Composite Shell Element Research Articles

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.

Geometrically nonlinear analysis of functionally graded composite shells using MITC4 and MITC9 elements

In this paper, the geometrically nonlinear behaviors of functionally graded composite shells under large displacements and large rotations are analyzed. Instead of constructing conventional layer-wised models, equivalent single-layer composite shell elements based on general displacement fields are developed to model the inhomogeneity of composite materials. The mixed interpolation of tensorial components technique is used to eliminate membrane locking and shear locking phenomena. The assumed covariant strain fields are initially constructed before being used to evaluate the second Piola–Kirchhoff stress and construct stiffness matrices in local Cartesian coordinates. The standard full Newton–Raphson method is utilized to solve a system of nonlinear equations. Geometrically nonlinear analyses are performed on different thin-walled composite structures including thin cantilever beams, slit annular plates, pinched cylindrical shells, and hemispherical shells. Obtained results demonstrate good convergence characteristics and modeling capability of the developed quadrilateral composite shell elements in analyzing thin-walled composite structures.

Simulation of Static Tyre–Pavement Interaction Using Two FE Models of Different Complexity

The aim of this research study was to analyse the approaches for establishing a spatial model of a radial truck tyre, based on the finite element method, in order to perform a realistic analysis of static as well as dynamic tyre–pavement interactions. A complex rubber tyre model having a large number of elements was formulated combining current state-of-the-art modelling techniques and, from that model, a simplified model having a smaller number of elements was derived. The complex model proved to be useful only for static loading, because of its high computational demand, while the simplified model proved to be also suitable for dynamic modelling. The two tyre models having different numbers of elements were compared by analysing the contact areas and stresses. Our results indicate that the basic idea of not changing material characteristics while simplifying the model, rebuilding only the carcass using composite shell elements, did not prove to be a satisfactory direction. The results given by the simplified model do not describe the behaviour of the radial tyre well but, rather, describe the behaviour of the diagonal tyre, regarding contact areas and stresses. On the contrary, when analysing stresses and strains in the road pavement structure, the two finite element models provided similar results in practice. Based on our comparison calculations, applying the average contact pressure q at analysis points at a 5–8 cm depth, the contact behaviour of the finite element tyre model can be used in any elastic-layer theory-based software.

An alternative three-node triangular composite shell element in terms of Reddy-type higher-order theory

Composite curved shells are widely utilized as structural components in aerospace engineering. To inspire the potentiality of such structure, it is very necessary to well understand mechanical behaviors of composite curved shells. Compared to the composite plates, it is more difficult to predict accurately interlaminar stresses of composite curved shells. Therefore, this paper attempts to propose an alternative triangular composite shell element in terms of the Reddy-type global–local higher-order theory. In the present model, the continuity conditions of transverse shear stresses are enforced in advance to fulfill compatibility of transverse shear stresses at adjacent layers, which can improve precision of interlaminar stresses. In order to evaluate performance of the proposed shell element, several typical examples have been analyzed. Moreover, the results acquired from the present model are compared with the three-dimensional elasticity solutions and other published results. At the same time, a compression experiment of the thin-walled cylindrical grid structure is carried out to further verify the capability of the present model. These examples show that the proposed composite shell element can be used as an alternative method for static analysis of multi-layer thin and thick shell structures.

Structural Fire Analysis of One‐storey Steel‐framed Buildings with Steel Claddings

AbstractTraditionally the structural stability of steel building frames is ensured by frame action or bracing elements. Recent European research projects have demonstrated that significant cost savings can be achieved, if cladding panels forming the building envelope are used to provide stability. The purpose of the paper is to investigate the possible stabilization effect of steel structures by steel claddings in fire, without additional wind bracings using Finite Element Method. The Finite Element analyses for full‐scale steel‐framed buildings with steel claddings under fires are still challenging due to large number of elements in the steel claddings. In this paper, the equivalent orthotropic shell element is used to model the trapezoidal roof sheeting, and composite shell element with soft core is used to model the sandwich panel in the cool compartment. Due to the delamination of inner steel face in fire, the sandwich panels in the fire compartment can be either neglected or modeled with two‐layer composite shell ignoring the inner steel sheet. The comparative study is performed, and the results suggest that the difference is small and the sandwich panels in the fire compartment can be neglected. The stabilization effect of steel claddings in fire is studied by the comparison of deformation and force responses between buildings with traditional steel bracings and with steel cladding only. In case of ISO fire, the fire resistance of entire one‐storey building with steel claddings only is 22% longer than the one with traditional steel bracings.

