Conventional Shell Elements Research Articles

Design of Type-IV Composite Pressure Vessel Based on Comparative Analysis of Numerical Methods for Modeling Type-III Vessels

Compressed gas storage of hydrogen has emerged as the preferred choice for fuel cell vehicle manufacturers, as well as for various applications, like road transport and aviation. However, designers face increasing challenges in designing safe and efficient composite overwrapped pressure vessels (COPVs) for hydrogen storage. One challenge lies in the development of precise software programs that consider a multitude of factors associated with the filament winding process. These factors include layer thickness, stacking sequence, and the development of particularly robust models for the dome region. Another challenge is the formulation of predictive behavior and failure models to ensure that COPVs have optimal structural integrity. The present study offers an exploration of numerical methods used in modeling COPVs, aiming to enhance our understanding of their performance characteristics. The methods examined include finite element analysis in Abaqus, involving conventional shell element, continuum shell element, three-dimensional solid element, and homogenization techniques for multilayered composite pressure vessels. Through rigorous comparisons with type-III pressure vessels from the literature, the research highlights the most suitable choice for simulating COPVs and their practicality. Finally, we propose a new design for type-IV hydrogen composite pressure vessels using one explored method, paving the way for future developments in this critical field.

Generic method of local thickening in shell element FEM models for orthotropic bridge decks

AbstractThis paper presents a method of estimating the hot‐spot stress in orthotropic bridge decks (OBD) using a shell Finite Element (FE) model, in which local thickening is applied around the welded. The dimensions of the area of local thickening are a function of the weld throat thickness and the plate thickness. A comparison of this method with 3D solid element FE models is presented for various fatigue sensitive details. The comparison is carried out for OBD with trapezoidal stiffeners, both with continuous stiffeners through crossbeams and with stiffeners welded in between crossbeams. It is concluded that the accuracy of estimating the hot‐spot stress with a shell element model using local thickening is significantly higher as compared to a conventional shell element model without thickening. The method of local thickening is adopted in the new prTS 1993‐1‐901. This paper functions as the background to this technical specification.

Joint modelling in advanced thin-walled beam models

A methodology for thin-walled frame analysis using displacement modes of beams at joint interfaces has recently been proposed. This paper introduces an implementation that uses a specific advanced beam element based on semi-analytical beam mode solutions of a generalised beam theory. The end cross-sections of the beam elements consist of wall elements with displacement degrees of freedom that can be joined to conventional finite shell element models of the joints. However, before joining the beam element and joint model at the interface, both beam and joint model are transformed into cross-section displacement mode degrees of freedom. This transformation enables the use of a reduced mode space at the interface as well as in the beam. The quadratic nature of the beam mode equations of the beam element leads to a non-unique number of beam displacement modes. However, this paper introduces an exact mode selection technique that leads to a unique set of modes. Necessary details of the beam element formulation are included in order to make a self-contained description of the mode selection technique. Mode reduction through a length scale dependent choice of the number of exponentially decaying distortional modes is investigated and discussed for three types of joint design in four examples. The three joint design types investigated are based on in-plane membrane action, flexural out-of-plane action and a combination of both membrane and flexural action.

Mixed Graph-FEM phase field modeling of fracture in plates and shells with nonlinearly elastic solids

This paper presents a mixed Graph-FEM (Finite Element Method) approach for the phase field modeling of fracture in plates and shells composed of nonlinearly elastic solids. In this approach, the finite element mesh is deemed equivalent to a typical graph in computer science. The equation for phase field evolution is thus discretized by a graph Laplacian on a curved surface. A corresponding solver is herein developed, considering the matrix sparsity of the discretized system, and constraining irreversible phase field variables (to values greater than zero and less than one). An alternating solution strategy between mechanical equilibrium and the phase field equation is proposed. Our method is then applied to the fracture of plates and shells of arbitrary curvature, exhibiting fast convergence and robustness compared with our previous work, as could be concluded from the several numerical benchmarks we performed. This method opens a new way to efficiently model the fracture of plates and shells, while utilizing conventional shell elements.

