Shell Elements Research Articles

Simplified Models to Assess the Mechanical Performance Parameters of Stents.

Ischemic heart disease remains a leading cause of mortality worldwide, which has promoted extensive therapeutic efforts. Stenting has emerged as the primary intervention, particularly among individuals aged 70 years and older. The geometric specifications of stents must align with various mechanical performance criteria outlined by regulatory agencies such as the Food and Drug Administration (FDA). Finite element method (FEM) analysis and computational fluid dynamics (CFD) serve as essential tools to assess the mechanical performance parameters of stents. However, the growing complexity of the numerical models presents significant challenges. Herein, we propose a method to determine the mechanical performance parameters of stents using a simplified FEM model comprising solid and shell elements. In addition, a baseline model of a stent is developed and validated with experimental data, considering parameters such as foreshortening, radial recoil, radial recoil index, and radial stiffness of stents. The results of the simplified FEM model agree well with the baseline model, decreasing up to 80% in computational time. This method can be employed to design stents with specific mechanical performance parameters that satisfy the requirements of each patient.

Dynamic analysis with point-masses of perforated pallet rack structural members by means of the Generalized Beam Theory

This paper presents two different formulations for introducing point-masses into a dynamic problem using the Generalized Beam Theory (GBT) method. The first one implies placing a point-mass at a beam-node (with or without eccentricities) while the other implies placing a point-mass at a cross-section node. In order to evaluate the accuracy of such formulations, different modal analyses of members have been performed using GBT beam elements, shell elements and classical beam elements. The values of natural modal frequencies obtained through different models have been successfully compared. The results of various harmonic analyses are also presented. Some of the studied structural members include perforations. Finally, the influence of GBT modes and perforations when using point-masses is discussed.

Development of Higher Order Stiffened Shell Element (HOST9) for the Static Analysis of Stiffened Laminated Plates

Abstract A new higher order stiffened shell element (HOST9) is developed comprising of a 9 noded flat shell element and a 3 noded stiffener element for analysis of stiffened laminated plates. The shell element is a lagrangian element. The stiffener is a beam element. The stiffness of the stiffener is computed separately and added to that of the shell element at appropriate locations. As a result, the stiffener can be located arbitrarily in the shell element. Static analysis of stiffened laminated plate is carried out using the newly developed element and is validated with the existing literature. It is seen that the proposed element gives comparable results and can be used for the analysis.

Modeling and vibration analysis of an aero-engine dual-rotor-support-casing system with inter-shaft rub-impact

In order to reveal the nonlinear dynamics of dual-rotor-support-casing system, a numerical procedure is proposed using the finite element method and the component mode synthesis method. Especially, the casing system is subdivided into the casings, struts and housings, which are modeled by shell elements, beam elements and rigid regions with mass elements, respectively. Furthermore, the inter-shaft rub-impact, which may occur in the aero-engine because of imbalance and other faulty, is considered in the dynamic model as a nonlinear excitation. The modal analysis verified the validity of the dual-rotor-support-casing system model. The motion equations are established using the reduced-order model and solved by Newmark-β method with Newton-Raphson iteration. The results show that larger rubbing stiffness will cause the rubbing to enter a self-excited vibration state, and the rotational speed ratio will change the speed region where the self-excited vibration occurs. Finally, the experiment is performed based on a real dual-rotor aeroengine under inter-shaft rub-impact and the results are consistent with the theoretical results, which proves the effectiveness of dual-rotor-support-casing system dynamic model.

Study on dynamics of thin shell elements of composite materials based on absolute nodal coordinate formulation