Hybrid FRP-timber thin-walled Cee section columns under axial compression: Numerical modelling

This study presents the first ever investigation aimed at accurate numerical modelling of the behavior of hybrid fibre reinforced polymer (FRP)-timber laminated (HFT) Cee section columns under axial compression. Existing numerical modelling approaches for modelling thin-walled structural members, such as modelling using composite laminate shell elements, orthotropic laminate shell elements with experimentally obtained properties, were found to either over-predict or under-predict the stiffness and capacity depending on the approach used. Existing modelling approaches fail to accurately capture the effects of possible interlaminar slips under combined flexural and axial loading. A new modelling approach using ABAQUS subroutine UGENS was proposed incorporating both in-plane stiffness matrix and bending stiffness matrix simultaneously, forming the general section stiffness matrix. Failure initiation criteria and a damage evolution law were incorporated in the subroutine to derive the damaged section stiffness matrix. The predictions from the proposed numerical model showed much improved agreement with the test results.

Numerical prediction of deformation in thin-plate welded joints using equivalent thermal strain method

Large welding-induced distortions are inevitably generated in a thin-plate welded joint due to its weak stiffness. In this study, an equivalent thermal strain method based on inherent strain theory is proposed to predict the welding deformation of thin plates. An artificial temperature and an orthotropic thermal expansion coefficient are adopted to directly simulate the welding shrinkage and bending behavior of the cooling phase in all directions. To describe the distribution of transverse inherent strain through thickness more accurately, a composite shell element is employed, which can divide the thickness into multiple layers and set different material properties. A three-dimensional (3D) thermo–elastic–plastic finite element method (TEP-FEM) model is also developed to simulate the welding process of a thin plate and compute the inherent strain. Moreover, an experiment was performed to verify the accuracy of the numerical model. Comparing the results from experimental data, TEP-FEM, and the proposed method, it is discovered that the new method can predict the deformation of a thin-plate welded joint with good computational accuracy.

A new triangular shell element for composites accounting for shear deformation

In this paper, we propose an efficient 3-node shell element with 6 DOFs per node based on Naghdi-Reissner-Mindlin theory. This new composite shell element, further denoted as DKMT18, takes into account shear deformation and coupled bending-membrane energy. DKMT18 element passes membrane, bending, and shear patch tests with no spurious mode. It also performs successfully in standard tests for thick and thin shells problems without membrane or shear locking. The proposed shell element is capable of dealing with composite laminated shell structures. The computed results by the DKMT18 element converge more rapidly towards the reference solution compared to any state of-the-art shell element.

Aeroelastic tailoring method of tow-steered composite wing using matrix perturbation theory

In this study, a computational method based on matrix perturbation theory was proposed to solve the aeroelastic sensitivity of the fibre angle of tow-steered composite wings and find the optimal local fibre paving path for aeroelastic tailoring. Firstly, the finite element model of straight fibre composite wing was created with the multilayer composite shell element in MSC/NASTRAN. Then, the flutter velocity-sensitive region with local fibre angle was determined using matrix perturbation theory. The fibre angles were carefully adjusted only in the highly sensitive region to increase the flutter velocity, and the optimal fibre paving path was obtained. Genetic algorithm based on traditional aeroelastic tailoring method was used to carry out aeroelastic tailoring for the wings of straight and curved fibre laminated plates. Calculation results of the two tailoring methods indicate that the proposed method only needs to optimise the fibre angle in a small region to achieve the same aeroelastic tailoring effect of the traditional optimisation algorithm for tow-steered composites. The obtained maximum curvature of the fibre is also greatly decreased, which effectively reduces the difficulty in the paving process of the curvilinear fibre. The designability of tow-steered composite wings can be further improved.

Multiscale analysis of woven composite structures in MSC.Nastran

In the finite element analysis (FEA) of composite structures, shell and beam elements with homogenized material properties are often used to reduce the computational costs and modeling efforts. However, significant loss of accuracy may occur due to constitutive modeling limitations of commercially available software packages for complex mesostructures such as woven composites. In this paper, CQUAD4, CQUAD8 and CBEAM elements in MSC.Nastran have been enabled to analyze complex woven composite structures using mechanics of structure genome (MSG). The plate and beam stiffness matrices are computed using MSG plate and beam models and transformed into MSC.Nastran element and material properties to perform the structural analysis. A three-dimensional (3D) orthogonal woven plate is analyzed using MSC.Nastran CQUAD4 elements based on MSG plate model. In addition, a 3D woven beam with extension-bending couplings is analyzed using MSC.Nastran CBEAM elements with homogenized properties with the help of MSG beam model. The beam and shell elements in MSC.Nastran powered by MSG models provide a new way to analyze complex woven composite structures. A graphical user interface (GUI) has been developed for MSC.Nastran to incorporate the constitutive modeling and to enable the automation of the information passing between constitutive modeling and structural analysis.