Finite element modeling of crushing of CFRP cylindrical tubes under low-velocity axial impact

The dynamic axial crushing response of cylindrical tubes made of unidirectional (UD) carbon fiber-epoxy material is investigated numerically with emphasis on generating realistic crushing modes and crushing morphologies besides predicting crushing force with good accuracy. The emphasis is on the crushing modes since only the strong similarity between predicted crushed modes by the FE model and experimental observations can assure that the FE model dissipates the energy in the same manner that real composite absorbers dissipate it during the experimental trial. The impact behavior of two multi-layer models of laminated cylindrical tubes having different stacking sequences, namely cross-ply and angle-ply, were simulated using stacked layers of conventional 2D shell elements (S4R) bonded with the cohesive element interface model in ABAQUS. The FE progressive failure model of UD composite layers, including the damage initiations, damage evolution law, and element removal, is executed through a user-defined material subroutine (VUMAT) in ABAQUS/Explicit code. The implemented progressive failure material model represented well the various crushing modes, including fragmentation mode, splaying mode, and axial splitting of UD lamina in the splaying crushing mode. The FE model was validated by experimental test results obtained by the authors for cross-ply and angle-ply tubes subjected to axial impact.

An improved and robust finite element model for simulation of thin-walled steel bolted connections

Thin-walled cold-formed steel (CFS) structures are widely used in low-storey buildings and are seeing increased applications in multi-storey buildings as well as long-span structures. The bolted connection is one of the most common types of fasteners employed in CFS structures. The bolt slippage and load-bearing mechanism in CFS connections have a significant influence on the structural behaviour of cold-formed steel construction assemblies, which are typically numerically simulated using spring/connector elements. However, the determination of input parameters for the spring/connector elements generally requires load-deformation characteristics obtained from physical tests of lap joints, which are costly and time-consuming. Moreover, the use of spring/connector elements fails to explicitly capture the bolt bearing behaviour, resulting in inaccuracy in the simulation of CFS connections. In this paper, an accurate, efficient and robust numerical method that can fully replicate the behaviour of CFS connections considering both the effects of bolt slippage and bearing has been introduced. In the proposed numerical methodology, the cold-formed plates are modelled using the conventional shell elements, while a number of solid elements are introduced around the bolt holes, enabling the bolt-plate interaction to be explicitly accounted for, with contact pairs defined between the bolts and their surrounding solid element surfaces. The proposed numerical method could find a convergence solution using dynamic implicit solver in the general-purpose finite element (FE) software ABAQUS. Good agreement between the FE models using the proposed method and the available test results of CFS bolted connections were achieved, which sheds light on the promising application of the proposed method for simulating CFS assembled using bolted connections.

Efficient free vibration analysis of FGM sandwich flat panels with conventional shell elements

An efficient finite element model based on conventional shell elements available in ABAQUS software has been developed for free vibration analysis of FGM monolayer and sandwich flat panels. Applications to sandwich plates with an FGM layer embedded as either a core or face sheets with different through-the-thickness material gradations in the form of power (P-FGM), sigmoid (S-FGM), and exponential (E-FGM) distributions are considered. A user-defined material subroutine UMAT was used to implement functionally graded properties of the constitutive FGM layer. Numerical studies are given for free vibrations of monolayer and sandwich plates subjected to various boundary conditions and with different structural parameters such as span-to-thickness, face sheet-core-face sheet thickness and aspect ratios, and volume fraction index. The studies showed very good agreement between the present results and those existing in the literature that confirmed the accuracy of the developed model at minimal computational costs. This emphasizes the efficiency of the shell-based modeling strategy proposed for the calculations. A series of numerical solutions obtained in the research extends the results of known testing examples and may serve as additional benchmark data for other analysts.

Potential and challenges of a solid-shell element for the macroscopic forming simulation of engineering textiles

Finite element (FE) forming simulation offers the possibility of a detailed analysis of the deformation behaviour of engineering textiles during forming processes, to predict possible manufacturing effects such as wrinkling or local changes in fibre volume content. The majority of macroscopic simulations are based on conventional two-dimensional shell elements with large aspect ratios to model the membrane and bending behaviour of thin fabrics efficiently. However, a three-dimensional element approach is necessary to account for stresses and strains in thickness direction accurately, which is required for processes with a significant influence of the fabric’s compaction behaviour, e.g. wet compression moulding. Conventional linear 3D-solid elements that would be commercially available for this purpose are rarely suitable for high aspect ratio forming simulations. They are often subjected to several locking phenomena under bending deformation, which leads to a strong dependence of the element formulation on the forming behaviour [1]. Therefore, in the present work a 3D hexahedral solid-shell element, based on the initial work of Schwarze and Reese [2,3], which has shown promising results for the forming of thin isotropic materials [1], is extended for highly anisotropic materials. The advantages of a locking-free element formulation are shown through a comparison to commercially available solid and shell elements in forming simulations of a generic geometry. Additionally, first ideas for an approach of a membrane-bending-decoupling based on a Taylor approximation of the strain are discussed, which is necessary for an accurate description of the deformation behaviour of thin fabrics.