Most solar panels use composite materials to suit the development objectives of large-scale and lightweight spaceship components, resulting in complex nonlinear dynamic characteristics. When describing the dynamic characteristics of thin shell elements in composite materials, the standard 48-DOF fully parameterized thick plate element based on absolute nodal coordinate formulation cannot accurately account for the coupling between the large range of motion and large deformation of thin shell elements, exposing issues such as shear locking, slow convergence, and low computational efficiency. In this study, the absolute nodal coordinate formulation is used to create the 36-DOF reduced-order composite thin shell element. The strain and strain energy of the thin-shell element are calculated using the Green-Lagrange strain tensor, while the bending deformation energy of the thin shell element is calculated using the exact expression of curvature, based on continuum mechanics theory and the constitutive relation of the composite material. The generalized mass matrix and stiffness matrix are developed, and the nonlinear dynamic model of the thin shell element is established using the virtual work principle, with numerical simulation used to validate the dynamic characteristics. The results reveal that the dynamic characteristics of the 36-DOF reduced-order composite thin shell element are consistent with those of the virtual prototype, confirming the validity of the model. The proposed model not only addresses the element locking issue, but it also creates a more realistic dynamic model and increases simulation accuracy. The findings could serve as a theoretical foundation for satellite solar panel on-orbit operations.

Nonlinear inelastic behaviors of concrete-filled steel tubular beam-column structures

A new advanced method combining stability function and distributed plasticity model has been developed using Fortran programming language to predict the nonlinear inelastic behavior of concrete-filled steel tubalar (CFST) under static loading. The advantage of this method is the ability to accurately study the nonlinear behavior using only one or two beam-column elements per member instead of using solid and shell elements as traditional methods, thereby improving the model analysis time. The Generalized Displacement Control (GDC) algorithm, capable of analyzing beyond the limit point, will be used to solve the nonlinear equilibrium equations instead of the traditional Newton-Raphson algorithm. The element stiffness matrix is integrated through the Gauss-Lobatto numerical integration framework, while the nonlinear geometric effects P-Δ and P-δ are considered using stability functions and a corresponding geometric matrix. The reliability and accuracy of the proposed method are verified by comparing the analysis results with experimental data. The obtained results have demonstrated that using beam-column elements for simulation, the proposed method still provides accurate results while significantly reducing computational resources. Therefore, this new method holds promise as a useful tool for practical design and analysis of statically loaded CFST structures.

Modelling of welded aluminium connections in large-scale analyses

This article addresses large-scale analyses of welded aluminium connections where the weak zones are to be represented by a few shell elements. A combined experimental and numerical study on the behaviour and modelling of welded aluminium connections is presented, where a shell-element modelling framework applicable in large-scale analyses is proposed, accounting for geometrical instability, thinning, and ductile fracture. The proposed modelling framework is calibrated and validated using cross-weld tension tests. The test campaign involves tension testing of two Al–Mg–Si alloys and two welding techniques widely used in industrial applications. The shell-element simulations represented the response of the tests reasonably well.

Simulation of the Performance of Kevlar Impregnated Shear Thickening Fluid Ballistic Test Results (STF) Ballistic Test Results

This study explores the enhancement of Kevlar fabric’s ballistic performance through impregnation with Shear Thickening Fluid (STF) for potential application in soft body armor. The experimental approach often fails to elucidate mechanical phenomena critical for the development of lightweight and high-strength body armor designs. To address this limitation, the finite element method, specifically using ANSYS/LS-DYNA R.13, was employed for a comprehensive analysis. The simulation aimed to evaluate the impact of STF on Kevlar fabric by assessing projectile velocity, force exerted by the projectile onto the fabric, displacement, stress distribution, and fabric failure mechanisms. Kevlar yarn was modeled as a shell element formed into fabric with a sine wave profile, investigating two types of STF: SiO2-PEG200 (S0) and SiO2-PEG200-B4C (S1), differing in maximum viscosities. The addition of STF resulted in increased coefficients of friction on Kevlar, with the highest values observed for the SiO2-PEG200-B4C impregnated fabric ( =0.87 and =0.82). The incorporation of the second STF type (S1) significantly reduced the projectile’s velocity from an initial 200 m/s to 153.2 m/s upon impact. Additionally, the force on the S1 fabric surged to 121,556 N, a threefold increase compared to neat Kevlar. STF's influence was further evidenced by enhanced fabric displacement and more uniform stress distribution upon ballistic impact. The fabric's thickening upon failure indicated STF's ability to enlarge the deformation area, facilitating uniform distribution of ballistic kinetic energy across the impact zone. Notably, the fabric impregnated with the second type of STF, featuring boron carbide (S1), demonstrated superior ballistic performance. This study concludes that STF-impregnated Kevlar fabric, particularly the SiO2-PEG200-B4C variant, not only surpasses the ballistic performance of neat Kevlar but also meets the criteria for NIJ Level IIIA standards, highlighting its potential as a highly effective material for advanced soft body armor designs.

