Shell Elements Research Articles

A hierarchic isogeometric hyperelastic solid-shell

The present study aims to develop an original solid-like shell element for large deformation analysis of hyperelastic shell structures in the context of isogeometric analysis (IGA). The presented model includes a new variable to describe the thickness change of the shell and allows for the application of unmodified three-dimensional constitutive laws defined in curvilinear coordinate systems and the analysis of variable thickness shells. In this way, the thickness locking affecting standard solid-shell-like models is cured by enhancing the thickness strain by exploiting a hierarchical approach, allowing linear transversal strains. Furthermore, a patch-wise reduced integration scheme is adopted for computational efficiency reasons and to annihilate shear and membrane locking. In addition, the Mixed-Integration Point (MIP) format is extended to hyperelastic materials to improve the convergence behaviour, hence the efficiency, in Newton iterations. Using benchmark problems, it is shown that the proposed model is reliable and resolves locking issues that were present in the previously published isogeometric solid-shell formulations.

Capacity assessment of uncorroded and corroded dapped‐end beams by NLFE and strut‐and‐tie based methods

AbstractThe verification of dapped‐end beams degraded by corrosion is a problem, especially for existing bridges in service. This paper proposes a nonlinear finite element (NLFE) modeling procedure and a simple strut‐and‐tie based procedure for predicting the response of dapped‐end beams subjected to chloride corrosion. Firstly, the finite element modeling strategy, based on the adoption of multilayer shell elements and the PARC_CL 2.1 crack model is described. Then, the degradation effects on concrete, rebars, and steel‐to‐concrete interaction are defined as a function of the propagation period of corrosion. In particular, the effects of corrosion on the reinforcement are modeled by applying a reduction of tensile strength that considers for both the reduction of cross‐section and the ultimate strain caused by pitting. Concrete splitting cracking due to volume expansion during rust formation is modeled by reducing the mechanical properties of concrete. Corrosion effects in steel‐to‐concrete interaction are modeled by applying a bond strength decay to the spring elements connecting corroded rebars—modeled with truss elements—and concrete multilayer shell elements. The proposed finite element procedure is used to study two scenarios based on different spatial distributions of corrosion‐prone areas. Subsequently, a simplified analytical approach based on the strut‐and‐corroded tie method—called S&CT method—is proposed and compared with the finite element outcomes. Finally, the validations of the two proposed methods are presented with respect to a corroded dapped‐end beam, showing that corrosion of rebars affects the resistance mechanisms of the dapped‐end beam, by reducing both resistance and ductility. The proposed simplified analytical S&CT method provides conservative and safe results compared to the numerical NLFE model and to experimental data.

The generalized Kelvin chain-based model for an orthotropic viscoelastic material

We propose a constitutive material model to describe the rheological (viscoelastic) mechanical response of timber. The viscoelastic model is based on the generalized Kelvin chain applied to the orthotropic material and is compared to the simple approach given by standards. The contribution of this study consists of the algorithmization of the viscoelastic material model of the material applied to the orthotropic constitutive law and implementation into the FEM solver. In the next step, the fitting of the input parameters of the Kelvin chain is described, and at least a material model benchmark and comparison to the approach given by standards were done. The standardized approach is based on the reduction of the material rigidity at the end of the loading period using a creep coefficient, whereas the loading history state variables are not considered when establishing the result for a specific time step. The paper presents the benefits of the rheological model. It also demonstrates the fitting algorithm based on particle swarm optimization and the least squares method, which are essential for the use of the generalized Kelvin chain model. The material model based on the orthotropic generalized Kelvin chain was implemented into the FEM solver for the shell elements. This material model was validated on the presented benchmark tasks, and the influence of the time step size on the accuracy of model results was analyzed.

Response of Reinforced Concrete Shell Elements Subjected to In-Plane and Out-of-Plane Shear

Response of Reinforced Concrete Shell Elements Subjected to In-Plane and Out-of-Plane Shear

Development of a Homogenized Finite Element Model for Pouch Lithium-Ion Battery Cells Considering Porosity and Pressure Sensitivity

In light of the growing safety concerns associated with lithium-ion batteries integrated in electric automobiles, there is an escalating need to explore the mechanical behavior of lithium-ion batteries under diverse loading conditions using finite element simulations. In this paper, a homogenized finite element model was proposed to predict the material behavior of pouch lithium-ion cells using finite element simulations under various loading conditions. This homogenized model consisted of four layers of solid elements wrapped by shell elements, and it was made to consider especially the porosity and the pressure sensitivity of a pouch cell. The material properties of this homogenized model were calibrated based on the out-of-plane compression, in-plane confined compression, and 3-point bending test data for a single cell. The simulations using the model exhibited good agreement with the experimental load-displacement data not only for a single cell but also for two stacked cells. Additionally, the effects of the pouch and the vacuum on the mechanical behavior were examined.

