Shell Finite Element Analyses Research Articles

Microscale geometrical modulation of PIEZO1 mediated mechanosensing through cytoskeletal redistribution

The microgeometry of the cellular microenvironment profoundly impacts cellular behaviors, yet the link between it and the ubiquitously expressed mechanosensitive ion channel PIEZO1 remains unclear. Herein, we describe a fluorescent micropipette aspiration assay that allows for simultaneous visualization of intracellular calcium dynamics and cytoskeletal architecture in real-time, under varied micropipette geometries. By integrating elastic shell finite element analysis with fluorescent lifetime imaging microscopy and employing PIEZO1-specific transgenic red blood cells and HEK cell lines, we demonstrate a direct correlation between the microscale geometry of aspiration and PIEZO1-mediated calcium signaling. We reveal that increased micropipette tip angles and physical constrictions lead to a significant reorganization of F-actin, accumulation at the aspirated cell neck, and subsequently amplify the tension stress at the dome of the cell to induce more PIEZO1’s activity. Disruption of the F-actin network or inhibition of its mobility leads to a notable decline in PIEZO1 mediated calcium influx, underscoring its critical role in cellular mechanosensing amidst geometrical constraints.

Resistivity model of carbon fiber cloth considering the effect of interlayer contact resistance

A resistivity model of a plain-woven carbon fiber dry cloth that considers the interlayer contact resistance is proposed for induction heating and welding analysis of carbon fiber reinforced thermoplastics. Although the cloth, which is regarded as a single-layer thin plate, does not exhibit homogeneous resistivity, homogenized effective thin-shell resistivity is required to analyze the thin-shell complex structures of aircraft. The influence of the direction angle and strip width on the effective resistivity can be expressed using this model. The mechanism for the generation of a large difference in resistivity between the 0° and 45° directions of the cloth is clarified. The proposed model is verified through comparison with experimental results. According to the induction heating experiments, the overall temperature distribution of the cloth is predicted well by the shell finite element analysis using the effective resistivity.

Proposed Improvements to AISC 360-22 Chapter F for Built-Up I-Section Members

Recent analytical and experimental data has shown that the AISC 360–22 Ch. F lateral-torsional buckling (LTB) resistance equations significantly overpredict the strengths of a wide range of built-up I-girders. These overpredictions are mainly attributed to unaccounted-for yielding effects and an insufficient characterization of the plateau strengths by the AISC 360–22 compact- and noncompact-web limits. The objective of the current study is to present and justify the implementation of a new set of recommended AISC 360 Ch. F provisions (AISC 360 Rec.) for built-up I-girders. These recommended provisions were developed by making six targeted improvements to AISC 360–22, which consist of changes to the web classification limits, the inelastic/elastic LTB strength threshold, the handling of moment gradient, and the representation of the LTB strength curve itself. Two independent studies evaluate the performance of the AISC 360 Rec. equations. In the first study, professional factors (Mtest/Mn) were calculated and statistically evaluated using a newly updated LTB experimental database. The second study compares the LTB strength curves for targeted cross sections to the results from nonlinear shell finite element analysis (FEA) test simulations. The findings demonstrate that the recommended approach provides accurate-to-conservative strength predictions that meet or exceed a targeted minimum reliability index of 2.6, which AISC 360–22 does not achieve for a range of I-section member characteristics. The development of the AISC 360 Rec. provisions is significant as it fixes the strength overprediction problems recently observed for built-up I-girders while maintaining good accuracy for members where the AISC 360–22 equations perform well.

Cold-formed steel strength predictions for torsion and bending–torsion interaction

Locally slender cross-section members, such as cold-formed steel open sections, are susceptible to significant twisting and high warping torsion stresses. Torsion considerations are complicated by whether it is derived as a first-order effect from loading or a second-order effect from instability. Previous direct torsion experiments on lipped Cee sections have shown significant inelastic reserve. Furthermore, the current design for combined bending–torsion interaction has limitations, including only considering the first yield and ignoring the cross-section slenderness in torsion. Two parametric studies were conducted to predict both the torsion capacity and the combined bending–torsion interaction in locally slender cross-sections. Shell finite element analysis of lipped Cee and Zee sections for both the torsion only and the combined bending–torsion cases were created using a validated model. For the torsion-only study, various cross-section geometries, steel grades, and member lengths covering the range of practically expected torsional slenderness were investigated. A set of bimoment parameters, including yield, buckling, and plastic bimoments, were calculated and the ultimate bimoment was determined by shell finite element collapse analyses. A simple uniform equation predicting the bimoment capacity was adopted and two bimoment strength curves are proposed for local and distortional buckling-controlled cases respectively. For the combined bending–torsion case, various practical cross-sections and bracing conditions were investigated with various ratios of applied torsion and bending. Shell finite element buckling and collapse analyses were performed to determine the critical and ultimate moments and bimoments. It was found that the current AISI standard is conservative under most scenarios. Updated torsion–bending interaction equations incorporating bimoment and bending moments are proposed. The interaction equations are dependent on the cross-section, the direction of the applied torsion, and the bracing condition.