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.

Deployment Simulation of Foldable Membranes Using Absolute Nodal Coordinate Formulation and Validation

It has become a trend to use foldable membranes to construct large spacecraft structures such as solar sails, antennas, and drag sails with the advantages of being lightweight and having high packing efficiency. To enhance the existing numerical simulation of membrane deployment, the nonlinear behavior of the crease is finely described based on experiments and integrated into the numerical model via the principle of virtual work. Specifically, a foldable membrane is modeled as a multibody system (MBS) based on the absolute nodal coordinate formulation (ANCF), where the flexible facet is meshed with both ANCF triangular and quadrilateral thin shell elements and the crease is treated as a virtual torsional spring with special constraints along the fold line. The MBS modeling method is validated via the deployment experiment of a Z-folding membrane. The deployment of a four-unit Miura-ori membrane is further analyzed to show the capability of the approach in modeling foldable membranes with complicated configurations. Good agreement is obtained on the membrane-deformed configurations between the simulation and experiment. Additionally, the driving force at the corners is obtained. This research is expected to provide a more accurate simulation to facilitate the design and optimization of the space deployable membrane structure.

Non-linear buckling analysis of thin-walled beams modeled with 7-parameter shell elements

The non-linear quasi-static buckling of thin-walled beams with arbitrary cross-sections is studied by developing coupling strategies between the composing plates (web, flanges). The element adopted for modeling the plates is a 7-parameter shell element using the Enhanced Assumed Strain concept (Büchter et al., 1994). Different nodal shell directors exist at the interface between plates for thin-walled beams with arbitrary cross-sections, requiring appropriate strategies. The coupling between plates first considers Lagrange multipliers at the interface, following the mortar method on the surface between the plates. Second a simplified pre-processing method is proposed by modifying the shell directors of the nodes close to the interface. In the case of the quasi-static buckling of thin-walled beams with L-shaped and I-shaped cross-sections, the two coupling strategies are thoroughly assessed by using three different solution procedures: Newton–Raphson, Newton–Riks and Asymptotic Numerical Method (ANM). The pre-processing method is simple and turns out to be robust and efficient.

Transient state analysis of rehabilitated RC beams using finite element modelling and prediction using an artificial neural network

The present research develops and verifies a simpler numerical approach for analyzing the thermal transient state of rehabilitated concrete beams reinforced with various types of FRP (fiber-reinforced polymer) subjected to high temperatures and specifically built as under-reinforced concrete beams. This approach offers a straightforward, efficient, and exact instrument for numerical analysis. The proposed analytical technique has been validated by load-displacement curves and cross-section temperature data, indicating its dependability and practicality. Subsequently, the validated approach was used to examine the impact of significant variables on the outcome and restoration of FRP-reinforced concrete beams at high temperatures. The methodology gives the Comparing conventional and CFRP, GFRP, AFRP reinforced beams using beam, truss, and shell elements. Thermal and UDL loads were applied, mesh at 25 mm × 25 mm. Transient analysis contrasts performance via displacement and temperature. The temperature versus displacement curve shows the FRP comparisons. Identifying the critical temperature before failure is crucial, emphasizing the curve’s significance in assessing structural performance and potential failure points. Nodal temperatures ranged 939 °C–963 °C (rehabilitated) versus 958 °C (conventional). 200 °C difference affects thermal boundary conditions for structural analysis and Conventional peaks at 320 °C, while AFRP, GFRP, and CFRP reach 358 °C, 385 °C, and 390 °C respectively. CFRP lasts 2400 min. Neural network models demonstrate effective generalizability, enabling satisfactory predictions of RC beam rehabilitation with CFRP laminates within the study’s parameter range.