Finite element modeling ofCFRPcomposite tubes under low velocity axial impact

AbstractThe dynamic axial crushing response of circular tubes made of unidirectional carbon fiber‐epoxy composite was investigated numerically applying a new approach to the modeling of the delamination process. In the proposed approach, delamination (interface damage) was modeled by inserting isotropic resin plies capable of damage. They are tied to the adjacent laminae and replace the commonly used surface‐based cohesive model. Two multi‐layer models of laminated tubes having cross‐ply and angle‐ply stacking sequences were simulated using stacked conventional shell elements layers to capture the crushing response and intralaminar and interlayer damage of laminated tubes. The progressive failure analysis in Abaqus/Explicit was utilized to model the successive damage of both the interface and laminae. Both the intralaminar layers and isotropic resin layers were modeled by the conventional reduced integration shell element (S4R). The suggested modeling technique offers some advantages compared to the main‐stream interface modeling of the axial impact of laminated tubes. The computational cost is reduced and yet accurate predictions are obtained. The FE models based on the proposed delamination approach were validated by experimental test results obtained by the authors for cross‐ply and angle‐ply tubes subjected to a low‐velocity impact.

Design tailoring of curvilinearly grid-stiffened variable-stiffness composite cylindrically curved panels for maximum buckling capacity

In this paper, the buckling performance of curvilinearly grid-stiffened variable-stiffness composite cylindrically curved panels subjected to in-plane compressive loads under different boundary conditions is addressed. A Python-Abaqus script is developed to perform the buckling analysis of the panels. A novel planar mesh wrapping based approach is proposed to ease modelling of such curved panels with complex geometry. This approach offers numerous advantages including but not limited to separately modelling the skin and stiffeners using conventional shell elements as well as studying the mesh convergence of each component independently leading to more efficient and robust finite element models appropriate for optimization implementation. Using the proposed approach various parametric studies are conducted to investigate the influence of the panel curvature and the stiffness variation created by the fibers and stiffeners on the buckling response. Subsequently, an optimization routine is implemented to simultaneously determine the optimal fiber and stiffener paths for maximum buckling capacity. It is shown that by replacing the straight stiffeners by curvilinear ones the buckling resistance of the grid-stiffened quasi-isotropic skins can be enhanced. It is also shown that the panel curvature has a significant effect on the optimal layout of the grid-stiffeners. Optimization results demonstrate that for shallow curved panels up to 100% improvement in the buckling performance can be achieved by concurrently optimizing the curvilinear fiber trajectories of both the skin and stiffeners compared to their straight fiber and stiffener design counterparts.

Punching of RC slabs without transverse reinforcement supported on elongated columns

The paper investigates the influence of support elongation on punching resistance at internal slab column connections without shear reinforcement. Nonlinear finite element analysis (NLFEA) with 3-D solid elements is used to study the influence of column elongation on stress and strain in the slab around the column. Punching failure is shown to be triggered by localised peaks in shear stress around the corners of the support. Significantly, one-way shear is shown to increase the shear resistance of slabs supported on columns with cross sectional dimensions greater than around six times the slab effective depth (d). The common laboratory practice of supporting slabs in punching tests on elongated plates rather than columns is investigated numerically and is found to be reasonable despite uplift occurring in the central region of elongated plates. NLFEA with solid elements gives useful insights into punching failure but nonlinear shell elements are better suited to the practical assessment of slabs in building structures. The disadvantage of conventional nonlinear shell elements is that shear failure can only be detected through post processing of results. To circumvent this, the authors have previously developed a novel modelling approach in which 3-D joint elements are used to connect shell elements located to either side of a punching control perimeter positioned at 0.5d from the column face. The joint shear resistance is calculated using the Critical Shear Crack Theory (CSCT) in which punching resistance is related to slab rotation. Based on insights gained using the solid element modelling, this paper extends the use of the joint model to the modelling of punching failure at elongated supports by including one-way joints to model linear shear.

