Shell Finite Element Research Articles

Nonlinear Model for LTB Prediction of RHS Beams Under Combined Axial and Bending Loads With Distortional Deformation Allowed

ABSTRACTThe aim of the present study is to develop an efficient and accurate analytical model for the lateral torsional buckling (LTB) prediction of RHS beams. To this end, a coherent nonlinear geometric theory is formulated assuming large torsion angles. This theory is based on a new kinematic model that incorporates the distortion deformations in addition to the bending and torsion ones. Ritz's method is employed to discretize the governing equilibrium equations basing on trigonometric shape functions, and then the eigenvalue problem is defined according to the fundamental state. The Buckling loads are obtained by imposing the singularity condition of the tangential stiffness matrix. The numerical investigation is carried out to prove the accuracy of the proposed model in LTB load evaluation, when compared with the nonlinear shell finite element simulation using Abaqus software. The numerical results reveal that the classical linear models associated with moderate torsion angles, such as those provided by Generalized Beam Theory (GBT) and the classical eigenvalue shell finite element method, tend to underestimate the correct value of LTB loads of simply supported RHS beams. In accordance with linear and non‐linear models, the numerical study is focused on the impact of load height, intensity of introduced compressive load and section ratio b/h in the LTB loads prediction.

Numerical and experimental investigation on angle multiple slit bolted connections for precast wall panels

Flat Multiple Slit Devices (MSDs) have been introduced in steel constructions located in earthquake-prone areas as compact hysteretic dampers connected to braces, and were further proposed to be employed also in other structural typologies, including aligned precast concrete walls. Nevertheless, similar angle connections needed for horizontal joints of orthogonal walls are not tackled in literature. The shape of MSDs, obtained by selective weakening by removing part of the steel area of flat plates, may allow to attain a highly ductile and stable dissipative behaviour, given local plate buckling is avoided, protecting the bolted joints through capacity design. Laser cutting as an alternative to mechanical milling introduces the possibility to easily optimise the shape of the slits in order to attain better performance under laterally imposed cyclic load. This paper analyses the application of right-angle-bent MSDs for the horizontal connection between orthogonal precast walls typical of panel structures with rigid diaphragms. In particular, bolted angle plates with hourglass-shaped multiple slits obtained after laser cutting are investigated numerically via non-linear finite shell elements and experimentally with original cyclic tests. The effect of the aspect ratio of the plate and of the restraint condition, possibly affecting the performance under imposed shear deformation due to the presence of the bent corner, is investigated by parametric analysis. Finally, general design rules and recommendations are presented.

Lateral-Torsional Failure and DSM Design of CFS Lipped Channel Beams at Room and Elevated Temperatures

About a decade ago, in-depth investigations on the behaviour of cold-formed steel (CFS) single-span simply supported lipped channel beams failing in lateral-torsional modes at both room and elevated temperatures were reported at QUT (Queensland Technical University). They revealed a significant underestimation of the lateral-torsional (LT) failure moments by the Direct Strength Method (DSM) global design curve at room temperature, then codified in the Australian/New Zealand and North American specifications. In order to remedy this situation, these authors proposed two novel DSM-based beam strength curve sets, which were found to substantially improve the LT failure moment prediction quality, both at room and elevated temperatures. This work aims at extending the scope of the above investigations, by analysing a visibly larger set of CFS lipped channel beams at elevated temperatures (up to 800 °C), exhibiting (i) various cross-section dimensions and yield stresses, selected to cover wider LT slenderness ranges, (ii) two end support conditions, differing only in the end cross-section wall displacement/rotation and warping restraints (either fully free or fully prevented), and (iii) temperature-dependent steel material properties according with the model prescribed in Part 1-2 of Eurocode 3. The results presented and discussed consist of beam LT post-buckling equilibrium paths and failure moments, obtained through Abaqus shell finite element GMNIA that include critical-mode (LT) initial geometrical imperfections. Lastly, the numerical failure moment data obtained in this work and reported in the literature are used to develop and propose a new unified set of DSM-based strength curves capable of adequately handling beam LT failures at room or elevated temperatures. Since it is shown that the proposed strength curve set provides a quite good LT failure moment 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 beams failing in LT modes at room and elevated temperatures.