Comparative Analysis of Finite Element Formulations for Simulating Hot Forming of Ti-6Al-4V Aerospace Components

This study presents a comprehensive finite element analysis to compare the performance of different element formulations (classic shell elements, solid elements, and continuum shell elements) in simulating the hot-forming process at 725 °C of a complex Ti-6Al-4V aerospace component with an initial blank thickness of 1.6 mm (0.063 inches). The Ti-6Al-4V blank is modeled as a deformable body exhibiting anisotropic plastic behavior, whereas the forming tools (matrix and punch) are assumed to be rigid bodies. The simulation accounts for temperature and strain rate effects on the material properties, incorporating phenomena such as friction and anisotropy. Three different element types are studied and compared: S4R and S4 (classic shells), C3D8R and C3D8 (solids), and SC8R (continuum shell with reduced integration). Finally, the model is validated by comparing the predicted final part geometry, especially the thickness distribution, against the experimental measurements. The model can also predict the springback effect on the final geometry. The SC8R continuum shell element provides the smoothest representation of thickness variations along critical regions of the final part. The study highlights the importance of selecting the appropriate element type for the accurate simulation of hot-forming processes involving large deformations and complex contact conditions. The ability of continuum shell elements to accurately capture the thickness variations makes them an ideal candidate for such applications.

Numerical modeling of RC column reinforced by new strategy using fiberglass tape and cloth

This paper presents the results of finite element analysis (FE) to study the axial compression behavior of reinforced concrete columns wrapped with tapes and fiberglass cloths according to different techniques using ABAQUS software. In the beginning, columns are modeled as 3D solid elements with a concrete damage plasticity model (CDPM), as the columns in this study are considered to be low compressive strength reinforced concrete and the rebar as 3D mesh elements. And once assembled, the specimen is wrapped with tape and cloth in the form of three-dimensional shell elements. Then, in order to analyze the behavior of the ultimate loads, the deformation of the confinement material, and the distribution of deformations in the concrete, the controlled displacement method used to apply the uniaxial compression loads to the specimen. Finally, a new mixed confinement model between partial confinement and complete has been proposed using a database of the results of a numerical simulation for confined concrete by fiberglass tapes and cloths. And it was found that the confinement strategy proposed in this study is very effective for the behavior of the reinforced concrete column, as the stress decreases significantly with the expansion and widening of the confinement stiffness of concrete in the plastic phase which improves the axial stress resistance.

Alternative Low-Order Triangular Elements for Thick and Thin Shell Analysis

In this paper, the authors discuss the development of six low-order triangular elements for the linear static analysis of thick and thin shell structures. The elements combine two triangular plane stress elements with three triangular thick plate bending elements to produce three-node flat shell elements with 18 degrees of freedom. The two plane stress components are based on the free formulation and the template formulation, while the three plate bending components are based on the free formulation, the deviatoric strain formulation and the hybrid-Trefftz formulation. The theoretical backgrounds and formulations of all elements are briefly discussed to provide a concise summary, while further details are given in the quoted references. The elements are used to analyze five standard shell benchmark examples, and the results obtained are compared to previous work in this area. The elements provide accurate and robust results for the benchmarks, with only small differences for the results as the meshes are refined. While all the proposed elements can be recommended for general shell analysis, the combination of the template plane stress element and the hybrid-Trefftz plate bending element generally provides the best results.

Effective FE simulation methods for fillet welding process by continuous distributed heat input and element combination

This study proposed effective finite element methods for simulating the fillet welding process on T-shaped joints. The T-shaped fillet welded joints were fabricated, and the process was simulated by a Continuous Distributed heat input method (CD method) and combining shell and solid elements. This study compared the models by the Discontinuous Uniform heat input method (DU method) and the CD method. The results showed that the CD method not only simplified the modeling process but also reduced the calculation time compared to the DU method. Furthermore, combining solid and shell elements reduced the number of nodal points in the models. The calculation time of the models by the element combination was significantly reduced. By comparing with experiments, it was shown that the CD heat input method and the combination of solid and shell elements could save calculation time while keeping the analysis accuracy.

