Shell Finite Element Research Articles

Stability and design of stainless steel hollow section columns at elevated temperatures

This paper investigates the stability and design of stainless steel circular, elliptical, square and rectangular hollow section (CHS, EHS, SHS and RHS) columns at elevated temperatures. Nonlinear shell finite element models are employed to conduct comprehensive parametric studies whereby extensive benchmark structural performance data on the behaviour and resistance of stainless steel hollow section columns at elevated temperatures is generated. In total, 26,760 cold-formed and hot-rolled austenitic, duplex and ferritic stainless steel CHS, EHS, SHS and RHS columns at elevated temperatures are taken into account, considering various member slendernesses, cross-section geometries, cross-section slendernesses and elevated temperature levels. New flexural buckling design rules are put forward for stainless steel hollow section columns in fire, which consistently considers the elevated temperature strength at 2% total strain f2,θ as the reference material strength for all cross-sections classes. The accuracy, safety and reliability of the proposed new design rules are assessed for a wide range of cases. Comparisons are also made against the results obtained through the column fire design rules of the European structural steel fire design standard EN 1993-1-2 [1]. It is demonstrated that the proposed new design rules furnish more accurate, safe-sided and reliable flexural buckling resistance predictions for stainless steel hollow section columns at elevated temperatures relative to the column fire design provisions of EN 1993-1-2 [1].

Vibration mode shifting due to scale-dependency for cylindrical, conical, and spherical microshells

Microshells structures are broadly utilized in micro-electro-mechanical systems (MEMS) such as microresonator, microgyroscope, microsensor, microactuator, microantenna, and microgripper. Taking into consideration the scale-dependency in such a scale and the importance of vibration characteristics in design of such microstructures, the current study aims to analyze the role of scale-decency in mode shifting of common types of thin microshells in MEMS. A scale-dependent quadrilateral finite shell element based on the modified couple stress theory is developed to compute the frequencies and mode shapes of the system. Verification studies are presented to display the accuracy of the established numerical model for the prediction of the vibrational response of microshells with and without scale-dependency. A comprehensive examination is then carried out to disclose the impact of material length scale parameters together with geometrical parameters and boundary conditions on the mode shifting of microscale cylindrical, conical, and spherical shells. It is believed that the results of the present study are handy in the design of the microshells when the scale-decency is of great importance.

A Geometrically Exact Beam Finite Element for Non-Prismatic Strip Beams: The Spatial Case

A new beam finite element for non-prismatic (tapered and curved) beams with thin rectangular cross-section (“strip” beams) is proposed in this paper. The element is geometrically exact and constitutes the extension, to the large 3D displacement and rotation setting, of those proposed by the author for the 2D [R. Gonçalves, Int. J. Struct. Stab. Dyn. 23 (2022) 2350037] and linearized lateral-torsional buckling [R. Gonçalves, Int. J. Struct. Stab. Dyn. 23(12) (2023) 2350139] cases. The element incorporates torsion-related warping, as well as arbitrary mid-line warping, and allows nonlinear tapered geometries, arbitrary initially curved configurations (including pre-twist) and eccentric loads (loads offset from the centroid). All expressions required to implement the proposed element are given in a straightforward vector/matrix format. Several numerical tests are presented to show that the element has a very good predictive capability and a low computational cost, when compared with solutions obtained with refined shell finite element meshes, even for members with a high taper ratio and initial curvature.

КРУЧЕНИЕ НИЖНЕГО ПОЯСА ПОДКРАНОВО-ПОДСТРОПИЛЬНОЙ ФЕРМЫ

The lower belt of the crane secondary truss, along which the crane moves, is made of a thin-walled box profile. The largest local concentrated crane forces applied with eccentricity to the lower belt of truss made of thin-walled welded box cause its restrained torsion. The calculation method of the crane secondary truss does not consider the inclusion in the work of the lower belt for torsion and horizontal bending of the webs. A beam with a span equal to the span of the crane secondary truss is taken as the design scheme of the lower belt along which the crane moves. In fact, the work of the belt during torsion is different from the work of the beam.
 The objectives of the work are to assess the impact on the operation of the lower belt during torsion of the webs and the upper belt and to clarify the methodology for calculating the lower belt. The study of the influence of webs on the angular malleability and torque of the lower belt has been carried out. Various ratios of the stiffness of the belt and the entire crane secondary truss are considered. The design scheme of the belt for the calculation of torsion is proposed – a beam angular elastic supports at the points of junction of the webs. The formula for determining the stiffness of elastic supports has been adopted. The error in determining the bending moments in the lower belt according to the proposed method relative to the results of numerical calculation of the rod design scheme of the entire crane secondary truss does not exceed 2%. The stresses in the lower belt, considering the torsion component, are analytically determined. The results were verified numerically using shell finite elements and a full-scale examination.