ИЗУЧЕНИЕ ДЕФОРМАЦИЙ В УЗЛОВЫХ СОЕДИНЕНИЯХ ПОЛИМЕРНЫХ СЕТЧАТЫХ ОБОЛОЧЕК ГИПЕРБОЛОИДОВ ВРАЩЕНИЯ.

The article is devoted to the study of deformations and vertical displacements in the nodal joints of the mesh shells of hyperboloids of rotation, the study of the experience of operating objects in the form of hyperboloids of rotation (using the example of the V.G. Shukhov tower on Shabolovka in Moscow) made of polymer structures. As part of laboratory research, modeling of a mesh hyperboloid of rotation made of polymer materials was carried out, deformations of this type of structures under loads were studied. Laboratory studies were conducted in order to study physical loads on polymer elements, depending on the hyperboloid tier, the number of polymer elements of the mesh shell in the diameter of the tier, the study of material deformation, the construction of the hyperboloid as a whole. The data of the laboratory experiment give an idea of the physical features of structures in the form of a hyperboloid of rotation, an idea of possible load changes in the nodal joints of the tower tiers, in these types of structures made of polymer materials. The article presents the formed results of research on the study of deformations and changes in loads on nodal fasteners depending on the tier of the structure and the number of elements forming the tier. This article has scientific relevance, gives an idea of the change in load, deformation, resistance of structural elements and other processes.

Promoting bridging in adhesively bonded composites with polymer inserts: A computational perspective

Preventing catastrophic failure due to delamination in adhesively bonded carbon fiber reinforced polymer (CFRP) is crucial to enhancing the reliability of structures. Experimental evidence from another study demonstrated that introducing inserts into the adhesive bond line creates bridging, effectively arresting the delamination process. In this paper, a numerical model was proposed to mimic the experiment and then utilized for conducting parametric studies. An embedded cell approach was adopted, representing a double cantilever beam (DCB) with linear-elastic continuum shell elements, beam elements for the bridging bundles, and connector elements for the adhesive. The crack propagation was initiated with adhesive failure and subsequently followed by bridging bundle failure. The numerical simulation results closely replicated the experiment’s global response in the force–displacement curve, thereby effectively validating the existence of the bridging effect. Furthermore, our study revealed that enhancing the adhesive strength and insert ductility can further improve crack resistance.

AXISYMMETRIC DYNAMIC BEHAVIOUR OF THIN OBLATE SHELLS

This paper presents a theoretical investigation of the axisymmetric free vibrations of an isotropic thin oblate spheroid shell. The analysis depends on the Rayliegh – Ritz's method. The non – shallow shell theory is used for the analysis. The analysis based on considering the oblate spheroid as a continuous system constructed from two spherical shell elements matched at the continuous boundaries.Throughout the results, it is shown that when the eccentricity reaches zero, an exact thin sphere solution is emerged and when the eccentricity equals one an exact thin circular plate solution is emerged. Therefore, the eccentricity of an oblate shell at medium value lies between these two values.It was found that the Rayleigh – Ritz's method is suitable for all eccentricities, while the literature showed that the Rayleigh's method is suitable for eccentricities less than 0.6.

Towards Structural and Aeroelastic Similarity in Scaled Wing Models: Development of an Aeroelastic Optimization Framework