Complete transverse stress recovery model for linear shell elements in arbitrarily curved laminates

Out-of-plane failure is common in composite layered materials. Its detection in numerical simulations usually involves a high-level of spatial refinement which may lead to an excessive computational time for large structures. This paper presents a formulation for the recovery of the transverse stresses in conventional linear shell elements based on First-Order Shear Deformation Theory. Starting from the equilibrium equations, the proposed formulation allows the calculations to be made for arbitrary curvatures including variable ones. Compared to the Extended-2D method, it has the advantage of including all the contributions from the force and moment derivatives making it reliable in complex load cases. Several examples with different laminates, curvatures and loads are presented. The numerical results confirm the potential of the proposed method to be used both as post-processing tool for conventional models and as an enrichment criterion for adaptive modelling.

Development of a shell superelement for large deformation and free vibration analysis of composite spherical shells

Finite element analysis of huge and/or complicated structures often requires long times and large computational expenses. Superelements are huge elements that exploit the deformation theory of a specific problem to provide the capability of discretizing the problem with minimum number of elements. They are employed to reduce the computational cost while retaining the accuracy of results in FEM analysis of engineering problems. In this research, a new shell superelement is presented to study linear/nonlinear static and free vibration analysis of spherical structures with partial or full spherical geometries that exist in many industrial applications. Furthermore, this study investigates the effects of changing the superelement size and its number of nodes on solution accuracy. The governing equations of composite spherical shells are derived based on the first-order shear deformation theory and considering large deformations. For solving the nonlinear governing equations, the tangent stiffness matrix has been extracted and the Newton–Raphson method is employed. The capability of the presented shell superelement is investigated in several problems under linear/nonlinear static and free vibration analysis. The results acquired by the presented shell superelements are compared with available results in the literature and conventional shell elements in a commercial software. Results comparisons reveal high accuracy at a reduced computational cost in the superelement model.

An efficient ABAQUS solid shell element implementation for low velocity impact analysis of FGM plates

The main objective of this paper is to develop a numerical model susceptible to solve the numerical locking problems that may appear when applying the conventional solid and shell finite elements of ABAQUS. This model is based on a hexahedral solid shell element. The formulation of this element relays on the combination of the enhanced assumed strain (EAS) and assumed natural strain (ANS) methods with modified First Shear Deformation Theory (FSDT). The developed element is implemented into the ABAQUS user element (UEL) interface. The performance of this element is demonstrated by different benchmark tests from the literature. Our contribution consists on applying a single solid shell element through the thickness direction to predict the low velocity impact behavior on functionally graded material (FGM) circular plates.

Numerical and experimental investigation on dynamics of deployable space telescope experiencing deployment and attitude adjustment motions coupled with laminated composite shell

Nonlinear dynamic modeling methods for a flower-like clustered deployable space telescope (DST) with laminated composite material experiencing large deployment and attitude adjustment motions is proposed in present work. The flexible mirrors are discretized into shell elements in absolute node coordinate formulation (ANCF) considering nonlinear structures instead of using conventional shell elements in hybrid coordinate formulation (HCF). Meanwhile the stress–strain relations of laminated composite mirrors with considering nonlinear material and geometric properties are respectively deduced by high order shear deformation theory and continuum mechanics. Then, the accuracy of dynamic behavior is investigated by comparison of the results obtained by using ANCF and HCF, and it is indicated that ANCF shell elements are suitable for solving large deformation and deployment dynamic analysis of DST with high accuracy and strong convergence by numerical simulations. Further, the experiments for evaluating the dynamic behavior of surrounding mirrors with simultaneous deployment in different deployment strategies are conducted. Numerical results are in good agreement with those obtained from experiments to validate the correctness of the present nonlinear modeling formulation. And, the experiment and numerical simulation of the primary mirror experiencing attitude adjustment motions are also carried out. Those results illustrate the performance of the dynamic properties of DST with different deployment strategies and laminated composite structures in the present modeling method. These conclusions will have significant theory and engineering practice values for predicting surface accuracy, pointing accuracy and vibration performance of DST mechanism.