Vibration analysis of rotating variable-angle-tow composite cylindrical structures via high-fidelity shell models

The paper focuses on rotordynamics analyses of various rotating variable-angle-tow (VAT) composite cylindrical structures using both low- and high-fidelity structural models. To model the spatially varying composite shell structures, the Carrera Unified Formulation (CUF) is employed. The CUF provides a hierarchical and automated approach for developing shell finite element models. Various shell models are created using different kinematics models based on Taylor or Lagrange expansion functions. The linearized equations of motion include the Coriolis and initial stress contributions. Several VAT composite curved panels and thin and thick cylinders have been analyzed to validate the presented approach and provide benchmark solutions. The results are discussed and compared with commercial software solutions. The results demonstrate the good accuracy and reliability of the proposed numerical methodology.

Fabric soft pneumatic actuators with programmable turing pattern textures

This paper presents a novel computational design and fabrication method for fabric-based soft pneumatic actuators (FSPAs) that use Turing patterns, inspired by Alan Turing’s morphogenesis theory. These inflatable structures can adapt their shapes with simple pressure changes and are applicable in areas like soft robotics, airbags, and temporary shelters. Traditionally, the design of such structures relies on isotropic materials and the designer’s expertise, often requiring a trial-and-error approach. The present study introduces a method to automate this process using advanced numerical optimization to design and manufacture fabric-based inflatable structures with programmable shape-morphing capabilities. Initially, an optimized distribution of the material orientation field on the surface membrane is achieved through gradient-based orientation optimization. This involves a comprehensive physical deployment simulation using the nonlinear shell finite element method, which is integrated into the inner loop of the optimization algorithm. This continuous adjustment of material orientations enhances the design objectives. These material orientation fields are transformed into discretized texture patterns that replicate the same anisotropic deformations. Anisotropic reaction-diffusion equations, using diffusion coefficients determined by local orientations from the optimization step, are then utilized to create space-filling Turing pattern textures. Furthermore, the fabrication methods of these optimized Turing pattern textures are explored using fabrics through heat bonding and embroidery. The performance of the fabricated FSPAs is evaluated through three different deformation shapes: C-shaped bending, S-shaped bending, and twisting.

DSM design of cold-formed steel fixed-ended lipped channel columns undergoing distortional-global interaction

This work reports a numerical investigation dealing with the post-buckling behaviour, strength, and Direct Strength Method (DSM) design of cold-formed steel fixed-ended lipped channel columns experiencing coupling between distortional and global (flexural-torsional) buckling − distortional-global (D–G) interaction. Various cross-section dimensions and lengths are considered, to ensure that the columns selected undergo different levels and types (“true”, “secondary-bifurcation distortional” or “secondary-bifurcation global”) of D–G interaction. The results presented and discussed, determined by means of Abaqus shell finite element geometrically and materially non-linear analyses, consist of elastic and elastic-plastic post-buckling equilibrium paths, failure loads and collapse modes. The steel material behaviour is deemed elastic-perfectly plastic and several yield stresses are considered, thus making it possible to cover a wide column D–G slenderness range. Particular attention is devoted to identifying the most detrimental initial geometrical imperfection shapes, in the sense that they lead to the lowest column failure loads. The numerical failure load data gathered are subsequently used to assess the merits of the available DSM-based design approaches developed to handle cold-formed steel columns undergoing D–G interaction. Since these design approaches are shown to be either inefficient and/or improvable, the above failure load data are also used to propose modifications/improvements aimed at achieving an efficient failure load prediction in the specific context of fixed-ended lipped channel columns. The success of this endeavour provides encouragement to the authors in their search for a safe, accurate and reliable DSM-based design approach capable of handling cold-formed steel columns with arbitrary cross-section shapes and/or end support conditions that fail in D–G interactive modes.