Assessment of Collapse Pressure of Laminated Composite Subsea Shells Subjected to Hydrostatic Follower Force

A doubly curved composite shear deformable shell element has been developed for the buckling analysis of composite subsea shells which takes into consideration the effect of hydrostatic follower force. This element is based on first-order shear deformation theory considering the nonlinear curvature terms of the strain–displacement relations in order to simulate the realistic structural behaviour of thin composite shells. It has been employed for the prediction of collapse pressure, including the follower force effect of thin composite cylindrical and shallow shell panels, which form a part of subsea structures.

Nonlinear Performance of Concrete Beam Reinforced with Prestressed Hybrid Cfrp/Gfrp Composite Sheet

The consolidation technology of prestressed hybrid fibre CFRP/GFRP sheet takes full advantages of the initiative of the prestressed reinforcement and force transferring of the composite materials features, which belongs to relatively advanced reinforcement strategies in reinforcement area. This paper derives nonlinear composite element and shell element to simulate concrete beam and the prestressed hybrid fibre CFRP/GFRP sheet. Besides, the characters of nonlinear concrete beams are described by the Owen yielding criterion and the Hinton crushing criterion. Meanwhile, the three-dimensional prestressing effects of the composite CFRP/GFRP materials have been realized and the nonlinear finite element computer program of reinforced system has been compiled. In order to determine the best stress condition of prestressed hybrid fibre CFRP/GFRP composite materials, the optimal hybrid CFRP/GFRP ratio is achieved through the systematic calculation based on two main properties which take the strength and ductility properties into consideration. The results show that the optimal CFRP/GFRP hybrid ratio is one of the major factors to impact its mechanical properties of the reinforced structure which has been strengthened by the prestressed hybrid fibre CFRP/GFRP sheet. And the theoretical method and calculation model that determine the optimal hybrid CFRP/GFRP ratio in this paper is reasonable and reliable. The research conclusions can be used as a reference in practice construction design.

Modeling, simulation, and experiments of high velocity impact on laminated composites

High velocity impact on laminated composite panels is investigated by modeling, simulation, and experiments. Impact velocities of 100, 200, and 300 m/s are considered and normal as well as oblique impacts are studied. FEM simulations are conducted to design three different laminate configurations to achieve the cases of a reflecting, almost stucking, and fully perforating impactor, respectively. Within a domain where material nonlinearities are expected the shell-based ply-scale approach is used. Every ply is modeled by a layer of shell elements which are connected via cohesive zone elements. Both element types are assigned nonlinear constitutive laws to capture their mechanical behavior appropriately. Outside this domain, a single layer of composite shell elements is used. Corresponding laminated plates are produced and tested using a gas gun setup, where energy absorption and damage patterns are assessed.The comparison of simulations and experiments shows excellent agreement. The three cases are predicted well, and also the damage patterns and the energy absorptions match very well.

Shear deformable shell element DKMQ24 for composite structures

In this work we propose a new 4-node DKMQ24 shell element based on Naghdi-Reissner-Mindlin shell theory with 24 degrees of freedom. This new composite shell element, which is developed from DKMQ plate and shell elements, takes into account shear deformation, coupled bending-membrane energy and warping effects. This element has no spurious mode, passes patch tests for membrane, bending and shear problems. It has also successfully passed standard benchmark tests in the case of thick and thin shells without membrane and shear locking. In this paper, we extend the predictive capabilities of the DKMQ24 shell elements to composite laminated plates and shell structures. Numerical results obtained from DKMQ24 are compared against state-of-the-art shell elements. The results obtained by the proposed element converge more rapidly towards the reference solution.

Vibration of laminated-beams based on reference-plane formulation: Effect of end supports at different heights of the beam

Conventional beam elements based on the mid-plane formulation are often used to predict vibration frequencies of beams. Recently published work on the vibration of functionally graded materials (FGM) beams shows that if the positions of immovable end supports are at a different plane to the middle-plane, beam elements based on mid-plane formulation will yield inaccurate results. This paper extends this work further by critically examining the effect of end support positions along the height of the beam in the context of vibration analysis. A formulation for vibration analysis of beams based on reference-plane formulation is proposed. In order to verify the proposed formulation, we considered FE modelling of beams based on generalized beam elements, composite shell elements and 3D solid elements that are able to accurately capture the effect of end support height position on vibration frequencies. Two vibrating beam examples are considered. The first problem deals with a single layer beams and the second problem deals with a double layer beam. Both problems are analyzed using the proposed method and FE models based on generalized beam elements, composite shell elements and 3D solid elements for different end support conditions and heights. Single layer beam was also modelled in FE using conventional beam elements. The results clearly showed that if one uses conventional beam elements for vibration analysis of beams, the results will not be accurate if immovable end supports are applied at an eccentricity to the mid-plane. Vibration frequencies predicted from the proposed reference-plane formulation were shown to agree well with the results from FE models based on generalized beam elements, composite shell elements, and 3D solid elements.

