Shell Finite Element Model Research Articles

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.

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.

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%.

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.

Out-of-plane behaviour of imperfect beam-column with sinusoidally corrugated web

This paper presents an analytical formula for the second-order normal stresses in flanges of the imperfect I beam-columns with sinusoidal web corrugation. To deduce the analytical expression, the beam is separated into three parts. The flanges are modelled as thin-walled beam-columns and the corrugated web is modelled as a thin equivalent orthotropic plate with uniform thickness. The indispensable elastic critical loads are derived from the total potential strain energy of the imperfect beam-column using an energy method. To assess the accuracy of the proposed analytical formula, full shell finite element models were created in Abaqus software. The result of the benchmark example showed that the derived expression is accurate and applicable for geometrically nonlinear analysis of beam-columns with sinusoidal web corrugation. Based on the proposed analytical expression, the Ayrton-Perry type solutions for corrugated web columns and beams are also presented in this paper.

Stability design of cold-formed high and ultra-high strength steel thin-walled box sections using effective stress-strain model

This paper proposes an effective stress-strain model for integrated analysis and design of cold-formed steel structures with thin-walled sections. The study focuses on square and rectangular hollow sections made from high and ultra-high strength steel. Initially, a shell-finite element model (SFEM) was developed and validated using experimental data, specifically for cold-formed members subjected to axial compression. Subsequently, a comprehensive parametric study is conducted to establish the stress-strain relationship model through nonlinear finite element analysis. The proposed model incorporates material nonlinearity, cold-forming effect, local plate imperfection, and residual stresses into a unified stress-strain curve, leading to advanced structural analysis and design of cold-formed structures using simple one-dimensional beam-column element. Subsequently, the proposed method is then implemented in the conventional finite beam-column element analysis, demonstrating consistent agreement with both experimental tests and sophisticated finite shell element results. Finally, the robustness and validation of the proposed method are established, and its application is exemplified through the design of a modular integrated construction (MiC) structure. This study highlights the versatility and reliability of the proposed approach for the analysis and design of cold-formed steel structures.

COMPARATIVE STUDY BETWEEN SHELL AND SOLID FINITE ELEMENT MODELS FOR STEEL JOINTS CHARACTERIZATION

AbstractSolid and shell finite element models (FEM) are two commonly used possibilities to analyse the structural behaviour of steel joints. The choice between solid and shell models often comes down to a balance between computational resources and the level of detail required for the study. In this paper, a set of welded beam‐column joints with hot‐rolled open sections is studied using both modelling techniques. The joints' behaviour is assessed in terms of resistance and initial stiffness. An improved shell FEM is proposed. The results indicate that for the studied dataset, both techniques return comparable results. Hence, the use of shell FEM seems to be a possible alternative to solid FEM and can be efficiently used for the joint characterization.

Bending resistance of austenitic stainless steel hollow sections at elevated temperatures

The present research aims to increase the knowledge of the structural behaviour of stainless steel members under fire. Eight experimental bending tests at elevated temperatures (500, 700 ºC) built with RHS 150×100×3 austenitic stainless-steel beams, using two different grades (1.4301, 1.4571) also known as 304 and 316Ti, are presented. Both grades 1.4301 (X5CrNi18–10) and 1.4571 (X6CrNiMo17–12–2) have almost the same core chemical composition but there are some differences, especially the grade 1.4571 has 2–2.5% molybdenum and a small amount of titanium (less than 0.7%). Grade 1.4301 presents good rust resistance, sufficient acid resistance and good weldability, while grade 1.4571 presents very good rust resistance, very good acid resistance and also good weldability. Both have almost the same strength, but grade 1.4571 has superior strength at elevated temperatures. Both material grades were experimentally characterised with coupon tensile tests at room temperature. The load-displacement behaviour is validated with 3D shell finite element models, assuming a true stress-strain material model, based on the two-stage Ramberg Osgood constitutive law. With the developed numerical model, a parametric analysis is presented to study the fire resistance of beams from both materials, using three different cross-sections and eleven different temperatures. The bending resistance obtained with the finite element model is in good agreement with the cross-sectional design moment resistance, when considering the effective area, confirming that the design rules from EN1993–1–2 are safe for less slender cross-sections and unsafe for the most slender cross-sections.

GMNIA with beam elements and strain limits based fire design approach for steel beams and beam–columns

The use of advanced analysis techniques harnessing the capabilities of the currently available computational resources can lead to considerably more accurate fire design of steel structures relative to the currently adopted simple fire design methods in practice. In this paper, a structural steel fire design method by Geometrically and Materially Nonlinear Analysis with Imperfections (GMNIA) and using strain limits is put forward for the fire design of steel beams and beam–columns. In the proposed fire design method, the GMNIA of a steel member or structure is performed using computationally efficient beam finite elements and strain limits are adopted to account for the detrimental effects of local buckling on the ultimate capacities. To verify the accuracy of the proposed method, extensive numerical parametric studies are conducted through shell finite element modelling. The results indicate that the proposed approach provides accurate and safe ultimate resistance and limit temperature estimations for steel beams and beam–columns in fire, with a considerably higher level of accuracy and reliability relative to the provisions of the European structural steel fire design standard EN 1993-1-2.

