and compared with the cyclic hardening model without considering damage and degradation. Meanwhile, the effects of damage and degradation on the seismic performance of steel frame were discussed in depth. The analysis results showed that: damages would lead to larger deformations. Therefore, when the calculated results of steel structures subjected to rare earthquake without considering damage were close to the collapse limit, the actual story drift of structure might already exceed the limit, leading to a certain security risk. ECM could simulate the damage and degradation behaviors of steel structures more accurately, and improve the calculation accuracy of traditional beam element model with acceptable computational efficiency.

Modeling the Seismic Response of Modern URM Buildings Retrofitted by Adding RC Walls

Modern unreinforced masonry buildings with reinforced concrete slabs are often retrofitted by inserting reinforced concrete walls. The main advantages of this technique are the increase in strength and displacement capacity with respect to masonry structures. This article presents two modeling approaches for evaluating such structures: a shell-element model and a macro-element one. The objective is to formulate practical recommendations for setting up a macro-element model using as input the geometry of the structure and results from standard material tests. Structural configurations of masonry buildings, in which the insertion of reinforced concrete walls is an efficient retrofit technique, are also investigated.

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.

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.

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.

Application of Shell Element in Temperature Field Predication of Wind Turbine Blade

For anti-icing wind turbine blades, hot air heating method is widely adopted due to its various advantages such as easy maintenance. This article proposes a temperature field predication method for wind tribune blade based on AN- SYS SHELL131 shell element. Firstly, by building a solid model, it verifies the feasibility of merging plies of wind tur- bine blades of the same material. Then it uses an anti-icing apparatus with hot air heating to measure the temperature field data by experiment. Based on characteristics of SHELL131 element, it merges and simplifies plies of an actual wind tur- bine blade to obtain an appropriate shell element model. Finally, after computing the temperature field of the whole blade by ANSYS, it verifies the feasibility of this method by showing good agreement between the simulation and the experi- mental results. In practice, this method can be applied to temperature field computations for varies types of wind turbine blades and other laminated structures, and it can provide reliable theoretic guidance for heat transfer analysis of wind tur- bine blade and research on anti-icing equipment of blades.

Reliability-based assessment of steel bridge deck using a mesh-insensitive structural stress method

This paper aims to conduct the reliability-based assessment of the welded joint in the orthotropic steel bridge deck by use of a mesh-insensitive structural stress (MISS) method, which is an effective numerical procedure to determine the reliable stress distribution adjacent to the weld toe. Both the solid element model and the shell element model are first established to investigate the sensitivity of the element size and the element type in calculating the structural stress under different loading scenarios. In order to achieve realistic condition assessment of the welded joint, the probabilistic approach based on the structural reliability theory is adopted to derive the reliability index and the failure probability by taking into account the uncertainties inherent in the material properties and load conditions. The limit state function is formulated in terms of the structural resistance of the material and the load effect which is described by the structural stress obtained by the MISS method. The reliability index is computed by use of the first-order reliability method (FORM), and compared with a target reliability index to facilitate the safety assessment. The results achieved from this study reveal that the calculation of the structural stress using the MISS method is insensitive to the element size and the element type, and the obtained structural stress results serve as a reliable basis for structural reliability analysis.

Prediction of laser welding induced deformation in thin sheets by efficient numerical modeling

A local solid model and a global shell model were employed for fast prediction of deformation in laser welded thin sheets based on inherent strain theory. Transient thermo-elastic-plastic analysis was performed on the local three-dimensional solid model to obtain inherent strain for the global shell model. To ensure solution accuracy, the characteristics of the laser welding heat source were considered in determination of the mesh size and time increment. The penetration shape of laser welded joint was well reproduced compared with the results by experimental observation. By applying inherent strain into shell element model, the out-of-plane welding deformation was predicted within a few minutes using elastic FEM. The predicted deformation mode and magnitude agreed with the measured ones for laser welded joints of different dimensions. By considering geometrical imperfection in the numerical model, it was reproduced that the laser welding induced deformation in thin sheets generally has the same mode as initial shape of the sheet.

A numerical approach for simulating fluid structure interaction of flexible thin shells undergoing arbitrarily large deformations in complex domains

We present a new numerical methodology for simulating fluid–structure interaction (FSI) problems involving thin flexible bodies in an incompressible fluid. The FSI algorithm uses the Dirichlet–Neumann partitioning technique. The curvilinear immersed boundary method (CURVIB) is coupled with a rotation-free finite element (FE) model for thin shells enabling the efficient simulation of FSI problems with arbitrarily large deformation. Turbulent flow problems are handled using large-eddy simulation with the dynamic Smagorinsky model in conjunction with a wall model to reconstruct boundary conditions near immersed boundaries. The CURVIB and FE solvers are coupled together on the flexible solid–fluid interfaces where the structural nodal positions, displacements, velocities and loads are calculated and exchanged between the two solvers. Loose and strong coupling FSI schemes are employed enhanced by the Aitken acceleration technique to ensure robust coupling and fast convergence especially for low mass ratio problems. The coupled CURVIB-FE-FSI method is validated by applying it to simulate two FSI problems involving thin flexible structures: 1) vortex-induced vibrations of a cantilever mounted in the wake of a square cylinder at different mass ratios and at low Reynolds number; and 2) the more challenging high Reynolds number problem involving the oscillation of an inverted elastic flag. For both cases the computed results are in excellent agreement with previous numerical simulations and/or experiential measurements. Grid convergence tests/studies are carried out for both the cantilever and inverted flag problems, which show that the CURVIB-FE-FSI method provides their convergence. Finally, the capability of the new methodology in simulations of complex cardiovascular flows is demonstrated by applying it to simulate the FSI of a tri-leaflet, prosthetic heart valve in an anatomic aorta and under physiologic pulsatile conditions.