Nonlinear vibration analysis of a hard-coating cylindrical shell with elastic constraints by finite element method

In this paper, the nonlinear vibration characteristics of the hard-coating cylindrical shell with base excitation are investigated based on a composite cylindrical shell element of 4 nodes and 48 degrees of freedom. An elastic constraint with continuous variable stiffness is constructed to simulate the real boundary conditions of the shell. Considering the material damping, the equivalent viscous damping and the strain dependencies of storage modulus and loss factor of hard coating, a unified nonlinear iterative solution method is developed for the vibration analysis. As an example to demonstrate the feasibility of the developed model, the experimental test of the cylindrical shell coated with NiCoCrAlY $$+$$ YSZ hard coating is implemented. The results of the developed model and experimental test show a good consistency, and both indicate that the hard-coating cylindrical shell with strain dependence has the unique properties of soft nonlinearity compared with the linear results.

A 4-Node Co-Rotational Quadrilateral Composite Shell Element

A 4-node co-rotational quadrilateral composite shell element is presented. The local coordinate system of the element is a co-rotational framework defined by the two bisectors of the diagonal vectors generated from the four corner nodes and their cross product. Thus, the element rigid-body rotations are excluded in calculating the local nodal variables from the global nodal variables. Compared with other existing co-rotational finite-element formulations, the present element has two features: (i) The two smallest components of the mid-surface normal vector at each node are defined as the rotational variables, leading to the desired additive property for all nodal variables in a nonlinear incremental solution procedure; (ii) both element tangent stiffness matrices in the local and global coordinate systems are symmetric owing to the commutativity of the nodal variables in calculating the second derivatives of strain energy with respect to the local nodal variables and, through chain differentiation with respect to the global nodal variables. In the modeling of composite structures, the first-order shear deformable laminated plate theory is adopted in the local element formulation, where both the thickness deformation and the normal stress in the direction of the shell thickness are ignored, and an assumed strain method is employed to alleviate the membrane and shear locking phenomena. Several examples involving composite plates and shells with large displacements and large rotations are presented to testify to the reliability and convergence of the present formulation.

Physics-Based Flexible Tire Model Integrated With LuGre Tire Friction for Transient Braking and Cornering Analysis

In transient vehicle maneuvers, structural tire deformation due to the large load transfer causes abrupt change in normal contact pressure and slip distribution over the contact patch, and it has a dominant effect on characterizing the transient braking and cornering forces including the history-dependent friction-induced hysteresis effect. To account for the dynamic coupling of structural tire deformations and the transient tire friction behavior, a physics-based flexible tire model is developed using the laminated composite shell element based on the absolute nodal coordinate formulation and the distributed parameter LuGre tire friction model. In particular, a numerical procedure to integrate the distributed parameter LuGre tire friction model into the finite-element based spatial flexible tire model is proposed. To this end, the spatially discretized form of the LuGre tire friction model is derived and integrated into the finite-element tire model such that change in the normal contact pressure and slip distributions over the contact patch predicted by the deformable tire model enters into the spatially discretized LuGre tire friction model to predict the transient shear contact stress distribution. By doing so, the structural tire deformation and the LuGre tire friction force model are dynamically coupled in the final form of the equations, and these equations are integrated simultaneously forward in time at every time step. The tire model developed is experimentally validated and several numerical examples for hard braking and cornering simulation are presented to demonstrate capabilities of the physics-based flexible tire model developed in this study.

Shape control of piezolaminated thin‐walled structures using nonlinear piezoelectric actuators

AbstractIn the present paper a 2D‐shell finite element model is proposed to carry out static analysis of piezolaminated composite shells by incorporating nonlinear constitutive relations in order to describe the electromechanical coupling under strong electric fields. The present shell element has 5 mechanical DOFs and 3 electrical DOFs per node. The developed composite piezolaminated shell element is employed to study the static behavior and shaping of spherical antenna reflector laminated with piezo‐patches under both weak and strong electric fields. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Simplified welding distortion analysis for fillet welding using composite shell elements

This paper presents the simplified welding distortion analysis method to predict the welding deformation of both plate and stiffener in fillet welds. Currently, the methods based on equivalent thermal strain like Strain as Direct Boundary (SDB) has been widely used due to effective prediction of welding deformation. Regarding the fillet welding, however, those methods cannot represent deformation of both members at once since the temperature degree of freedom is shared at the intersection nodes in both members. In this paper, we propose new approach to simulate deformation of both members. The method can simulate fillet weld deformations by employing composite shell element and using different thermal expansion coefficients according to thickness direction with fixed temperature at intersection nodes. For verification purpose, we compare of result from experiments, 3D thermo elastic plastic analysis, SDB method and proposed method. Compared of experiments results, the proposed method can effectively predict welding deformation for fillet welds.