Shell Elements Research Articles

Shaking table test of a full-scale lightweight bolt-connected concrete sandwich wall panel structure: Overview and seismic analyses

This study proposed a novel lightweight bolt-connected concrete sandwich wall panel structure with the advantages of thermal insulation, construction efficiency, demountability and remountability. The seismic design of the structure was employed a non-equivalent cast-in-place method, resulting in appropriate configurations of horizontal and vertical bolted joints. Subsequently, a shaking table test was carried out to investigate the damage pattern, dynamic characteristics and dynamic responses of a full-scale structure. The test results demonstrated that the overall damage was moderate, which exerted a few impacts on the structural capacity or integrity. The global responses, including small displacement response, minor torsion response, and high energy dissipation capacity were found, as well as local responses, such as small strains in the steel plates and a slight loss of bolt prestress. The maximum inter-story drift ratio was below the elastoplastic inter-story drift ratio limit θu = 1/120 defined in Chinese code GB 50011. In general, the structure presented high lateral stiffness and sufficient capacity against high-intensity ground motions. A numerical model was developed, wherein precast components were established by multi-layer shell elements and bolted joints were simulated by 3-DoF nonlinear springs. Linear modal and nonlinear time history analyses were performed and compared with the experimental results. The simulation results showed good agreement with the experimental ones, confirming the ability of the model to capture global responses.

Stepwise-Induced Synthesis and Excellent Corrosion Protection of Ce/Eu Codoped ZnO Solid Solution Materials.

Under purely inorganic conditions, a synthesis route was devised wherein elements were introduced stepwise via coprecipitation based on differences in compound solubility. This synthesis method can change the microscopic morphology of the material without relying on a templating agent, resulting in the formation of the multilayered lamellar Ce/Eu codoped zinc oxide solid solution (ZCEOSS) with a self-assembled nested imbrication structure. The study improves the critical matter of corrosion by focusing on the electron and energy transfer mechanisms. By introduction of the bandgap modulator cerium element and fluorescence enhancer europium element into the ZnO material, the anticorrosion material has been successfully endowed with both photocathodic protection and luminescent initiative/stress dual corrosion defense functions. Due to the energy level staircase protection mechanism synergistically generated by the 4f electron shell of rare-earth elements in concert with semiconductor zinc oxide, the energy band positions were modulated to progressively guide the direction of electron flow, thereby suppressing corrosion reactions. In particular, the ZCEOSS material synthesized by doping 1% cerium and 7% europium and adding rare-earth elements at pH 7 exhibited the best corrosion inhibition performance. After immersion in simulated seawater for 96 h, Tafel polarization test results showed that compared to epoxy resin and ZnO anticorrosion systems, the ZCEOSS anticorrosion system exhibited significantly improved corrosion inhibition efficiency with enhancements of 1028.3 and 402.9%, respectively. This study provides new insights into the development of highly efficient inorganic anticorrosion materials.

Stochastic Dynamic Buckling Analysis of Cylindrical Shell Structures Based on Isogeometric Analysis

In this paper, we extend our previous work on the dynamic buckling analysis of isogeometric shell structures to the stochastic situation where an isogeometric deterministic dynamic buckling analysis method is combined with spectral-based stochastic modeling of geometric imperfections. To be specific, a modified Generalized-α time integration scheme combined with a nonlinear isogeometric Kirchhoff–Love shell element is used to simulate the buckling and post-buckling problems of cylindrical shell structures. Additionally, geometric imperfections are constructed based on NURBS surface fitting, which can be naturally incorporated into the isogeometric analysis framework due to its seamless CAD/CAE integration feature. For stochastic analysis, the method of separation is adopted to model the stochastic geometric imperfections of cylindrical shells based on a set of measurements. We tested the accuracy and convergence properties of the proposed method with a cylindrical shell example, where measured geometric imperfections were incorporated. The ABAQUS reference solutions are also presented to demonstrate the superiority of the inherited smooth and high-order continuous properties of the isogeometric approach. For stochastic dynamic buckling analysis, we evaluated the buckling load variability and reliability functions of the cylindrical shell with 500 samples generated based on seven nominally identical shells reported in the geometric imperfection data bank. It is noted that the buckling load variability in the cylindrical shell obtained with static nonlinear analysis is also presented to show the differences between dynamic and static buckling analysis.