First-order GBT for truncated conical shells with circular cross-section

This paper presents a new and general first-order Generalized Beam Theory (GBT) formulation for thin truncated conical shells with circular cross-section. With respect to the previous formulations (Nedelcu, 2011; Mureşan et al., 2019), which were developed for the linear stability analysis case and therefore only required the consideration of rather simple load cases, the present one keeps all membrane strain terms and therefore is able to enforce the standard GBT membrane strain assumptions exactly. Even if the resulting expressions and the boundary conditions are more involved, it is shown that it is possible to define the so-called GBT “Vlasov warping deformation modes” also in the conical case, which are essential for the overall performance of the formulation. For instance, these deformation modes allow finding the shell inextensible deformation shapes. Several numerical tests are presented to show the excellent performance of the resulting finite element, through comparison with refined shell finite element models, and the advantages offered by the GBT modal decomposition features.

Numerical study of high-velocity impact on aeronautic carbon composites

This paper presents research concerning the numerical analysis of two new carbon composite materials subjected to high-velocity impact. These new composites were produced using new out-of-autoclave processes, making them more environmentally friendly. An experimental campaign was conducted on these materials in order to determine the effects of a metal sphere during impact. A numerical model using ABAQUS explicit is assembled using shell finite element models, and a non-linear dynamic analysis is applied. For the constitutive relation of the material, a fiber-reinforced composite damage model from the ABAQUS library is used. This initial numerical model is then compared with the outputs of the experimental campaign in order to validated it. Next, a numerical campaign is performed to understand carbon composites response to the impact of a hailstorm strike, in which it is possible to verify that one of the specimens presented higher performance, by displaying less penetration and damaged area.

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.

Pin-ended stainless steel equal-leg angle section members under compression and major-axis bending: Experimentation, FE modelling and design

The 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. An experimental investigation, including material testing, initial geometric imperfection measurements and physical tests on hot-rolled stainless steel equal-leg angle section members is first presented. 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 cylindrically-pinned 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. The reliability of the new design provisions, with a recommended partial safety factor γM1=1.1, is verified following the EN 1990 procedure.

Design and analysis of a conical origami tube (COT) composed of quadrilateral unit cells

Kresling origami is a topic that is constantly being researched, especially when it comes to the cylindrical mechanisms made up of special quadrilateral units. It’s also fascinating that the conical mechanisms based on the Kresling pattern are gaining more attention lately. However, designing conical mechanisms with stable behavior and solving the stress concentration in crease areas for practical engineering applications remains less researched. Therefore, this study considers quadrilateral unit cells as the research object, designs a conical origami tube (COT), and establishes a theoretical model with five variables to systematically investigate the COT. Based on this, the design domain related to the design variables is proposed, and the COT is analyzed in three cases. We further explored the influence of η (conical degree) on the COT. In addition, this study implements a cutting design on each crease vertex to reduce the impact of stress concentration on the nonlinear response through finite element shell models and uniaxial compression experiments. The findings of this study reveal that the setting of η and the crease-cutting design have a remarkable impact on the mechanical properties and stability behavior.

Strength design of built-up radially battened columns subject to axial compression and arbitrary directional bending moment

Built-up radially battened columns (RBCs), comprising several identical circular steel tubes interconnected by multiple radial-shaped battens, represent an innovative column design that combines aesthetic appeal with exceptional load-bearing capacity. This makes them well-suited for architectural applications in large public buildings such as stations and airports. The axial compressive strength design methods for the built-up RBC have been extensively explored in the authors' prior studies. However, in real-world engineering applications, built-up RBCs may experience simultaneous axial compression and varying directional bending moments, particularly when considering potential eccentric compression or wind and earthquake loads in public buildings. Currently, strength design methods for this loading condition are still lacking. To address this deficiency, this paper primarily delves into the failure mechanism and strength design methods for built-up RBCs experiencing combined axial compression and arbitrary directional bending moments. Initially, the sectional strength of the built-up RBC is investigated by using a shell finite element model (FEM) for the built-up RBC. It is revealed that the compression-bending sectional strength of the built-up RBC exhibits significant differences with varying bending directions and tube numbers. Moreover, in some bending directions, the M-N sectional strength curve of the built-up RBC exhibits convexity. By integrating theoretically derived equations grounded in the principles of materials mechanics with FEM numerical calculations, concise and practical design equations are proposed for accurately predicting the sectional strength of the built-up RBC under combined axial compression and arbitrary directional bending moments. Subsequently, The buckling strength of the built-up RBC is studied using the FEM, considering initial geometrical imperfections consistent with first-order flexural buckling and accounting for geometric nonlinearity. It is noted that the bending direction of the built-up RBC may deviate during loading. Besides, the M-N buckling strength curve of the built-up RBC is not as convex as its M-N sectional strength curve. Based on calculations from numerous examples, practical design equations for predicting the buckling strength for the built-up RBC under axial compression and any directional bending moments are introduced. The key findings of this paper contribute to the compression-bending strength design of RBCs, enriching RBC design theory and promoting the widespread application of built-up RBCs in actual engineering projects.

