Composite Shell Element Research Articles

Structural behavior of sandwich panels with asymmetrical boundary conditions

Asymmetrically supported and loaded sandwich panels with a polyurethane soft core and isotropic or orthotropic steel faces were analyzed in laboratory tests and numerical simulations. The influence of the steel face microprofilation on the mechanical and kinematical responses of the sandwich panel is considered in the paper. The real experiments were conducted for two supporting systems. For each supporting system isotropic and orthotropic sandwich faces were taken into account. The numerical simulations, in which 2D composite shell elements were used, correspond to the real experiments. The laboratory tests showed that introducing the orthotropic face layer significantly increases the load capacity of the sandwich panel. In the case of asymmetrically supported systems effective flexural rigidity increases too. The paper demonstrates that a relatively simple FE model can be successfully used to assess the global behavior of sandwich panels in complex boundary conditions. Satisfactory consistency of the numerical and real results in the linear range of structural behavior was obtained. Further improvement of the model is possible by introducing a definition of the failure criteria.

A new triangular composite shell element with damping capability

This paper presents a new triangular composite shell element with damping capability. Formulation of the composite triangular shell element is based on stacking individual homogeneous triangular shell elements on top of each other. The homogeneous shell element is an assembly of a triangular membrane element with drilling degrees of freedoms and a plate element. Damping capability is provided by means of complex element stiffness matrix of individual flat layers of the composite element. These elements with damping capability allow modelling general structures with damping treatments. A few test cases are modelled using triangular finite element developed here and the results of the complex eigenvalue analyses are compared with those of the quadrilateral shell elements proposed recently. The results obtained using the presented triangular and previous quadrilateral composite elements are also compared with those based on modal strain energy method and experimental results. Comparisons of the experimental and the theoretical results confirm that the modal properties including modal damping levels of structures with damping treatments can be predicted with high accuracy using the proposed finite element.

Development and validation of a composite finite element with damping capability

This paper presents development and validation of a new composite Finite Element (FE) with damping capability. The damping capability is added to the composite shell element with physical drilling degrees of freedom by means of complex element stiffness matrix of the individual layers. The formulation is implemented in a FE code that allows modelling damped structures and performing modal analysis of the resulting complex eigenvalue problem. Some test cases are prepared and frequency response functions are measured in order to validate the predictions. The material properties used in the sample structures are identified experimentally using the Oberst Beam Method. Furthermore, the results obtained using the proposed composite FE are compared with those based on modal strain energy method. Comparisons of the experimental and the theoretical results confirm that the damping levels and the natural frequencies of damped structures can be predicted with high accuracy using the proposed formulation.

Compressive response of tapered curved composite plates based on a nine-node composite shell element

Tapered laminated structures have considerable potential for creating significant weight savings in engineering applications. The objective of the present work is to investigate the compressive response of curved composite plates with longitudinal internal ply-drop-off configurations. A nine-node tapered curved composite finite element is developed based on six well-established first-order shear deformation shell theories. The buckling loads obtained using Finite Element Method (FEM) are compared with that of the existing analytical and experimental results. A comprehensive parametric study is carried out and design guidelines for the tapered curved plates are established based on this study.

325 有限要素解析によるカーブキックのインパクトにおけるボール挙動シミュレーション(スポーツにおける打撃(1))

This study constructed finite element models of the simplified foot and soccer ball, and examined the factors affecting the ball behavior in curve kick. A 3D finite element model of the foot was developed using the barefoot and footwear shapes, which were obtained from a 3D laser scanner. A finite element model of the ball consisted of composite shell elements that include a hyperelastic model to define the latex bladder layer and a viscoelastic model to define the outer panels. Five experienced male university soccer players performed curve kicks. The kicking motions were captured three-dimensionally by two high-speed cameras at 2,500 fps. The models were validated by comparing the results of the finite element analysis to those of the experiment. Simulations of the ball behavior were conducted using the finite element models. The simulation results indicated the following. The ball velocity is largely affected by the foot velocity immediately before impact but barely affected by the Young's modulus of the shoe upper and the coefficient of friction. The ball rotation is affected by the foot velocity immediately before impact and the coefficient of friction; however, these factors had no significant effect.