The pursuit of more efficient transport has led engineers to develop a wide variety of aircraft configurations with the aim of reducing fuel consumption and emissions. However, these innovative designs introduce significant aeroelastic couplings that can potentially lead to structural failure. Consequently, aeroelastic analysis and optimization have become an integral part of modern aircraft design. In addition, aeroelastic testing of scaled models is a critical phase in aircraft development, requiring the accurate prediction of aeroelastic behavior during scaled model construction to reduce costs and mitigate the risks associated with full-scale flight testing. Achieving a high degree of similarity between the stiffness, mass distribution and flow field characteristics of scaled models and their full-scale counterparts is of paramount importance. However, achieving similarity is not always straightforward due to the variety of configurations of modern lightweight aircraft, as identical geometry cannot always be directly scaled down. This configuration diversity has a direct impact on the aeroelastic response, necessitating the use of computational aeroelasticity tools and optimization algorithms. This paper presents the development of an aeroelastic scaling framework using multidisciplinary optimization. Specifically, a parametric Finite Element Model (FEM) of the wing is created, incorporating the parameterization of both thickness and geometry, primarily using shell elements. Aerodynamic loads are calculated using the Doublet Lattice Method (DLM) employing twist and camber correction factors, and aeroelastic coupling is established using infinite plate splines. The aeroelastic model is then integrated within an Ant Colony Optimization (ACO) algorithm to achieve static and dynamic similarity between the scaled model and the reference wing. A notable contribution of this work is the incorporation of internal geometry parameterization into the framework, increasing its versatility and effectiveness.

Harmonic in-plane patch loading induced nonlinear dynamic instability of unidirectional and bidirectional stiffened composite plates

A finite element framework is established to study the nonlinear dynamic instability of stiffened plates subjected to in-plane harmonic patch loading. An eight-noded isoparametric degenerated shell element and a three-noded curved beam element are used to model the skin and the stiffener, respectively. The Green–Lagrange strain displacement relationship is adopted to formulate the system matrices for the plate and the stiffener, adopting the total Lagrangian approach. The Bolotin method is adopted to trace the boundaries of linear dynamic instability region. The Incremental Harmonic Balance (IHB) method is used to investigate the nonlinear instability behavior of stiffened plates. The effect of varying loading patches along with the number of stiffeners in unidirectional ( x-directional and y-directional) and bidirectional ( x as well as y-directional) stiffened plates on the nonlinear frequency response is studied. It is observed that the cross-stiffened plates with the higher number of stiffeners are dynamically more stable than the unidirectional stiffened plates. Moreover, the stiffened plates with smaller loading patches are dynamically more stable than those with larger loading patches.

Novel Computational Design of Polymer Micromachined Insect-Mimetic Wings for Flapping-Wing Nano Air Vehicles.

The flapping wings of insects undergo large deformations caused by aerodynamic forces, resulting in cambering. Insect-mimetic micro wings for flapping-wing nano air vehicles mimic these characteristic deformations. In this study, a 2.5-dimensional insect-mimetic micro wing model for flapping-wing nano air vehicles is proposed to realize this type of wing. The proposed model includes a wing membrane, a leading edge, a center vein, and a root vein, all of which are modeled as shell elements. The proposed wing is a 2.5-dimensional structure and can thus be fabricated using polymer micromachining. We conducted a design window search to demonstrate the capabilities of the wing. The design windows, which are areas of desirable design solutions in the design parameter space, are iteratively searched using nonlinear finite-element analysis under quasi-steady aerodynamic modeling. Here, thickness is selected as a design parameter. The properties of real insects, polymer materials, and fabrication conditions are used to determine the other parameters. A fabricable design solution that generates sufficient camber is found from the design windows.

Predicting the Dynamic Parameters for Milling Thin-Walled Blades with a Neural Network

Accurately predicting the time-varying dynamic parameters of a workpiece during the milling of thin-walled parts is the foundation of adaptively selecting chatter-free machining parameters. Hence, a method for accurately and quickly predicting the time-varying dynamic parameters for milling thin-walled parts is proposed, which is based on the shell FEM and a three-layer neural network. The time-dependent dynamics of the workpiece can be calculated using the FEM by obtaining the geometrical parameters of the arc-faced junctions within the discrete cells of the initial and machined workpiece. It is unnecessary to re-divide the mesh cells of the thin-walled parts at each cutting position, which enhances the computational efficiency of the workpiece dynamics. Meanwhile, in comparison with the three-dimensional cube elements, the shell elements can reduce the number of degrees of freedom of the FEM model by 74%, which leads to the computation of the characteristic equation that is about nine times faster. The results of the modal test show that the maximum error of the shell FEM in predicting the natural frequency of the workpiece is about 4%. Furthermore, a three-layer neural network is constructed, and the results of the shell FEM are used as samples to train the model. The neural network model has a maximum prediction error of 0.409% when benchmarked against the results of the FEM. Furthermore, the three-layer neural network effectively enhances computational efficiency while guaranteeing accuracy.