Development of nonlinear flat shell element with nonlinear thickness variation for highly flexible wind turbine blade

Large deformation from continuously varied thicknesses on existing and wind turbine blade shell structures is investigated. Various structure models having complicated outer shapes and thickness variations are considered and validated in this paper. A co-rotational method is developed to analyze geometric nonlinearity with a triangular shell structure. The updated stiffness matrix from interpolated thickness function and integral formulation is suggested to consider complicated geometry and thickness variation. Moreover, the co-rotational flat shell element based on the updated stiffness matrix is developed to analyze various nonlinear shell structures, which are the main feature of this research. The numerical analysis for structure deformations show well matched trends in static load analysis. Furthermore, the deformation of a simplified flexible wind turbine blade having tapered geometry and various thickness cases is adopted as a practical case. Moreover, modal analysis for composite beam structure is performed to verify the dynamic problems. The structural behaviors of the nonlinear thickness shell are validated against the solid and the shell models in commercial software, ABAQUS.

Thecal and Epithecal Ossifications of the Turtle Shell: Ontogenetic And Phylogenetic Aspects.

The problem of the origin of the bony shell in turtles has a two-century history and still has not lost its relevance. First, this concerns the issues of the homology, the sources of formation and the ratio of bones of different nature, that is, thecal and epithecal, in particular. This article analyzes various views on the nature of the shell elements, and proposes their typification, based on modern data on developmental biology. It is proposed that the defining characteristic of the types of shell ossifications is not the level of their anlage in the dermis (thecality or epithecality), but, first of all, the primary sources of their formation: (1) neural crest (nuchal and plastral plates); (2) vertebral and rib periosteum (neural and costal plates); and (3) dermal mesenchyme (peripheral, suprapygal and pygal plates, as well as epithecal elements). In addition, there is complete correspondence between these types of ossifications and the sequence of their appearance in the turtle ontogenesis. The data show fundamental coincidence of the modifications of the ontogenetic development and evolutionary formation of the shell ossifications and are in agreement with a stepwise model for the origin of the turtle body plan. Particular attention is paid to the origin of the epithecal elements of the turtle shell, which correspond to the additional or supernumerary ossifications and seem to have wider distribution among turtles, than previously thought.

A spot weld element formulation and implementation for mesh‐insensitive fatigue evaluation of lightweight structures

AbstractWith the rising importance of virtual engineering in an increasingly competitive marketplace, there is a growing need for simplified representations of finite element (FE) modeling for spot joints in lightweight structures without losing accuracy in structural life evaluation. For this purpose, this paper presents a spot weld element with an implicit weld representation and its numerical implementation as a user element for deployment in commercial FE code for reliably computing traction structural stress in a mesh‐insensitive manner. The spot weld element is formulated by degenerating conventional first‐order four‐nodes shell elements by imposing kinematic constraints with respect to a series of virtual nodes placed in the region around a spot weld. The simplicity and effectiveness of the spot weld element have been validated by comparing with the explicit weld representation for computing mesh‐insensitive structural stresses and fatigue life correlation of welded components.

Pure distortion of symmetric box beams with hinged walls

This paper is concerned with the analysis of the pure torsion and distortion of straight box beams with trapezial cross-sections and hinged walls. A one-dimensional mechanical model for this kind of system subjected to anti-symmetric loads on the end cross-sections and no warping constraints is developed. The distortional stiffness of the system is provided by the torsional rigidity of the wall panels. The cross-sectional kinematic condition for which torsion and distortion are uncoupled has been determined. Novel explicit expressions of the internal and external distortional moments, the distortion constant, and the distortional warping pattern have been deduced; they can be directly translated to the classical distortion theory. Results of representative test cases with different section shapes and loads show excellent agreement with finite element models using shell elements. The model is a first step to analyse bridge decks with a distortionable central cell for wind engineering applications. Finally, an extension of the model, including the distortional stiffness provided by the frame bending stiffness of the cross-section walls, is presented. The extended model is applicable to assess the large-scale torsional–distortional effects in long beams with closed cross sections.