Research of the accuracy and efficiency of typical structures using wave shell finite element models

Research of the accuracy of wave shell finite element models was carried out. The results were compared with the results of analytical calculations. According to the research results, for all considered vibration modes of standard structures, the discrepancy in the values of natural frequencies does not exceed 5%.

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.

Influence of perforation on static characteristics of the enclosing corrugated panel under the wind action

The application of the enclosing panels with perforation in construction practice for protective structures is economic advantageous due to reduction of financial costs for their production, transportation and installation. But influence of perforation on static and dynamic characteristics of the enclosing panels was not enough investigated. With the purpose of wind protection of the buildings and structures at the Ukrainian Antarctic station „Akademik Vernadsky” static stress and stability analyses of the protective structure were executed in according with the first and second groups of limit states of State building regulations of Ukraine. The protective structure as the enclosing corrugated steel panel and supporting columns was appeared. In the article the results of numeral research of the stress strain state and stability of the corrugated panel are presented. The panel width and height were accepted permanent, and a panel thickness was explored and accepted according to requirements for its stiffness, strength and stability. The four corrugations in the form of trapezoids are located along the panel height. Perforation of the panel in the form of round holes with a radius of 12.5 mm was presented. Two finite element models of the corrugated panel using the software NASTRAN were built. The corrugated panel without perforation model as a collection of rectangular shell finite elements with six degrees of freedom at the node was modeled. This model contained 35161 finite elements and 32540 nodes. The finite element model of the enclosing corrugated panel with perforation contained 383043 triangular shell finite elements with six degrees of freedom at the node and 211609 nodes. Boundary conditions were imposed on the modal nodes along the height on both sides of the corrugated panel in the form of fixing, taking into account its rigid attachment to the columns. Wind action on the enclosing panel was presented as uniform distributed static load, the limit calculation values of which were got according to State building regulations of Ukraine and statistical data of wind at the Ukrainian Antarctic station. The main attention was given to research of influence of perforation on the corrugated panel equivalent stresses and displacements, critical values of wind load and form of loss of corrugated panel stability. Computational procedures of static stress and stability analyses of software NASTRAN were applied.

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.

Ultimate bearing capacity analysis of self-anchored suspension bridge with steel box girders considering local buckling

The local stability may dominate the design of a self-anchored suspension bridge with steel box girders. Due to geometric imperfections and welding residual stresses rarely considered for its ultimate bearing capacity analysis, the influences of the local buckling on the global structural behavior remain unknown. This paper presents a multi-scale finite element (FE) model for a self-anchored suspension bridge incorporating geometric imperfections and residual stresses in a steel box girder segment simulated by shell elements. Also, the pattern considering the defects in the shell FE model is validated by experiments. An extended parametric study is carried out via multi-scale FE models under various defects. Results illustrate that: ➀ the effects of local buckling on the ultimate bearing capacity of the bridge is small and can be ignored if geometric imperfections and residual stresses are not considered; ➁ the influences of local buckling becomes significant if geometric imperfections and residual stresses are included; and ➂ ultimate bearing capacity decreases with increase of defects, with geometric imperfection being the main factor influencing the ultimate bearing capacity of the bridge. Additionally, the thickness of steel plates has significant influences on the ultimate bearing capacity of the bridge. A comparison between the EN 1993–1-5 and the FE analysis results indicates that the former is conservative. This study provides useful insights for analyzing and designing local buckling from the perspective of steel bridge system.