A stabilized co‐rotational curved quadrilateral composite shell element

AbstractA new curved quadrilateral composite shell element using vectorial rotational variables is presented. An advanced co‐rotational framework defined by the two vectors generated by the four corner nodes is employed to extract pure element deformation from large displacement/rotation problems, and thus an element‐independent formulation is obtained. The present line of formulation differs from other co‐rotational formulations in that (i) all nodal variables are additive in an incremental solution procedure, (ii) the resulting element tangent stiffness is symmetric, and (iii) is updated using the total values of the nodal variables, making solving dynamic problems highly efficient. To overcome locking problems, uniformly reduced integration is used to compute the internal force vector and the element tangent stiffness matrix. A stabilized assumed strain procedure is employed to avoid spurious zero‐energy modes. Several examples involving composite plates and shells with large displacements and large rotations are presented to testify to the reliability, computational efficiency, and accuracy of the present formulation. Copyright © 2011 John Wiley & Sons, Ltd.

Free vibration of composite skewed cylindrical shell panel by finite element method

In this paper a composite triangular shallow shell element has been used for free vibration analysis of laminated composite skewed cylindrical shell panels. In the present element first-order shear deformation theory has been incorporated by taking transverse displacement and bending rotations as independent field variables. The interpolation function used to approximate transverse displacement is one order higher than for bending rotations. This has made the element free from locking in shear. Two types of mass lumping schemes have been recommended. In one of the mass lumping scheme the effect of rotary inertia has been incorporated in the element formulations. Free vibration of skewed composite cylindrical shell panels having different thickness to radius ratios ( h/R=0.01–0.2), length to radius ratios ( L/R), number of layers and fiber orientation angles have been analyzed following the shallow shell method. The results for few examples obtained in the present analysis have compared with the published results. Some new results of composite skewed cylindrical shell panels have been presented which are expected to be useful to future research in this direction.

Geometrically nonlinear finite‐shell elements with magnetostrictive layers

AbstractIn this paper a geometrically nonlinear composite shell element with integrated magnetostrictive layers is presented. Three translational and two rotational nodal degrees of freedom are used for the first‐order transverse shear approximation. The finite element is used in order to investigate shape and stability control problems of structures with magnetostrictive actuator layers in the range of large deformations. The numerical approximations to this static problem are obtained using the total Lagrangian formulation for the moderate rotation shell theory. The aforementioned finite element is used to numerically investigate the actuation behaviour of the integrated magnetostrictive layers. Since the magnetic field is prescribed, the coupled magnetoelastic problem turns into a decoupled problem. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A Co-Rotational 8-Node Resultant Shell Element for Progressive Nonlinear Dynamic Failure Analysis of Laminated Composite Structures

A nonlinear resultant shell element is developed for the solution of problems of composite plates and shells undergoing nonlinear static and nonlinear dynamic behavior with progressive layer failure. The formulation of the tangent stiffness is defined on the mid-surface and is efficient for analyzing thick laminated plates and shells by incorporating bending moments and transverse shear resultant forces in the geometric stiffness. The composite element is free of both membrane and shear locking behavior by using the assumed natural strain method, such that the element also performs very well as thin laminate shells. An equilibrium approach is used to derive the improved transverse shear stiffness, instead of using a shear correction factor. The proposed formulation is computationally efficient and the test results show good agreement with references. The composite shell element is extended to determine ply failures in laminated composite structures undergoing nonlinear static or dynamic behavior. The failure analysis is done by first, computing for the inter-laminar stresses at each gauss point in an element. Having obtained the stresses in each layer, checking for failure is performed based on a chosen failure criterion. Four failure criteria are available to enable the user to adopt the appropriate criterion for the type of problem parameters present.

Nonlinear Transient Analysis of Laminated Composite Shells

In this study the geometrically nonlinear transient response of the laminated composite doubly curved shells is investigated using the finite element method. The finite element model includes nonlinearity due to large deflection. A nine-noded isoparametric composite shell element including the first-order shear deformation is developed in curvilinear coordinates for the nonlinear transient analysis. The present formulation is based on the total Lagrangian approach and the material behavior is assumed to be linear and elastic. The governing equations have been solved by the Newton–Raphson iteration technique, wherein the Newmark method has been used for the time integration. The present results are found to compare well with those available in the literature. The nonlinear transient response of the cross-ply and three specially laminated spherical, cylindrical, and hyperbolic paraboloidal shell panels are also analyzed and the results are discussed.