On the compatibility between Reissner–Mindlin shell and GBT-based finite elements

This technical note discusses aspects related to the combination of standard Reissner–Mindlin shell and GBT-based (beam) finite elements, with the purpose of modelling, efficiently (with degree-of-freedom economy) and accurately, the structural behaviour of thin-walled members and frames with complex geometry, undergoing global-local-distortional deformation. Following the approach previously proposed by the authors (Manta et al., 2020 [1]; 2021 [2]; 2020 [3]), each element type is employed where it is most efficient: (i) GBT-based elements in the prismatic zones and (ii) shell elements in the geometrically complex zones (e.g., tapered, joints, etc.). While lack of compatibility obviously leads to over-flexible solutions, it is shown that full compatibility can lead to locking. Consequently, a well-balanced compatibility statement is proposed. Several numerical examples are presented to show the advantages of the proposed approach over the previous one, in linear static and buckling (bifurcation) analyses.

Research on Dynamic Response of Pipeline under the Reeling Process and Laying Process

During the process of laying submarine pipelines using the R-lay (short for reel-lay) method, the interaction between the pipeline and the laying equipment undergoes continual fluctuations, leading to bending in the pipeline induced by the stochastic dynamics of various external loads. Considering the challenge in forecasting the dynamic behavior of pipeline bending moments and ovality throughout this procedure, we constructed a finite element-based shell element model for a 6-inch pipeline. In this paper, a multi-step simulation approach was used to replicate the pipeline laying process, and the dynamic response in pipeline bending moments and ovality during the winding, unwinding, and straightening processes was analyzed. Additionally, the effects of the pipeline’s diameter–thickness ratio and material properties on the dynamic response process were also studied. The results show that the dynamic response in bending moments and ovality is closely related to the curvature of the pipeline; a brief peak will appear at the critical point where the pipeline deforms, and the peak is related to the different bending stages of the pipeline, with the winding stage having a greater impact on the peak than the unwinding stage. During the unwinding process, a reverse bending moment will occur. The dynamic response of pipeline bending moments and ovality is influenced to some extent by the pipeline’s diameter–thickness ratio and material properties, with the diameter–thickness ratio demonstrating a more conspicuous impact.

Rigorous Analysis of Energy Conservation During Dynamic Deployment of Elastic Thin-Shell Structures

Abstract This paper studies the dynamic deployment of cylindrical thin-shell structures with open cross section, attached to a rigid base. The structures are elastically folded and then released. Previous experiments have shown that the total energy decreases while a fold moves back and forth along the structure, which was explained in terms of energy losses related to the fold “bouncing” against the boundary. This paper uses a rigorous numerical simulation, based on an in-house isogeometric shell finite element code that simultaneously eliminates shear locking and hourglassing without any intrinsic energy dissipation, to show that the total energy of the system is conserved during deployment. The discrepancy with the previous results is explained by showing that energy transfers from low-frequency, “rigid body” modes, to higher frequency modes.

Efficiency of the grid analogy method in the analysis of solid slabs: study of a residential floor

Given the importance of structural analysis, slabs, particularly those made of solid concrete, have several models that allow analyzing them and obtaining the necessary efforts for their dimensioning, among them the grate analogy method. Since this is attractive for this purpose, since it has a simple approach without losing efficiency, this work proposes to study, using this approach, the mechanical behavior, in the linear elastic regime, of solid slabs of a residential floor. Thus, the general objective is to obtain the efforts and displacements of the referred pavement with this technique. For that, a computational code was developed in the Scilab programming language. In order to establish a comparison with other methods, the pavement was also analyzed using Kirchhoff's plate flexion theory and using shell finite elements with the aid of the SAP2000 software. It can be proved, through the study, the efficiency of the analysis of slabs through grid analogy. In addition, the importance of the study is verified considering the floor coupled to the beams, as well as taking into account the cracked state of the concrete, ensuring the achievement of more realistic results, which is important for design purposes.