Coupled thermomechanical analysis using isoparametric curved shell elements

This study focuses on the coupled thermo-mechanical formulation in isoparametric shell elements and its implementation in curved laminar structures. The formulation is based on the direct isoparametric formulation, specifically designed for flat and curved shell elements, and relies on the theory of degenerated solids. The research provides a comprehensive description of the coupled thermo-mechanical analysis, including the mechanical equilibrium equations, the interrelations between stress, temperature, displacement, deformation, and the conservation of thermal energy. It adopts a simultaneous approach to addressing the impacts of temperature and mechanical loads. The paper elaborates on various numerical examples that substantiate the formulation. These examples include simulations that encompass linear scenarios, which are then compared to analytical solutions and results derived from other numerical software. The examples highlighted include one-dimensional temperature diffusion, radial diffusion, and the thermal behavior of a cylindrical cover and a pipe under a linear temperature gradient. These simulations demonstrate the formulation's capacity to accurately capture the interactions between temperature variations and structural displacements. They also confirm the alignment of the proposed model with existing analytical and numerical solutions. In conclusion, the research provides a good framework for coupled thermo-mechanical analysis. The flexibility of the formulation is evidenced across different configurations and scenarios, accommodating various types of boundary conditions such as constant and linear temperature fields, distributed loads, and constraints on displacements and rotations. It effectively manages temperature flows across one, two, and three dimensions, highlighting its extensive applicability in the realm of structural analysis. This versatility underscores its broad applicability in the field of structural analysis.

Motion state factor driven for doubly-curved shallow shell deformation reconstruction

The conventional shape sensing method, based on C0 continuity, is recognized for its computational efficiency. However, it is prone to shear locking due to low-order polynomial interpolation in shell analysis, introducing two primary challenges. Firstly, it lacks consideration for C1 continuity. Secondly, existing high-order polynomial interpolation methods significantly increase the number of degrees of freedom (DOF), reducing computational efficiency. Therefore, a brand-new real-time structural health monitoring (SHM) method driven by motion state factor instead of nodal factors is proposed. This method accommodates all deformation modes of shallow shells with C1 continuity and improves the shape function's order without additional DOF. It begins with deriving motion states from compatibility equations, leading to a polynomial shape function expression. Subsequently, conversion equations for real constants and DOF are developed, establishing a least-squares model for theoretical strains and measured values. Following that, the higher-order element formula, optimized for minimal DOF, is then inferred from varied displacement data. Finally, simulations and experiments demonstrate this method's effectiveness, accuracy, and reliability in analyzing shallow shell elements.

Adjacent vertebral fractures in the lumbar and thoracic spine after balloon kyphoplasty: A finite element analysis.

The purpose of the present study was to mechanically verify after vertebral augmentation (AVA) scores using a finite element method (FEM) with accurate material constants of balloon kyphoplasty (BKP) cement. Representative cases with AVA scores of 1 (case 1), 3 (case 2), and 5 (case 3) among patients with vertebral body fractures who underwent BKP were analyzed. A FEM model consisting of 5 vertebral bodies was created, including the injured vertebral body in each case. The amount of displacement for each load (up to 4000 N) between the upper and lower vertebral bodies of each model was measured. Young modulus of the BKP cement was calculated from actual measurements using the EZ-Test EZ-S (Shimadzu Corporation, Kyoto, Japan). In all cases, the number of shell elements (209,296-299,876), solid elements (1913,029-2417,671), and nodes (387,848-487,756) were similar, indicating that FEM modeling was comparable among the cases. Young modulus of BKP cement, calculated using EZ-Test EZ-S, was 572 MPa. Fractures were detected by compressive forces of 3300 N (upper) and 3300 N (lower), 3000 N (upper) and 3100 N (lower), and 1200 N (upper) and 1200 N (lower) in cases 1, 2, and 3, respectively. The AVA scoring system was mechanically verified using the accurate material constants of BKP cement. A multicenter survey and external validation are therefore required for the clinical implementation of the AVA score.

Seismic behavior of reinforced concrete shear walls using a combined model of multi-layer shell and fiber beam elements

Seismic behavior of reinforced concrete shear walls using a combined model of multi-layer shell and fiber beam elements