Development and implementation of shear wall finite element in OpenSees

Shear walls are widely used as lateral load-resisting systems in high-rise building structures. The design and nonlinear analysis of shear walls under seismic loads for recoverability are complicated and challenging, which demands nonlinear computer modeling procedures. This paper presents a novel finite element named Double Vertical Beam-column with Shell Element (DVBSE) for the nonlinear analysis of complex reinforced concrete shear walls with columns. The DVBSE is implemented in the open-source finite element program OpenSees. The theoretical formulations of DVBSE are described in detail. The accuracy of the developed DVBSE is established by comparing the finite element analysis results with existing experimental data on recoverable steel-GFRP composite bar reinforced concrete shear walls. The comparative study demonstrates that the proposed DVBSE is superior to the commonly used finite element model in simulating the responses of recoverable complex shear walls under seismic loads. These research findings contribute to further advancements in the development of new shear wall elements and lay a solid foundation for the nonlinear numerical simulation of innovative shear walls.

A spectral finite element Reissner–Mindlin shell formulation with NURBS-based geometry definition

A curved non-isoparametric Reissner–Mindlin shell element is developed for analyzing thin-walled structures. The standard kinematic description of the element requires the calculation of the director vector. To address this demand accurately, similar to isogeometric analysis (IGA), the geometry is defined by utilization of the non-uniform rational B-splines (NURBS) imported directly from computer-aided design (CAD) files. Then, shape functions of the Legendre spectral element method (SEM) are used to interpolate the displacements. Consequently, the shell director vector and Jacobian of the transformation are calculated properly according to the presented formulation. On the other hand, in Legendre SEM combined with Gauss–Lobatto–Legendre quadrature, the integration points and the element nodes coincide. Thus, the easily computable local coordinate systems at the integration points can be used directly as nodal basis systems. A separate calculation of nodal basis systems at control points, which is the source of either complexity or error in IGA shells, is not required. Given the condition number of the stiffness matrix in the developed method, super high-order elements can also be used. Very high order p-refined elements are used in addition to h-refinement of the mesh to show the capability of higher order elements to analyze problems without mesh refinement. The validity and convergence rate of the method are investigated and verified through various cases of h- and p-refinement in challenging obstacle course problems.

Unconventional cyclic plasticity model implementation for shell and plane stress elements in UMAT/Abaqus

Finite element simulations are widely used in several industrial sectors (civil, aerospace, mechanical, naval, biomedical, etc.) to design components or structures. Often, the resolution of highly non-linear problems requires the recurse to dense meshes with the consequent increase in computation time. This aspect becomes particularly relevant for cyclic mobility problems where repeated loading might affect the computational cost. Therefore, the efficiency of finite elements represents a crucial aspect of speeding up the design process. Past works of the authors focused on developing the additive hypoelastic-based and multiplicative hyperelastic-based constitutive equations of the Extended Subloading Surface model for three-dimensional finite elements adopting fully implicit integration schemes. In this paper, the constitutive equations of the Extended Subloading Surface theory are reformulated for shell and plane stress elements, aiming to obtain an efficient computational tool suitable for cyclic mobility problems. The numerical implementation considers isotropic hardening, kinematic hardening, and material anisotropy. Numerical solutions obtained utilising shell/plane stress and solids elements are also discussed.

Operational modal analysis, seismic vulnerability assessment and retrofit of a degraded RC bell tower

This paper presents damage assessment through Operational Modal Analysis (OMA) and Finite Element (FE) model updating of the bell tower of the church of Castro in Bergamo, Italy. The tower is a 39 m high reinforced concrete structure with hollow cross-section and double-curved shape. The research was dictated by the need to identify the actual damage state of the structure, which was found through visual inspections. Piezoelectric accelerometers were used to record the ambient vibrations in subsequent test setups, using the roving technique for system identification. A detailed FE model was created with shell elements and calibrated to match the system identification results. A simplified beam model was then developed based on the modal analysis results of the detailed model. A sensitivity analysis was performed to identify the most influential model parameters on the modal characteristics of the system. Subsequently, the optimal values of these parameters were determined by an optimisation procedure carried out using a typical global optimization algorithm. The updating results allowed assessment of the actual condition of the bell tower and its seismic vulnerability. Finally, a seismic strengthening solution was recommended.