New OpenSees material model for simulating reinforced concrete shear walls subjected to coupled axial tension and cyclic lateral loads

In high-rise buildings, reinforced concrete (RC) shear walls, particularly those forming part of coupled wall systems or core wall systems, may be subjected to coupled axial tension and cyclic lateral loads during strong seismic events. A new two-dimensional material model named the “Fixed Angle Model Considering Crack Sliding” (FAM-CS) was proposed for simulating the nonlinear behavior of RC walls subjected to axial tension and cyclic lateral loads. The proposed model was implemented in the OpenSees platform. Nonlinear constitutive models for shear aggregate interlock effects of concrete and dowel action of rebars were incorporated into the proposed model to represent the shear transfer mechanisms along concrete cracks. The proposed model was validated against the test data of six wall specimens subjected to coupled axial tension and cyclic lateral loads. The results indicated that the proposed model reasonably predicted the lateral strength capacity (an average error of 6.2 %) and the residual strength at the maximum drift loading (an average error of 12.3 %) of the specimens. For comparison, three other commonly used models, the Shear-Flexure Interaction Multiple-Vertical-Line-Element-Model, the multi-layer shell element model and the Cyclic Softened Membrane Model were adopted for the simulation of the specimens. Compared with the three existing OpenSees models, the newly implemented material model provided improved predictions of the wall hysteretic behavior with respect to lateral strength capacity, lateral strength degradation, pinching characteristics and cyclic stiffness degradation. In addition, the proposed model reasonably captured the localized failure pattern as well as the energy dissipation characteristics of the test specimens. Finally, a mesh sensitivity study was conducted to assess the robustness of the proposed model. The results revealed that the proposed model was robust regarding the lateral load-drift responses of RC walls, with a mesh size ranging from approximately one to three times the average crack spacing.

Dynamic response of spherical tanks subjected to the explosion of hydrogen-blended natural gas

Hydrogen is a renewable and clean energy and obtains increasing attention all around the world. Blending hydrogen into natural gas can promote hydrogen development and storage tank farms play an essential role in the storage of hydrogen-blended natural gas (HBNG). However, upon leakage from the tank, HBNG accumulates to create a vapor cloud and may explode, resulting in more severe consequences than natural gas. Furthermore, the explosion has the potential to trigger the domino effect in the spherical tank storage area, leading to multiple explosions. But little attention has been paid on this research issue. This article analyzes the dynamic response of the spherical tank exposed to HBNG explosions. The fluid–structure interaction theory is adopted to establish the whole finite element model. Meanwhile, the advanced Arbitrary Lagrangian-Eulerian (ALE) method can reduce mesh distortion and enhance computational accuracy, and the process of explosion is analyzed through the coupling of the Lagrangian mesh for the structure and the Eulerian mesh for the vapor cloud. Then, the algorithm is employed that couples shell elements with solid elements by utilizing a penalty function. Besides, the dynamic response of the spherical tank and pillar surfaces is analyzed in the trends of effective stress, displacement, velocity, and structural damage under various parameters, evaluating the energy absorbed by the spherical tank and pillar. Accordingly, the equipment damage caused by HBNG explosions considering possible damage caused by secondary explosions can be obtained. Then, the effects of the HBNG explosion chain on equipment are analyzed in tank areas. The dynamic response of structures in the explosion is closely related to the different hydrogen blended ratios, distances, and structural thickness, which significantly impact the effective stress of the spherical tank and pillar. Moreover, the damage caused by the HBNG explosion is more serious for pillars than the spherical tank, making the role of pillars crucial in supporting the spherical tank. The results obtained in this study can be used to support the design and safety operation of HBNG storage areas.

A refined track dynamic model considering the bending properties of iron pad: Proposal and validation

Iron pads are crucial components in rail fastening systems, characterized by their load-bearing and force-transmitting capabilities. This study presents and validates a track dynamic model considering the bending properties of iron pad, offering a comprehensive analysis of their dynamic performance under train loads. The primary aim is to employ iron pads as key elements for monitoring and detecting potential defects throughout the track’s service life. Initially, the construction of the track dynamic model is outlined, followed by an in-depth explanation of how the iron pads integrate with the track model. This involves introducing an enhanced Kelvin-Voigt three-element model and elaborating on the parameter selection for the spring element using a nonlinear spring model that accounts for voids and their relevant conditions. Subsequently, a systematic comparative analysis is performed to evaluate the accuracy of simulating iron pads using solid, shell, and beam elements, along with a proposed strain correction method. Finally, the established model and methods are employed to simulate and analyze the dynamic response of iron pads under typical defect conditions. These results indicate that iron pads can effectively reflect the failure conditions of the railway track system, making them ideal sensing elements for the dynamic monitoring of track structures. The enhanced model developed in this study holds significant theoretical and practical value, contributing to the safety monitoring and defect analysis of railway operations.