Reduced-Integrated 8-Node Hexahedral Solid-Shell Element for the Macroscopic Forming Simulation of Continuous Fibre-Reinforced Polymers

Finite element (FE) forming simulation offers the possibility of a detailed analysis of the deformation behaviour of continuously fibre-reinforced polymers (CFRPs) during forming, in order to predict possible manufacturing effects such as wrinkling or local changes in fibre volume content. The majority of macroscopic simulations are based on conventional two-dimensional shell elements with large aspect ratios to model the membrane and bending behaviour of thin fibrous reinforcements efficiently. However, without a three-dimensional element approach, stresses and strains in thickness direction cannot be modelled accurately. Commercially available linear 3D solid elements for this purpose are rarely suitable for forming simulations since they are subjected to several locking phenomena under bending deformation, especially with large aspect ratios. To alleviate this problem, so-called solid-shell elements based on the assumed natural strain (ANS) and enhanced assumed strain (EAS) method can be used. Therefore, a locking-free explicit reduced-integrated 8-node-hexahedron solid-shell element, based on the initial work of Schwarze and Reese (2011), is implemented in the commercially available FE solver Abaqus. Its suitability for macroscopic modelling of the forming behaviour of fibrous reinforcements is outlined in this work. The presented element combines the advantages of a locking-free out-of-plane deformation behaviour of conventional thin shell elements with the advantage of maintaining a fully three-dimensional material model and geometry description.

Capability Analysis of Abaqus Shell Element Based on Finite Element Method

Shell-like structures are widely used in many engineering structures. This work is forcing on the performance of the S4 element and S4R element, two types of conventional shell element in Abaqus, in different R/h ratios. In the scenario of a pipe-like configuration, both DKQ and MPT have different positions in different R/h ratios.

Delamination assessment of composite curved angles using simplified FEA models build-up by 2-D layered shell elements

As widely known, an accurate analysis of the stress state across the thickness of a composite laminate requires the calculation of the interlaminar through-the-thickness stresses as well as the shear stress components at the layers’ interfaces. These so-called out-of-plane stresses are the key parameters when defining the delamination strength of curved composite laminates, particularly when their radius of curvature and the thickness of the composite are of the same size order. Since the use of layered solid elements is far from a reasonable approach in practical design applications, based on the finite element analysis results obtained through the use of conventional layered shell elements, the purpose of this paper is to propose a simplified post processing approach that enable to predict the interlaminar stress components originated across the thickness of symmetrically balanced curved composite laminates under the combined action of axial forces, shear forces and bending moments applied in curvature plane. A benchmark analysis to provide a critical comparison between a reference finite element model constructed based on 3-D layered solid elements and a simplified model build-up by 2-D layered shell elements is also considered.

Finite element analysis of mode-I interlaminar fracture of lignocellulosic laminate specimens by virtual crack closure technique

The paper aims to study the interlaminar fracture of lignocellulosic laminate specimens made of beech veneer with urea formaldehyde resin and rye flour under pure mode-I loading. In order to determine the critical value of strain energy release rate GIc, representing one of the material input parameters for a finite element analysis involving the interlaminar fracture behaviour of a laminate structure under complex loading conditions, a lot of double cantilever beam (DCB) specimens processed from a lignocellulosic laminate beech veneer plate were tested by applying the specific standard procedures in conjunction with the modified beam theory method for data reduction. The propagation of interlaminar fracture under pure mode-I was then simulated by finite element analysis using layered conventional shell elements, based on the Virtual Crack Closure Technique (VCCT) in Abaqus/Explicit. Good agreements between the load-displacement curves obtained through the use of finite element analyses and the experimental testing results were obtained.

On Nonlinear Dynamic Modeling for a Rotating Paraboloidal Thin-Shell Appendage Attached to a Spacecraft Mechanism with Paraboloidal Curved Shell Element

A methodology for modeling a rotating paraboloidal thin-shell structure attached to a spacecraft body is proposed considering its geometric nonlinear effect. Instead of using conventional shell elements to discretize the paraboloidal thin-shell in the Cartesian coordinate, the paraboloidal coordinates in the meridional, circumferential and normal directions are employed to completely express the deformations of the curved thin-shell. Then, explicit expressions for the generalized elastic forces and stiffness varying matrices are deduced on the basis of exact strain-displacement relations. And, the rigid-flexible coupled dynamic model for the flexible multibody system is derived by the principle of virtual work. In contrast with the previous modeling approaches, the present method shows an advantage in avoiding large calculation quantity of nonlinear stiffness matrix due to more formalized. Furthermore, a full analysis with specific numerical simulation is achieved by using the present model and conventional shell model, respectively. All simulation results obtained by the two modeling methods verify the correctness and better convergence of the proposed methodology.