A 4-node co-rotational ANS shell element for laminated composite structures

The formulation of a non-linear composite 4-node co-rotational resultant shell element is presented for the solution of bending, free vibration, critical buckling and postbuckling analysis of composite plates and shells. Using the ANS (assumed natural strain) method the present shell element generates shear locking behavior, and such element performs very well as much as shells get thin. The formulation of the geometrical stiffness presented here is exactly defined on the mid-surface and is efficient for analyzing stability problems of thin and thick laminated plates, and shells by incorporating bending moment and transverse shear resultant forces. The transverse shear stiffness is defined by an equilibrium approach instead of using the shear correction factor. The adoption of a second-order co-rotational formulation makes it computationally efficient compared to the most existing composite shell elements. The proposed formulation is computationally efficient and the test results showed good agreement.

Nine-Node Resultant-Stress Shell Element for Free Vibration and Large Deflection of Composite Laminates

The newly constructed formulation of an element-based resultant-stress nine-node composite shell element is presented for the solution of free vibration and large deflection problems of isotropic and composite laminates. In this paper, the effectiveness of this new formulation is investigated in the static and free vibration analysis. The strain–displacement relationship of the shell could be explained from the point of the new element-based Lagrangian finite element formulation. The newly added terms between bending strain and displacement reflect the contributions of displacements to the curvature. Natural coordinate-based strains, stresses, and constitutive equations are used throughout the element-based Lagrangian formulation of the present shell element which offers significant implementation advantages compared with the traditional Lagrangian formulation. Using the assumed natural strain method the present shell element generates neither membrane nor shear locking behavior, and such an element performs very well as much as shells become thin. The arc-length control method is used to trace complex load–displacement paths and the Lanczos method is employed in the calculation of the eigenvalues of shells. A number of numerical analyses are presented and discussed in order to explore the capabilities of the present shell element. The test results showed very good agreement.

Soccer ball anisotropy modelling

The work presented in this paper details the development of a finite element (FE) model of a soccer ball, allowing for a greater understanding of the performance of soccer balls under dynamic conditions that are representative of play. The model consists of composite shell elements that include a hyperelastic strain energy potential equation to define the latex bladder layer and a plane stress orthotropic elastic material model to define the anisotropic woven fabric outer panels. The model was validated through a series of experimental impact tests whereby the ball was impacted normal to a rigid plate at an inbound velocity of approximately 34ms−1 (76mph), with each impact recorded using high speed video (HSV) techniques. It was found that the combined effects of ball design and panel material anisotropy resulted in impact properties such as coefficient of restitution, contact time, deformation and the 2D shape taken up by the ball at maximum deformation, to vary with pre-impact ball orientation. The model showed good agreement with the measurements, and its ability to represent the effects of anisotropy in ball design.

Non-linear random response of laminated composite shallow shells using finite element modal method

This paper investigates the large-amplitude multi-mode random response of thin shallow shells with rectangular planform at elevated temperatures using a finite element non-linear modal formulation. A thin laminated composite shallow shell element and the system equations of motion are developed. The system equations in structural node degrees-of-freedom (DOF) are transformed into modal co-ordinates, and the non-linear stiffness matrices are transformed into non-linear modal stiffness matrices. The number of modal equations is much smaller than the number of equations in structural node DOF. A numerical integration is employed to determine the random response. Thermal buckling deflections are obtained to explain the intermittent snap-through phenomenon. The natural frequencies of the infinitesimal vibration about the thermally buckled equilibrium positions (BEPs) are studied, and it is found that there is great difference between the frequencies about the primary (positive) and the secondary (negative) BEPs. All three types of motion: (i) linear random vibration about the primary BEP, (ii) intermittent snap-through between the two BEPs, and (iii) non-linear large-amplitude random vibration over the two BEPs, can be predicted. Copyright © 2006 John Wiley & Sons, Ltd.

Longitudinal strength analysis of ship hulls of composite materials under sagging moments

An approach to estimate the longitudinal strength of ship hulls in composite materials is presented in the paper. Typical ship configurations have as dominant failure mode the failure of the deck under compression associated with sagging moments. Ship hulls are modeled as assemblies of stiffened composite panels. Buckling, material failure and ultimate collapse of the stiffened panels are predicted by nonlinear finite element analysis, which is based on a degenerated three-dimensional laminated composite shell element with updated Lagrangian formulation and first-order shear deformable kinematics. According to buckling, material failure and ultimate collapse of stiffened panels, the corresponding longitudinal strengths of ship hull are derived from a simplified method. A ship hull under sagging is analysed as an example application.