Influence of transverse stiffening on the lateral-torsional buckling resistance of built-up I-girders

Recent studies have shown that the AISC 360 Specification substantially overpredicts the strength of certain built-up steel I-girders subjected to high moment gradient. These strength overpredictions have been attributed to various effects, including (1) the direct scaling of the uniform bending lateral-torsional buckling (LTB) strength curve by the elastically-derived moment gradient factor, Cb, without considering the yielding induced at the larger predicted strengths, (2) reduction in the elastic LTB strength due to web shear and corresponding elastic distortional buckling effects, (3) compression flange lateral bending due to amplification of the initial flange sweep, and (4) intensification of the compression flange lateral bending due to web distortion. This paper scrutinizes the impact of transverse stiffening on the elastic and inelastic LTB resistance of a suite of I-girders previously evaluated experimentally and numerically without transverse stiffening through full-nonlinear shell finite element analysis test simulations. The results provide further insight into the sources of the AISC Specification overpredictions and the practical aspects of adding transverse web stiffeners to increase the LTB strength.

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.

Experimental investigation of doubly-symmetric built-up I–girders subjected to high moment gradient

Recent analytical studies have shown that the AISC 360-16 Specification overpredicts the flexural resistance of certain built-up steel I-girders. The largest overpredictions were observed in I‑girders subjected to a high moment gradient having unstiffened webs with a large web slenderness ratio. The objectives of the current research are to provide experimental validation of these strength overpredictions, validate the accuracy of full-nonlinear shell finite element analysis (FEA) solutions, and further investigate the behavior of these susceptible built-up I-girders. To accomplish the objectives, six largescale experimental tests targeted web slenderness ratios ranging from 77 to 192 and a moment gradient factor, Cb, of 1.74 (single curvature (SC) bending) and 2.31 (reverse curvature (RC) bending), calculated using common design equations. Additionally, full nonlinear shell FEA simulations were conducted to evaluate the correlation with the experiments. The tests showed flexural strengths smaller than the predicted resistances from AISC 360, with the predicted resistances ranging from 4% to 16% unconservative for SC members and 9% to 32% unconservative for RC members. Furthermore, the FEA simulation strengths were similar to the strengths measured in the experiments. The results indicate that there are two main phenomena leading to the overpredictions by AISC 360: web distortion effects exacerbated by web shear and the direct scaling of the uniform LTB strength curve by Cb up to the plateau resistance, overestimating the strength gains from moment gradient due to insufficient accounting for the onset of yielding.

Experimental and analytical assessment of LTB resistance of built-up steel I-section members

Analytical and experimental research investigations conducted subsequent to the development of the unified AISC 360–05 Section F4 and F5 and AASHTO [3] LRFD provisions for built-up I-section members have identified several areas where improvements are needed. However, the experimental data is relatively scarce within the design space for inelastic lateral-torsional buckling (LTB) of these member types. This study presents the results of eight experimental tests of doubly symmetric built-up I-section members and a large number of full-nonlinear shell finite element analysis (FEA) simulations validated against the experimental results. The study was conducted to supplement existing data and to evaluate three recommended changes to the AISC 360 Specification: (1) reduction of the ordinate at the transition between the elastic and inelastic LTB equations to ML = 0.5RpgMyc for the base uniform bending case, where Rpg is the web bend-buckling strength reduction factor and Myc is the yield moment to the compression flange; (2) use of the more general equation in AISC 360–16 Table B4–1 Case 16 for the compact-web limit, λpw; and (3) use of a variable crw factor from the current AASHTO LRFD Specifications for the calculation of the noncompact-web limit, λrw. Comparisons were also made to the predictions from the first generation of Eurocode 3. Results from the study support the recommended changes to the AISC 360 Specification and confirm the significant impact of flange lateral bending from the amplification of initial compression flange sweep for members with LTB slenderness close to the noncompact bracing limit associated with ML.