Macro-modelling of GFRG infilled RC frames incorporating pivot hysteretic model

GFRG (Glass Fibre Reinforced Gypsum) panels present a viable alternative to conventional masonry infills in masonry infilled RC frames. Based on the experimental study on the lateral load behaviour of GFRG infilled RC frames, it was understood that the GFRG panels enhance the structural performance of the RC framed structure. To delve further into this, numerical modelling of GFRG infilled RC frames with different fillings inside the cavities of the panel was performed using SAP2000. The GFRG panels were modelled using nonlinear layered shell elements, while the interface between the GFRG web and the infill material was represented using multilinear plastic link elements. The monotonic lateral load–deflection behaviour and the in-plane hysteresis response were simulated by performing monotonic and cyclic pushover analyses. The cyclic pushover analysis incorporated pivot hysteretic models for the materials, hinges and links. Validation of the proposed numerical models was carried out by comparing the results with those obtained from the experimental study. Key parameters such as peak load, initial stiffness, stiffness degradation, and energy dissipation were carefully compared to ensure the accuracy and reliability of the proposed model. It was observed that the proposed numerical model was able to capture the monotonic and cyclic load–deflection behaviour and other performance parameters. The numerical model accurately predicted the peak load in the positive direction but overestimated the corresponding value in the negative direction. Moreover, the overestimation observed in the cumulative energy dissipated for all the specimens is relatively minor and does not significantly affect the overall accuracy of the model.

REVERSE ENGINEERING MODELING PROCESSING AND FABRICATION OF VORONOI PERFORATED ANKLE-FOOT ORTHOSIS

The ankle may not function optimally because of an ankle foot injury due to torn ligaments or foot drop, a post-stroke effect of hemiplegia. One treatment that can be done for sufferers of ankle foot injury and foot drop is using an ankle foot orthosis (AFO). Reverse engineering (RE) and additive manufacturing (AM) technologies can be utilized within the medical domain, specifically for producing prosthetic devices and orthoses that include optimal fit, lightweight characteristics, and cost-effectiveness. This study aims to create an optimized design for an ankle-foot orthosis by utilizing reverse engineering techniques, followed by an analysis of its performance using finite element simulation. The research process involved several key steps, namely 3D Scanning, CAD modeling, model analysis, and 3D printing. The findings of the model study after the implementation of Voronoi ventilation holes indicated that the highest equivalent stress observed in the model, with a shell element thickness of 1.4 mm, amounted to 21.12 MPa. This result represented an elevation of 11.74% compared to the model before introducing Voronoi ventilation holes. Nevertheless, there was a reduction in the model's mass by 20.3%, specifically from an initial weight of 400.86 grams to a final weight of 319.51 grams. On the contrary, despite a fall in the safety factor, it continues to be considered safe, with a value of 2.84.

Shape and size optimization framework of stiffened shell using isogeometric analysis

A shape and size optimization framework is developed to improve the structural performance of the stiffened shell using isogeometric analysis. To accurately model the stiffened shell, the Lagrange multiplier method is employed to establish the coupling relationship of isogeometric degenerated shell elements and isogeometric degenerated beam elements. Due to the advantages of the non-uniform rational B-spline (NURBS), the unit normal direction vectors of the shell can be defined analytically, which guarantees stiffeners perpendicular to the skin. Additionally, the stiffeners can be easily generated based on the mapping relationship of the parametric space and the physical space of the shell. Analytical sensitivity is derived in detail, and the gradient-based optimization method can be used to solve the minimum compliance optimization problem owing to the high order continuity of NURBS. Three numerical illustrative examples are presented to verify the effectiveness of the proposed framework for the shape and size optimization of stiffened shells, consisting of a cylindrical shell patch, a hyperbolic shell, and a complex engineering segment. It is worth noting that the proposed framework is especially suitable for optimization problems of the stiffened shell, eliminating the need of complex feature extraction.