Linear static and dynamic analysis of laminated composite plates and shells using a 4-node quasi-conforming shell element

Quasi-conforming formulation of 4-node stress resultant shell element is presented for the linear static and dynamic analysis of composite plates and shells. The element formulations use interrelated displacement-rotation interpolations making it applicable for moderately thick and thin composite shells. The formulation also includes drilling degrees of freedom, allowing the modeling of stiffened composite plates and shells. The transverse shear stiffness is defined by an equilibrium approach instead of using the shear correction factor. The stiffness matrices for the present elements are explicitly expressed and the stresses are taken accurately at the nodal points. A lot of numerical tests were carried out for the validation of present 4-node composite shell element and the results are in good agreement with the references.

Thermal Residual Stress Analysis of Ni–Al2O3, Ni–TiO2, and Ti–SiC Functionally Graded Composite Plates Subjected to Various Thermal Fields

This study investigates the thermal elastic residual stresses occurring in Ni–Al2O3, Ni–TiO2, and Ti–SiC functionally graded plates due to uniform, linear, and parabolic temperature fields through the plate thickness. A 3D eight-noded isoparametric layered (no limit layer number) finite element with three degrees of freedom at each node was implemented to the residual stress problem analogous to the shell elements proposed by Ahmad et al. (Ahmad, S., Irons, B.M. and Zienkiewicz, O.C. (1970). Analysis of Thick and Thin Shell Structures by Curved Finite Elements, Int. J. of Numerical Methods in Engineering, 2: 419–451.) and Yunus and Khonke (Yunus, S.M. and Khonke, P.C. (1989). An Efficient Through-Thickness Integration Scheme in an Unlimited Layer Doubly Curved Isoparametric Composite Shell Element, Int. J. of Numerical Methods in Engineering, 28: 2777– 2793.). The longitudinal stresses (11, 22) and transverse shear stresses (13, 23) were dominant. The shear stresses become important especially at the free edges of the plate. As the compositional gradient was increased the normal and shear stresses increased. Whereas the normal stresses become tensile in both ceramic-rich and metal-rich regions; the shear stresses, which are not severe in both the regions, change their directions and become a maximum inside the plate. The thermal and mechanical properties of constituents played an important role on the stress magnitudes rather than on the profiles of the through-thickness variations of normal and shear stresses. Thus, the difference of the coefficients of thermal expansion of the ceramic and metal phases affected the magnitudes of the normal and shear stresses. In addition, the continuous temperature fields through the plate thickness resulted in similar normal and shear stress variations.

Stochastic finite element analysis of shells with combined random material and geometric properties

In this work, an extended stochastic formulation of the triangular composite facet shell element TRIC is presented for the case of combined uncertain material (Young’s modulus, Poisson’s ratio) and geometric (thickness) properties. These properties are assumed to be described by uncorrelated two-dimensional homogeneous stochastic fields. The stochastic finite element analysis of shell structures is performed using the spectral representation method for the description of the random fields in conjunction with Monte Carlo simulation (MCS) for the computation of the response variability. Useful conclusions regarding the influence of each one of the structural parameters on the response variability are derived from the numerical tests examined.

A co-rotational 8-node assumed strain shell element for postbuckling analysis of laminated composite plates and shells

The formulation of a nonlinear composite shell element is presented for the solution of stability problems of composite plates and shells. The formulation of the geometrical stiffness presented here is exactly defined on the midsurface and is efficient for analyzing stability problems of thin and thick laminated plates and shells by incorporating bending moment and transverse shear resultant forces. The composite element is free of both membrane and shear locking behaviour by using the assumed natural strain method such that the element performs very well as thin shells. The transverse shear stiffness is defined by an equilibrium approach instead of using the shear correction factor. The proposed formulation is computationally efficient and the test results showed good agreement. In addition the effect of the viscoelastic material is investigated on the postbuckling behaviour of laminated composite shells.

Stochastic finite element analysis of shells

In the present paper the stochastic formulation of the triangular composite (TRIC) facet shell element is presented using the weighted integral and local average methods. The elastic modulus of the structure is considered to be a two-dimensional homogeneous stochastic field which is represented via the spectral representation method. As a result of the proposed derivation and the special features of the element, the stochastic stiffness matrix is calculated in terms of a minimum number of random variables of the stochastic field giving a cost-effective stochastic matrix. Under the assumption of a pre-specified power spectral density function of the stochastic field, it is possible to compute the response variability of the shell structure. Numerical tests are provided to demonstrate the applicability of the proposed methodologies.