The effect of cross-section geometry on the lateral–torsional behavior of thin-walled beams: Analytical and numerical studies

In this paper, the elastic lateral–torsional behavior of simple beams is discussed by presenting a novel analytical solution and performing numerical studies. The motivation of the presented research is the observation that classic analytical prediction and finite element prediction are, typically, significantly different when the second-order nonlinear behavior of beams with initial imperfections is analyzed. To understand and explain the observed differences, a novel analytical model is worked out for the geometrically nonlinear analysis of beams with initial geometric imperfections. The advancement in the presented analytical solution is the explicit consideration of the changing geometry as the load increases. The most important steps of the derivations are summarized, and the resulting formulae are briefly discussed. The derivations are done for general cross-sections, however, the bending is assumed to act in one of the principal planes. Numerical studies are also presented, focusing on mono-symmetric cross-sections. As part of the numerical studies, first, the results of the new analytical formulae are compared to those from shell finite element analysis. The results suggest that the new formulae can capture the most essential elements of the behavior observed in the shell finite element calculations, justifying that the cross-section shape might have a significant effect on the nonlinear lateral–torsional behavior of beams. Then the effect of the lateral–torsional buckling is predicted by calculating buckling reduction factors, using the results of the geometrically nonlinear finite element calculations. The capacity prediction results, again, justify that the cross-section shape, as well as the sign of the assumed geometric imperfection, might have a non-negligible effect on the buckling reduction factors, and on the capacity of the member.

Analytical GNI Analysis for Lateral-torsional Behavior of Thin-walled Beams with Doubly-symmetric I-Sections

In this paper elastic lateral-torsional behavior of simple beams is discussed. The motivation of the presented research is the observation that classic analytical prediction and finite element prediction are, typically, considerably different, when the second-order nonlinear behavior of beams with initial imperfections is analyzed. In order to understand and explain the observed differences, a novel analytical solution is presented for the geometrically nonlinear analysis of beams with initial geometric imperfection. The presented analytical solution is derived for doubly-symmetric cross-sections, but with the novelty that it takes into consideration the changing geometry as the load is increasing. The most important steps of the derivations are summarized, and the resulted formulae are briefly discussed. Numerical studies are performed, too: the results of the new analytical formulae are compared to those from shell finite element analysis. The results suggest that the new formulae are able to capture the most important elements of the behavior. By the analytical and numerical results, it is proved that classic analytical solutions for the geometrically nonlinear analysis of beams with geometric imperfections are necessarily different from the numerical results obtained by incremental-iterative procedures.

Graded infill design within free-form surfaces by conformal mapping

The infill design for free-form surfaces is challenging due to the mismatch of both the geometric feature and physical response between the curved surface on the macroscale and the regular-shaped infill unit cells on the meso/micro scale. Thus, this study proposes a novel optimization method to provide insight into the optimal design for the free-form surfaces consisting of micro-structured infills, where both the microstructural geometry and macroscopic distribution of the spatial-varying infills are optimized concurrently. In this method, a local level sets approach is proposed to generate a series of graded and connectable infill microstructures that are related to the volume fraction of each unit cell. The cubic polynomials interpolation is utilized to predict the effective properties for those graded infills rapidly. A computational conformal mapping technology is used to map the geometries between a 3D free-form surface and a regular 2D parameter space, such that the graded infills can be properly filled into the parameter domain, and then conformally mapped back onto the free-form surface to allow the infill unit cells to fit the curved surface without losing any geometric feature. Conformal shell finite element analysis defined in an orthogonal curvilinear coordinate system is derived in the lower-dimensional parameter domain to calculate the physical responses for the infill optimization during the conformal mapping. The infill optimization formulation for the free-form surface is established, which is recast as a 2D optimization problem defined in the parameter domain, aiming at minimizing the structural compliance subject to a global volume constraint. Thus, the dimension of the 3D free-form surface design problem is reduced. Several examples of the free-form surface demonstrate the features of the proposed method.

Lateral-distortional buckling of steel-concrete composite beams: Kinematics, constrained-mode GBT and analytical formulae

This paper investigates and sheds fresh light on the kinematics and mechanics involved in the lateral-distortional buckling (LDB) behaviour (involving web single or double curvature) of simply supported I-section steel beams elastically restrained by concrete slabs under uniform negative (hogging) bending. The findings obtained are used to derive and illustrate the application of analytical formulae to calculate LDB moments of the steel-concrete composite beams considered. The study is based on a Generalised Beam Theory (GBT) approach to perform buckling analyses using constrained deformation modes that incorporate the displacement/rotation restraints, thus making it possible to obtain accurate buckling results with only a few deformation modes. The formulae provide the solution of the LDB equilibrium equation when only one or two constrained deformation modes are involved. Their merits and accuracy are assessed through the application to problems of practical interest – the LDB moments determined are compared with values (i) provided by other available formulae and/or (ii) obtained from conventional GBT, finite strip and/or Ansys shell finite element analyses. It is found that (i) the proposed constrained-mode GBT clearly outperforms the conventional one, both in structural insight and computational efficiency, and (ii) the derived analytical formulae consistently yield accurate LDB moment estimates.