Structural buckling analysis of pre-twisted strips

This article focuses on the buckling response of columns formed by pre-twisting a flat, narrow and straight material strip of a rectangular cross section. The experimental analysis accomplished for birch plywood strips covers twisting up to 90 degrees. The corresponding computational analysis covers the twisting process (geometrically nonlinear analysis) and the subsequent compression (linear buckling analysis, including the residual stresses from the twisting process) and includes comparisons for 3D solid and 2D shell finite elements within orthotropic linear elasticity. A further finite element analysis provides findings up to twisting angles of 400 degrees and includes nonlinear post-buckling analyses for the compression subsequent to twisting, in addition to the linear buckling analyses. These sets of analyses reveal some new findings regarding this classical problem. Most importantly, there are four characteristic twisting angles which are associated to mode jumps in buckling, to a plateau in the curve relating the critical load and the twisting angle and, finally, to a loss of stability during the twisting process. The influence of the twisting-induced stresses on the buckling response is investigated as well.

The effect of prebuckling deflections on the lateral‐torsional buckling of beams: numerical studies

AbstractIn this research the effect of prebuckling in‐plane deflections on the critical moment to lateral‐torsional buckling of beams is investigated. Though this topic is already discussed in the literature, the relevant papers show that there are some discrepancies in the proposals and results from the various authors. In this paper a numerical parametric study is reported, conducted on doubly symmetric simple supported I‐shaped beams. The critical moment values were calculated with and without considering the effect of prebuckling deflections. Various methods were considered, including analytical formulae, thin‐walled beam finite element, and shell finite element calculations. The results justify that the in‐plane deflection has a positive effect on the critical moments, and that the effect is essentially determined by the ratio of in‐plane and lateral rigidities. However, the results highlight that the moment‐increasing effect of the prebuckling deformations can be much smaller compared to the prediction of the analytical formulae, if a shell finite element model is employed.

Generic method of local thickening in shell element FEM models for orthotropic bridge decks

AbstractThis paper presents a method of estimating the hot‐spot stress in orthotropic bridge decks (OBD) using a shell Finite Element (FE) model, in which local thickening is applied around the welded. The dimensions of the area of local thickening are a function of the weld throat thickness and the plate thickness. A comparison of this method with 3D solid element FE models is presented for various fatigue sensitive details. The comparison is carried out for OBD with trapezoidal stiffeners, both with continuous stiffeners through crossbeams and with stiffeners welded in between crossbeams. It is concluded that the accuracy of estimating the hot‐spot stress with a shell element model using local thickening is significantly higher as compared to a conventional shell element model without thickening. The method of local thickening is adopted in the new prTS 1993‐1‐901. This paper functions as the background to this technical specification.

Lateral‐Torsional Buckling of welded I‐members with flame‐cut flanges: Experimental and numerical studies

AbstractEurocode 3 design rules for the lateral stability of welded I‐members are based on the assumption of hot‐rolled flanges. In practice, a large amount of welded I‐section members is made of flame cut flanges. However, residual stresses of hot‐rolled and flame‐cut flanges are quite different. The latter are more favourable with respect to out‐of‐plane buckling. The beneficial effect of flame‐cuts commonly performed at the flanges tips is then neglected in design standards. A literature review of lateraltorsional buckling tests on welded I‐members with flame‐cut flanges highlights a scarcity of results on mono‐symmetric and/or non‐uniform members. In addition, tests are generally performed on stocky cross‐sections while welded members are usually slender. Lateral‐torsional buckling tests have thus been conducted on four S355 slender welded members made of flame‐cut flanges: two uniform beams and two tapered beams. Within both couples of beams, one had a doubly symmetric cross‐section, the other one being mono‐symmetric. Experimental results highlight the impact of tapering and/or increasing the compression flange thickness whatever the beam type.These experimental tests are then modelled with shell finite elements considering imperfections, residual stresses and material laws measured experimentally. The results are in good agreement with experimental tests. Additional finite element analyses are performed varying the residual stresses distribution. A significant impact of the flange fabrication process is confirmed, flame‐cuts increasing substantially the lateral‐torsional buckling resistance.