Synthetic turf finite element model development and validation

Assessment of synthetic turf performance has been undertaken using a variety of experimental methods but is limited in understanding the complex physics of cleat-turf interaction. Computational models could provide insight, but there is currently no validated model of synthetic turf available. The scope of this study was to develop a Finite Element (FE) model of synthetic turf using a hierarchical approach and validate the model using independent test data. A physical third-generation synthetic turf comprising slit-film fibers with sand and rubber crumb infill was constructed. Experiments were conducted using a direct impact (Clegg) device and an artificial cleat-form. Material characterization tests were performed on the individual turf components, integrated into constitutive models, and a full turf FE model was constructed. The carpet was modeled with shell elements while the granular infill was modeled using smoothed-particle hydrodynamics (SPH) elements. A method to simulate the physical pre-conditioning performed on the experimental turf was developed. Both unconditioned and pre-conditioned turfs were assessed using Clegg tests. The re-created Clegg tests on the turf model demonstrated good agreement with the physical tests, with higher acceleration for the pre-conditioned turf. The turf model was validated using experiments with a turf test apparatus including dynamic translation and rotation of a cleat-form. The model predicted results in good agreement with the experiments (average CORA rating of 0.863) on pre-conditioned turf. The resulting model and methods can be expanded to synthetic turf of different constituent materials, to investigate their effects on cleat-surface interaction, optimizing performance, and reducing injury risk.

Enhanced beam and plate finite elements with shear stress continuity for compressible sandwich structures

This paper concerns and presents new improved beam and plate finite elements for analysing sandwich structures from the structural and modal points of view. In this study, the material behaviour is supposed to be linear elastic and orthotropic, but the method could be extended for nonlinear problems as well. The current models are able to treat the compressibility of the soft core materials, besides the interlaminar continuity conditions and the zero shear stresses on the shear-free surfaces are granted by the Lagrange multiplier method. In order to provide stress continuity along the element boundaries, the Hermite interpolation is employed for the elementary formulations that yields subparametric finite elements. On the contrary, the semi-analytical solutions of these enhanced beam and plate models are also discussed here for particular boundary conditions. The verification of the new finite elements is carried out by two case studies. The test examples are modelled and solved in commercial finite element software (ANSYS) with general shell and solid elements, too. The results derived from different models are subjected to a comprehensive comparison. Also, the structural and modal analyses of the test examples are presented during the case studies. The structural analysis of an overconstrained sandwich panel is also discussed to point out the significance of the proper shear stress distributions. Finally, the advantages and disadvantages of the newly developed elements and semi-analytical solutions are revealed in detail.

Transverse shear parametrization in hierarchic large rotation shell formulations

AbstractConsistent treatment of large rotations in common Reissner–Mindlin formulations is a complicated task. Reissner–Mindlin formulations that use a hierarchic parametrization provide an elegant way to facilitate large rotation shell analyses. This can be achieved by the assumption of linearized transverse shear strains, resulting in an additive split of strain components, which technically simplifies implementation of corresponding shell finite elements. The present study aims at validating this assumption by systematically comparing numerical solutions with those of a newly implemented hierarchic and fully nonlinear Reissner–Mindlin shell element.

Probabilistic buckling assessment and reliability of fiber-metal laminate, composite and aluminum cylindrical panels under compression with load and fabrication uncertainties

The objective of this article is to study the buckling behavior and reliability of fiber metal laminated (FML), composite and aluminum cylindrical panels under uniaxial compression taking into account fabrication and loading uncertainties. A 3D finite element modeling with ANSYS software has been implemented for this purpose. The panels are discretized using shell elements and the eigenvalue buckling analysis is conducted for the prediction of elastic buckling. The influences of load and fabrication uncertainties on the buckling load factor are studied with probabilistic analyses and the reliability of the panels is calculated. It is found that the thickness of aluminum layers is the most significant uncertain variable for the critical buckling load factor of FML panels, whereas the fiber misalignment angle of their composite layers is insignificant. As the metal volume fraction decreases, the sensitivity of the elastic buckling load factor to variations of the axial load distribution is reduced whereas its sensitivity to variations of the thickness of composite layers is increased. Consequently, the metal volume fraction is an important design parameter for the uncertain buckling behavior of the panels.