Retrieving the GBT modal decomposition from large displacement shell finite element results

This paper proposes an efficient procedure to post-process non-linear shell finite element analysis results, in order to recover the unique modal decomposition features of Generalised Beam Theory (GBT). This procedure extends, to the large displacement range, a previous one developed for first-order elastoplastic, bifurcation and vibration analyses of thin-walled members (Manta et al., 2021). This means that the structural insight typically obtained through GBT analyses can be quite straightforwardly recovered from shell finite element collapse analysis results. The proposed procedure retrieves modal strains rather than modal displacements, since the GBT kinematic description is not suited to describe cross-section finite rotations. To show the capabilities and potential of the proposed procedure, two validation examples, in which a comparison with analytical solutions is made, and two application examples, involving large displacements and plasticity, are presented and discussed.

Parameters and Ratios of Metal Cylindrical Mesh Shells

Finite element modeling, calculation and analysis of metal cylindrical mesh shells are carried out. The choice of the surface topology is justified and the recommended ratios of overall dimensions are adopted. The criteria for determining the stability of the grid are given. The limits of permissible curvature and the main geometric parameters are obtained. The effect of increasing the rigidity and height of the structure on the work of the mesh surface is analyzed. Patterns of changes in nodal deviations and internal force factors of vulnerable areas of the shell are revealed. The results of changes in the shape and features of the critical deformation of the system are presented.

Geometrically nonlinear flutter analysis with corotational shell finite element analysis and unsteady vortex-lattice method

In this paper, an aeroelastic framework developed in the previous works has been extended for a geometrically nonlinear aeroelastic stability analysis. In the aeroelastic stability analysis, modal mass and stiffness matrices are constructed using shell finite elements with the corotational approach, which can take into account the geometric stiffening under large deformations. A generalized aerodynamic force matrix is derived by accommodating the unsteady vortex-lattice method based on a modal approach. The derived modal aeroelastic equations are solved using the p-k method. Individual modules to calculate generalized structural matrices with the corotational approach and aerodynamic forces based on the unsteady vortex-lattice method are verified. The present geometrically nonlinear aeroelastic framework for aeroelastic stability analysis is also validated in a comparison with an experimental result in the flutter wind tunnel test showing a reasonable accuracy for a prediction of flutter speed, while there still is room for further improvement in the estimation of flutter frequency. In addition, the present method allows studying the flutter characteristics of flexible wings with different incident angles, which cannot be evaluated by traditional linear flutter simulations. Finally, effects of geometric nonlinearity and large deformation on flutter characteristics of flexible and high-aspect-ratio wings were explored by using the present method. The present method can help to understand aeroelastic stability characteristics for such high-aspect-ratio wings.

Flexural–torsional failure and DSM design of fixed-ended cold-formed steel columns at elevated temperatures

Recently, Dinis et al. (2019,2020) reported in-depth numerical investigations showing that the current Direct Strength Method (DSM) global design curve may severely underestimate the flexural–torsional (FT) failure loads of fixed-ended cold-formed steel (CFS) columns with slenderness above 1.5. This finding was based on the analysis of columns exhibiting various cross-section shapes and geometries, and covering wide slenderness ranges. Moreover, these authors used the failure load data gathered to develop, and propose a novel DSM column strength curve set that was shown to improve considerably the FT failure load prediction for those columns. The purpose of this work is to extend the scope of the previous investigations to fixed-ended CFS cold-formed columns failing in FT modes under elevated temperatures (up to 800 °C). The results presented and discussed consist of column FT post-buckling equilibrium paths and failure loads, obtained through geometrically and materially non-linear Ansys shell finite element analyses — to ensure covering wide FT slenderness ranges, several room-temperature yield stresses are considered. The model prescribed in Part 1–2 of Eurocode 3, for cold-formed steel, is adopted to describe the temperature-dependence of the steel material properties. Lastly, the numerical failure loads assembled in this work, together with numerical and experimental ones collected from the literature, are used to propose a modification of the DSM-based FT strength curve set developed by Dinis et al. (2020), making it capable of handling FT failures under elevated temperatures. Since the merit assessment of the modified strength curve set shows a visible improvement in FT failure load prediction quality, it is fair to argue that it constitutes a good starting point to search for an efficient general DSM-based design approach for CFS columns failing in FT modes at elevated temperatures.