Structural analysis of rack upright frames under a pure compression load by means of a nonlinear Generalized Beam Theory analysis

AbstractRack upright frames of conventional pallet racking systems are obtained by the assembly of uprights and braces or diagonals. Rack uprights are commonly mono‐symmetric open thin‐walled members with regular perforations along their length. These perforations are used to enable the connection with braces and beams by means of bolts or hooks. The structural behaviour of a rack upright frame under a pure compression load, in which the buckling phenomenon has a relevant influence, depends on several geometrical parameters, such as the column cross‐sectional dimensions, perforations characteristics, frame length, distance between braces, etc. Therefore, these particular issues should be considered to perform a proper structural analysis.In this paper, the structural behaviour of a pallet rack frame under a pure compression load is analysed by means of eigenbuckling and geometrically nonlinear Generalized Beam Theory (GBT) analyses. The influence of GBT deformation modes involved in the analysis is discussed. Moreover, different approaches to reproduce the connection between uprights and braces are presented and discussed. Finally, GBT results are compared with beam, shell finite element analysis and experimental values.

Structural response and design of stainless steel hollow section columns at elevated temperatures

AbstractThis paper investigates the flexural buckling behaviour and design of stainless steel circular, elliptical, square and rectangular hollow section (CHS, EHS, SHS and RHS) columns at elevated temperatures through numerical modelling. Shell finite element models are utilised to perform numerical parametric studies whereby benchmark structural performance data are generated. A large number of cold‐formed and hot‐rolled austenitic, duplex and ferritic stainless steel CHS, EHS, SHS and RHS columns at elevated temperatures are taken into account, considering various cross‐section and member slendernesses. Since the fire design provisions provided in the European fire design standard EN 1993‐1‐2 for stainless steel columns are largely based on those originally developed for carbon steel columns, they typically lead to rather inaccurate ultimate resistance predictions for stainless steel columns at elevated temperatures. To address this, in the present study, a new flexural buckling design method for stainless steel hollow section columns at elevated temperatures is put forward. The accuracy, safety and reliability of the proposed design method and the provisions in EN 1993‐1‐2 are assessed. It is observed that the proposed fire design method leads to more accurate, safe‐sided and reliable flexural buckling resistance predictions for stainless steel hollow section columns at elevated temperatures relative to the provisions in EN 1993‐1‐2.

Major‐axis buckling of pin‐ended stainless steel equal‐leg angle section members: FE modelling and design

AbstractThe behaviour and design of cylindrically‐pinned stainless steel equal‐leg angle section members under compression and compression combined with strong‐axis bending are investigated herein. Numerical models are developed by means of shell finite element modelling formulated within ABAQUS and validated against experimental data. A numerical parametric study is then presented considering both hot‐rolled and cold‐formed stainless steel equal‐leg angle section columns alongside beam‐columns with a wide range of cross‐section and member geometries. Finally, new design proposals for pin‐ended stainless steel equal‐leg angle section members under compression and compression plus major‐axis bending are developed and verified against the results of physical experiments and numerical simulations. The proposed design rules are shown to offer substantially more accurate and consistent resistance predictions compared to existing codified design rules.

Novel formula for the elastic critical moment of beams with corrugated web

AbstractThis paper presents a novel analytical expression to determine the elastic lateraltorsional buckling resistance of I‐beams with corrugated web. The corrugated web beams have higher torsional stiffness than the flat web beams; therefore, the self‐weight of the beam can be reduced. The appropriate hand calculation methods to determine the elastic critical moment of corrugated web beams are based on the modification of warping constant of the cross‐section. In this paper, instead of modifying the warping constant the approximate expression is derived from the total potential strain energy of the beam using an energy method. During the solution, the beam is separated into three parts. The flanges are modelled as thin‐walled beams and the corrugated web is modelled as a thin equivalent orthotropic plate with uniform thickness. To assess the accuracy of the proposed analytical formula full shell finite element models were created in Abaqus software. The accuracy of the proposed expression is examined for sinusoidal and trapezoidal corrugation also. The results of the parametric study showed that the derived formula is accurate and applicable for elastic lateral‐torsional buckling analysis of I‐beams with web corrugation.