A modeling strategy for the simulation of box sections with layered shell elements

This paper presents a numerical strategy to model box sections from bridge girders using horizontal layered shell finite elements. The basic idea is to avoid the construction of more computational expensive meshes based on the use of folded shell and brick finite elements. The numerical strategy imposes the deactivation of those layers related to empty spaces within the bridge cross-section. The performance of this technique is explored by means of two demanding practical applications related to bridge structures with constant and variable deck thicknesses. The first application deals with the static truck load test of the Caynarachi Bridge, located in Peru, and for which measured field data exists, while the second application is related to the construction stage analysis of a box bridge structure including time effects due to concrete creep, shrinkage and steel relaxation. The results demonstrate that the studied technique acceptably correlates with the measured field data,expressed in terms of vertical displacements,with correlation coefficients exceeding 0.94.Additionally, the outcomes align well with the results of other numerical techniques, allowing applicants to use this simplified modeling approach in daily design office.

Fluid-Structure Interactions Response of a Composite Hydrofoil Modelled With 1D Beam Finite Elements

_ In this paper, the hydroelastic response of a NACA0015 composite hydrofoil is studied experimentally and numerically. The foil is made of composite materials with fibers not aligned with the span of the foil, which results in the occurence of a bend-twist coupling in the material. Computations are performed using a partitioned approach. The flow problem is solved using a boundary element method. The structural response of the foil is modelled with two different finite element models. In the first one, the foil is modelled with 2D shell and 3D solid finite elements and in the second model, the foil is modelled with 1D beam finite elements. The experiments are conducted in an open circulation water channel. Hydrodynamic forces and structural displacements are measured for several angles of attack, free stream velocities and submergence depth. This paper shows that the mechanical behaviour of a composite hydrofoil submitted to hydrodynamic loads can be modelled with 1D beam finite elements. This model gives results very similar to a finite element analysis realized with 2D shell and 3D solid finite elements, which are commonly used to model composite structures. The present work also shows that the experimental results can be well predicted by numerical simulations, but it requires a precise modeling of the bend-twist coupling in the materials constituting the foil. Keywords Hydrofoil; Equivalent Beam; Fluid-Structure Interactions; Composite; Bend-Twist Coupling

Experimental and Numerical Analyses of Timber–Steel Footbridges

In addition to traditional building materials, such as steel and concrete, wood has been gaining increasing prominence in recent years. In the past, the use of wood was limited due to its susceptibility to damage by fungi, insects, and temperature. These shortcomings were gradually eliminated as the quality of wood processing increased and thanks to modern high-quality insulating and protective materials. The return to the utilisation of this natural building material was also supported by the development of new wood-based materials, such as glued laminated wood, and new types of mechanical fasteners, as well as by the introduction of new design methods provided in the Eurocodes. Within this context, this paper focuses on using wood in transport infrastructure, especially as the basic material for footbridges and small road bridges. Combined timber–steel bridges emerge as a very effective type of superstructure in contemporary road bridges and footbridges, especially in areas with natural exposure. Usually, wood is used for the main bridge girders, while steel is preferred for bridge deck elements—stringers and cross-girders. The results of this parametric study offer optimal structural solutions for footbridges with spans of 12.0–24.0 m, reflecting satisfactory static and dynamic footbridge behaviour. Particular attention is paid to a problematic structural detail—the connection between the steel cross-girder and the timber main girder. Firstly, this connection’s characteristics were measured experimentally using nine laboratory samples made of two glued laminated timber blocks, simulating main girders connected with a hot-rolled steel cross-girder. The connection was prepared in three variants, with different heights of the end plates and different numbers of bolts. Subsequently, these characteristics were computed using two numerical FEM models. The first model was created using SCIA Engineer software with a combination of shell and beam finite elements. The second, more sophisticated model was created in the ANSYS software environment using 3D finite elements, allowing us to better take into account the plasticity and orthotropic properties of wood and the points of contact between the individual members. Finally, the experimental results produced by sample testing in the laboratory were compared to the outputs of FEM numerical studies.