Analysis of pallet rack beam members through a nonlinear GBT formulation with sectional constraints

AbstractThin‐walled open cross‐sections are commonly used in steel storage pallet rack structures. In some cases, open sections are employed as beam members. These beam members usually have weld spots along their length in order to reduce the distortional deformation under a flexural load. On the other hand, beam members are typically connected to columns by means of claws, which typically exhibit a nonlinear moment ‐ rotation relationship. These two characteristic should be taken into account in order to properly reproduce their structural response.In this paper, the Generalised Beam Theory (GBT) is used to perform a geometrical nonlinear analysis of a pallet rack beam members taking weld spots and the beam‐to‐column connection behavior into account. The influence of the number and location of weld spots, as well as the beam‐to‐column connection behavior, in the distortional deformation of a beam member is evaluated by means of GBT nonlinear analyses. The results show that the use of a small number of weld spots could be enough to minimize the beam distortional deformation. Moreover, the stiffness of the beam‐to‐column connection also has influence on the beam distortional deformation. Finally, GBT results are successfully compared with shell finite element analyses.

A harmonic approach to the non-uniform torsion of box girder with edge cantilevers by fully considering the secondary torsional moment deformation effect

The restrained torsion analysis of open and purely closed cross-section thin-walled beams has been well addressed by applying the classical Vlasov and Benscoter non-uniform torsion theory, respectively. However, the warping torsion of the thin-walled box girder with wide overhanging slabs has to date received relatively less attention, although it exhibits notable and complicated shear lag phenomena. In this paper, a semi-analytical approach based on the harmonic analysis is presented to consistently take into account the secondary torsional moment deformation effect (STMDE) in edge cantilevers and closed cell of the box girder. The non-uniform warping and the associated strain field are reasonably determined by fulfilling the following requirements as (i) the longitudinal local equilibrium, (ii) the traction-free boundary conditions, and (iii) the shear flow continuity at joints connecting wall branches of the cross section. The advantage of the proposed method lies in that regardless of the applied loading and boundary conditions each harmonic term of the state variables can be manually determined to save a large amount of computing resources and time. Convergence study shows that the resulted Fourier series of state variables can be made converged if only first few terms are retained. Some benchmark problems, which primarily focus on thin-walled box girders having single- and multi-cellular cross sectional shapes under typical constraints and applied torques, are solved to demonstrate the reliability of the harmonic approach for non-uniform torsion of the box girder with edge cantilevers. It is shown by comparing with the results of shell finite element analysis that the semi-analytical solutions by the harmonic approach generally have better accuracy than the numerical results using 3D beam element with seven nodal degrees of freedom and analytical results by classical thin-tube theory (TTT).

Buckling of compressed plates with closed-section longitudinal stiffeners: Two new mathematical models for resistance prediction

Longitudinally stiffened plates appear in many structural engineering applications. One of the typical failure modes is induced by the buckling of the stiffeners, therefore enhancing our understanding of buckling behavior is of crucial importance. Recently, buckling resistance of longitudinally stiffened plates with trapezoid stiffeners has been investigated by numerous research projects. A large amount of capacity prediction data is available for stiffened plates with diverse geometries, obtained by advanced shell finite element analyses. In the research reported in this paper such data have been collected from two recent researches. Two mathematical models have been worked out for calculation of the load-bearing capacity, by curve fitting technique. The first developed method is similar to the Direct Strength Method: a single reduction factor is applied on the gross cross-section resistance in order to get the buckling resistance, and the reduction factor is calculated by one single Winter-type formula. The second method is based on the Effective Width Method, but for the middle part of the stiffened plate a further reduction factor is applied, which reduction factor is obtained from one single Ayrton-Perry-type formula. Though the two mathematical models show some differences in certain cases, they give very similar results, both leading to satisfactorily precise resistance values. The mathematical models have been applied to study buckling behavior, in order to understand how the plate geometry influences the resistance. The proposed mathematical models are potentially applicable in design calculations.

Geometrically nonlinear analysis of perforated rack columns under a compression load by means of Generalized Beam Theory

This paper presents a simplified methodology to take perforations in rack columns into account by means of a geometrically nonlinear Generalized Beam Theory (GBT) analysis. A new GBT formulation, which considers perforation effects through the addition of supplementary terms in the finite element internal force and tangent stiffness matrices during the member analysis, is developed and evaluated. The critical loads, ultimate elastic loads, equilibrium paths and displacement fields obtained by the GBT formulation with perforations are successfully compared using a shell finite element analysis for distortional and global dominant failure modes. Furthermore, the possibility to extend an equivalent thickness approach to handle rack columns perforations in a nonlinear buckling analysis is assessed. Finally, the influence of deformation modes and limitations of the presented GBT formulation are discussed.