Local buckling response and design of stainless steel hollow sections at elevated temperatures

AbstractThe structural behaviour and design of stainless steel hollow sections in fire, including stainless steel (i) circular hollow sections (CHS), (ii) elliptical hollow sections (EHS), (iii) square hollow sections (SHS) and (iv) rectangular hollow sections (RHS), are explored in this paper. Shell finite element models of stainless steel CHS, EHS, SHS and RHS able to replicate their structural response at elevated temperatures are created. Numerical parametric studies are performed on cold‐formed and hot‐rolled austenitic, duplex and ferritic stainless steel CHS, EHS, SHS and RHS subjected to (i) pure compression, (ii) pure bending, (iii) combined axial compression and bending and (iv) combined bending and shear in fire, covering different cross‐section slendernesses and elevated temperature levels. Calibrated against the benchmark structural performance data obtained from the numerical parametric studies, the new design proposals for predicting the ultimate resistances of stainless steel CHS, EHS, SHS and RHS in fire put forward in Quan and Kucukler [1,2] are set out. It is demonstrated that relative to the design recommendations provided in the European structural steel fire design standard EN 1993‐1‐2, the proposed cross‐section design methods provide more accurate and safe‐sided ultimate resistance predictions for stainless steel CHS, EHS, SHS and RHS at elevated temperatures.

Resistance and behaviour of carbon steel and stainless steel columns with axial and rotational end‐restraints in fire

AbstractDue to the presence of neighbouring structural elements, carbon steel and stainless steel columns are typically axially and/or rotationally restrained at their ends in fire. Despite the significant influence of the axial and rotational end‐restraints on the behaviour, the fire design rules for steel columns provided in the European structural steel fire design standard EN 1993‐1‐2 were originally developed considering the structural response of axially unrestrained steel columns with pin‐ended support conditions. Thus, EN 1993‐1‐2 may provide inaccurate ultimate resistance predictions for axially and/or rotationally restrained steel and stainless steel columns in fire. Considering this, this paper investigates the behaviour and design of carbon steel and stainless steel columns with axial and/or rotational end‐restraints at elevated temperatures. A number of carbon steel and stainless steel I‐section columns are considered, taking into account different axial and rotational end‐restraint stiffnesses, room temperature loading ratios, member and cross‐section slendernesses. A new design method for the fire design of axially and/or rotationally restrained steel and stainless steel columns is put forward. The accuracy of the proposed new design method is extensively verified against the results from nonlinear shell finite element modelling.

A Fourier‐series numerical approach for the analysis of tubular members

AbstractThis paper provides an efficient and robust numerical solution for the linear buckling analysis of tubular members, such as the supporting tower structures of wind turbines. The method uses Fourier‐series approximations for the displacement functions. Longitudinal discretization can optionally be applied, i.e., the member can be divided into segments. The strain‐displacement relationship directly considers the curved geometry. The implementation allows for arbitrary support conditions. Four pure loading situations are considered, uniform – in each segment – along the length: normal force, bending moment, torque, and shear force; however, they can arbitrarily be combined, as is commonly occurring in wind turbine towers. The applied methodology results in a computational advantage compared to the shell finite element method, while still maintaining much more generality and applicability compared with common analytical solutions. Furthermore, the method is supplemented with features, as spectral analysis and buckling length calculation.

Effective Modulus Method (EMM) concept applied to thin‐walled steel columns.

AbstractThe design of thin‐walled steel members, subjected to compressive stresses, requires complex analysis to account the interaction between local, distortional and global instabilities. There are simplified methodologies that allow simulating the effects of local and distortional post‐buckling behavior in usual structural members. The Effective Width Method (EWM) performs this simulation by changing the geometry of the cross‐section, being the pioneer methodology for the analysis of thin‐walled members. The Direct Strength Method (DSM) allows the determination of resistant forces through simple‐to‐use formulas, eliminating the calculation of the geometric properties of the section as required by the EWM. This paper presents the Effective Modulus Method (EMM) concept, which simulates the effects of local and distortional post‐buckling, to establish simplified design methodologies, desirably leading to more rigorous results than those provided by the available methodologies. In this approach, local and distortional post‐buckling effects are simulated by changing the mechanical characteristics (namely the modulus of elasticity) of the cross‐section of the members. Specifically, the article presents (i) the proposal of the new design methodology and (ii) the comparison with experimental and numerical results obtained by finite element shell models.