Shell element-based prediction of process-induced deformation considering the different fabric parameters and stacking sequences of CFRP woven composites

Herein, we present a finite element method (FEM) based curing analysis for predicting the process-induced deformation (PID) of CFRP woven composites using shell-type elements. This method can efficiently consider various fabric parameters and stacking sequences, even for complex structures. For woven composite plates and L-shaped flanges, FEM-based PID prediction using shell elements reduced computation times by 50–59% compared to solid elements, while maintaining acceptable accuracy with relative errors of 0.17–7.35%. Furthermore, the impacts of various fabric parameters and stacking sequences on the PID of woven composites are analyzed in detail. The main finding is that the variation in material properties due to fabric parameters and stacking sequences significantly impacts the PID of woven composite structures. This prediction method can be applied in the design of composite structures and molds, thereby enhancing the dimensional precision and performance of composite structures.

Component tests and numerical simulations of 3D steel frame structures for progressive collapse

This paper presents a comprehensive study on three-dimensional steel frame structures subjected to progressive collapse, drawing insights from a full-scale steel frame substructure test. The investigation encompasses connection component tests and numerical simulations, focusing on extended end plate and double-angle cleat connections employed in the substructure test. The mechanical properties of the connection components were tested, forming a basis for defining component properties in subsequent connection models. Finite element (FE) models of the test substructure were developed, utilizing hybrid elements for the steel frame part, which include beam, connector, and spring elements based on the component method. To simulate reinforced concrete slabs, a combination of refined solid elements and simplified shell elements was employed. The former accurately captures detailed failure modes, while the latter efficiently simulates the collapse behavior of large-scale steel frame structures. Validation of the established models against test results encompassed load-displacement responses, internal forces in structural members, and failure modes. The validated FE models were then utilized to analyze and discuss the contributions of various structural components in resisting progressive collapse. Specific focus was placed on the development of load-resisting mechanisms in the floor slab and the influence of beam-column connection types on structural behavior. The paper explores the role of bracing systems in a building in resisting progressive collapse. Additionally, it evaluates the effectiveness of the restraint systems used in the test, shedding light on their ability to accurately reflect real restraint effects from the surrounding structure. The findings presented herein contribute valuable insights to the understanding of progressive collapse behavior in steel frame structures, with implications for robustness design of multi-story steel buildings.

Study on Seismic Behavior and Component Vulnerability of Corroded RC Shear Walls Subjected to Flexural Shear Failure

ABSTRACT The impact of corrosion degree, axial compression ratio, reinforcement ratio of longitudinal bar and horizontal distribution rebar, and stirrup of boundary column on seismic performance of RC shear walls were investigated. The corrosion forms (rust expansion cracks and corroded steel bars), failure process, hysteretic characteristics, bearing capacity, and deformability were compared. Subsequently, a numerical model of corroded RC shear walls was established adopting shell elements. Finally, according to the numerical simulation method, considering the uncertainty of corrosion degree and material parameters, the vulnerability models of RC shear wall components with different corrosion degrees were built. The results show that the mechanical properties of the shear wall were seriously deteriorated due to the corrosion of steel bars, and the ultimate displacement and ductility coefficient of severely corroded specimens were reduced by 28.5% and 12.27% respectively, compared to non-corroded specimens. A proposed numerical modeling method for corroded RC shear walls based on shell element is accurate, and the bearing capacity error and energy dissipation error of the simulation and test results were less than 20%. As the degree of corrosion grew, the probability of shear wall components experiencing more severe failure added significantly. When the displacement angle was 1/120 (This is the limit value of elastic-plastic displacement angle specified in the code), the probability of DS3 and DS4 occurring in the shear wall with a corrosion degree of 0% were 56% and 39.44%, and the probability of DS4 and DS5 occurring in the shear wall with a corrosion degree of 10% were 41.1% and 38.44%.