An equivalent spring model for seam-clip connections of high-vertical standing seam metal cladding systems

The mechanical behavior of the seam-clip connections plays a pivotal role in the effective wind resistance design of the extensively used high vertical standing seam metal cladding system (SSMCS). An equivalent spring model is developed to represent the mechanical behavior of these connections to simplify the contact problems in the general finite element model, which is time-consuming due to the highly nonlinear contact boundary conditions. The developed model is composed of continuous horizontal and rotational springs as well as dispersed vertical rigid connections. A series of tensile experiments are first conducted to investigate the mechanical behavior of seam-clip connections to calibrate the spring parameters in the developed model. Subsequently, the equivalent spring model is validated by the structural response of a double-span sheet module (DSSM) using experimental investigation and finite element analyses. It is found that the shell finite element model incorporating the developed equivalent spring model can achieve an acceptable structural response while remarkably reducing memory requirements and computational time to about 0.3 % and 0.4 ‰, correspondingly, compared to the contact boundary condition analysis. It highlights the advancement in evaluating the structural response of high-vertical SSMCS in practical engineering applications using this developed model. Furthermore, the developed equivalent spring model has proved to be effective in predicting wind-induced seam-clip pullout failures according to the established failure criteria derived from the structural response of the system.

Thermal-dynamic coupling analysis of space truss antennas in actual space thermal environment

Space truss antennas may undergo thermally induced vibration due to temperature changes caused by thermal mutations in the space environment, which will result in antenna performance degradation or even vibration failure. This paper aims to investigate the thermal-structural coupled dynamics of a space truss antenna in the orbital space thermal environment. A spatial thermal analysis model is established based on the spatial heat flux model, Fourier-temperature element, finite element method (FEM) and astrometric model to calculate temperature variation of the antenna structure during its operation in orbit. In this model, the effective solar heat flux received by the antenna structure is calculated on the basis of an astrometric model, with consideration of the Earth's shadow effect and the shading effect of the reflective surfaces. Additionally, a thermo-structural coupled dynamic model of the antenna structure is constructed considering the coupled effects of structural deformation and absorbed effective solar heat flux, which was validated using a finite element shell model. Numerical cases are arranged to comparatively analyze the thermal-structural coupling effects, light shading by reflective surfaces, and thermodynamic response during the space operation cycle, respectively. It is demonstrated that both the earth shadow effect and the shading effect of components have great effect on the temperature distribution and variation of the antenna structure. Moreover, significant vibrations will occur at certain moments especially when the thermal radiation flux to the structural components changes suddenly due to light shading from the earth shadow and reflective surfaces. The thermal-structural coupling dynamic model of the antenna structure presented in this work can provide guidance for thermal compensation and thermal-induced vibration attenuation of truss antenna structures.

Refined beam finite element model for thin-walled multi-cell box girders considering distortion and secondary distortional moment deformation effect

In this paper, a novel one-dimensional refined beam finite element model (FEM) accounting for non-uniform distortional warping and secondary distortional moment deformation effect (SDMDE) is formulated for the distortional analysis of thin-walled multi-cell box girders with cantilevered flanges. The extra distortional angle is introduced to incorporate SDMDE, and the validity of which is proved through rigorous theoretical derivation. The in-plane and out-plane deformations at any point around the edge of transverse section built upon the distortional center are unified in the same form and described in detail. The governing differential equations in terms of two generalized displacements, distortional angle χ and primary distortional angle curvature Θ, are derived based on the principle of minimum potential energy (MPE) and solved exactly so as to provide non-polynomial shape functions for the establishment of element stiffness matrix and nodal load vector. A series of multi-cell rectangular hollow section (RHS) girders are analyzed and particular extensions are given to single-cell and multi-cell bridge girders with cantilevered flanges. Comparisons to the results generated from corresponding ones provided by pioneering work or shell FEM analyses not only validate the correctness and reliability of the present beam element formulations but also highlight the significance of the inclusion of SDMDE when the cantilevered flanges are arranged.

A Seven-Parameter Spectral/hp Finite Element Model for the Linear Vibration Analysis of Functionally Graded Shells with Nonuniform Thickness

This contribution presents a finite element shell model capable of performing linear vibration analyses of shell-type structures made of functionally graded material (FGM). The model is based on the seven-parameter spectral/hp finite element formulation, which allows the analysis ofFG shells of either uniform or nonuniform thickness. Equations of motion are derived using the Hamilton’s principle and the material properties of the constituents are considered to follow a power-law volume distribution through the thickness direction. The verification of the present model is carried out by comparing with numerical results available in the literature, and with numerical simulations performed in a commercial software. To demonstrate the capabilities of the present formulation, the free vibration response of different shell structures, with nonuniform thickness, to the variation of the geometrical parameters (e.g., radius-to-thickness ratio) and the mechanical properties is reported.

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].

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.

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.