Formulating strain-based quadrilateral membrane finite elements with drilling rotations

Membrane finite elements with drilling degrees of freedom have sparked interest in many research works since they can be conveniently combined with plates to form shell elements. This study presents two non-conforming strain-based four-node quadrilateral membrane elements, SBQ13 and SBQ13E, for static analysis. SBQ13 partially satisfies the equilibrium equations, while SBQ13E completely fulfils the force balance equations. Both elements carry drilling rotations at each node. One difficulty when formulating quadrilateral elements is the singularity in the transformation matrix, which is addressed in this study by utilising the properties of singular matrices. Both quadrilateral elements were tested in several benchmark problems. It has been found that both elements passed the higher-order patch test but failed the constant stress patch test. Nevertheless, SBQ13 produced accurate responses in most numerical tests, but SBQ13E unreasonably overestimated the solution. Solving the eigenvalue problem revealed that the SBQ13E element has a near-zero energy deformation mode, which might explain the anomaly. Although fulfilling equilibrium does not always enhance solution accuracy, it is essential to overcome volumetric locking. Apart from the newly developed elements, this paper presents several new ideas that may apply to strain-based element formulations.

A method: multi-scale calculation life of welded beams with residual stress

To improve the accuracy of the probability of life value calculation while ensuring computational efficiency, a study was conducted on the finite element probability of life calculation method for beam-shell coupling. On the basis of the finite element heat and stress coupling model of Type I welded beam, a fatigue fracture model of residual stress and cyclic load coupling was established. The probability of life calculation of beam-shell elements was theoretically derived, and the expression of the probability of life model was unified. The probability of life of Type I welded beam was calculated, and it was compared with the model of beam assumption and the full life test result. The results show that the computational efficiency of the beam-shell coupling model is higher than that of the shell element model. In addition, the probability of life calculation result obtained by the beam-shell coupling model is highly consistent with the experimental result in statistical terms, and it has higher accuracy at low stress levels than the calculation result of the beam element, with the relative error between the median of the calculation result and the experimental result being less than 10%.

Geometrically nonlinear analysis of plates and shells by a cell-based smoothed CS-MITC18+ flat shell element with drilling degrees of freedom

A development of a 3-node triangular flat shell element to analyze geometric nonlinearity of plate and shell structures is presented in this study. The proposed flat shell element has 6 degrees of freedom per node, including the drilling rotational ones, by using the Allman-type approximations for the in-plane displacements and the bending displacement approximations enriched by a cubic shape function at the bubble node located at the element's centroid. The geometrically nonlinear behaviors are described by the von Karman's large deflection assumption. The membrane and bending strains of the presented flat shell elements are averaged over sub-triangular elements based on the cell-based smoothed (CS) technique. To attenuate the shear locking phenomenon, the transverse shear strains are re-interpolated following the mixed interpolation of tensorial components (MITC) technique designed for the 3-node triangular degenerated shell elements enriched by a cubic bubble function (MITC3+). Combined with the Newton-Raphson iterations and load increments predicted by the arc-length method, the suggested 3-node triangular flat shell elements, namely the CS-MITC18+ element, can analyze moderately geometrical nonlinearity, including the snap-thought and snap-back behaviors, of various plates and shells with the different shapes, thickness, and boundaries. The numerical investigations show that the load-displacement curves provided by the CS-MITC18+ flat shell elements well agree with other references.

Study on Rubbing-Induced Vibration Characteristics Considering the Flexibility of Coated Casings and Blades

Rubbing between a blade and its coated casing is one of the main failures in aero-engine systems. This paper aims to study the effects of coated casings on rubbing-induced dynamic responses considering the flexibility of the coated casing and the flexibility of the blade. Firstly, an actual compressor blade is established by the shell element and verified by the experiment and ANSYS 19.2 software. Subsequently, a new dynamic model for the coated casing is proposed based on the laminated shell element, and the proposed dynamic model for the coated casing is verified by comparing the natural characteristics calculated by ANSYS software. Moreover, a comprehensive analysis is conducted to analyze the influences of the casing model, coating parameters, and casing parameters on vibration characteristics. Finally, the results show that the coating can diminish the severity level of rubbing. Notably, the material and thickness of the coating can change the nodal diameter vibrations of the casings (NDVCs) induced by rubbing. This study provides valuable guidance for the optimization and design of blade–casing systems.