Layerwise Finite Element Model Research Articles

A quasi-3D layer-wise finite element model for vibroacoustic analysis of finite sandwich plates with frequency-dependent viscoelastic core

This article presents a quasi-3D layer-wise finite element approach to investigate the vibroacoustic characteristics of finite constrained layer damping (CLD) plates with a viscoelastic material (VEM) core. The frequency-dependent properties of the VEM core are integrated into the kinematic governing equation. The sound transmission loss (STL) behavior under oblique plane sound wave excitation is studied in narrow frequency bands, thus the variation caused by resonance modes can be captured clearly. Results show that the STL values of the two CLD plates configurations are significantly increased in resonance frequency regions. The symmetric configuration is found to have better sound insulation performance.

On the layerwise finite element formulation for static and free vibration analysis of functionally graded sandwich plates

This paper presents a novel C0 higher-order layerwise finite element model for static and free vibration analysis of functionally graded materials (FGM) sandwich plates. The proposed layerwise model, which is developed for multilayer composite plates, supposes higher-order displacement field for the core and first-order displacement field for the face sheets maintaining a continuity of displacement at layer. Unlike the conventional layerwise models, the present one has an important feature that the number of variables is fixed and does not increase when increasing the number of layers. Thus, based on the suggested model, a computationally efficient C0 eight-node quadrilateral element is developed. Indeed, the new element is free of shear locking phenomenon without requiring any shear correction factors. Three common types of FGM plates, namely, (i) isotropic FGM plates; (ii) sandwich plates with FGM face sheets and homogeneous core and (iii) sandwich plates with homogeneous face sheets and FGM core, are considered in the present work. Material properties are assumed graded in the thickness direction according to a simple power law distribution in terms of the volume power laws of the constituents. The equations of motion of the FGM sandwich plate are obtained via the classical Hamilton’s principle. Numerical results of present model are compared with 2D, quasi-3D, and 3D analytical solutions and other predicted by advanced finite element models reported in the literature. The results indicate that the developed finite element model is promising in terms of accuracy and fast rate of convergence for both thin and thick FGM sandwich plates. Finally, it can be concluded that the proposed model is accurate and efficient in predicting the bending and free vibration responses of FGM sandwich plates.

Dynamic responses analysis of P and S-FGM sandwich cylindrical shell panels using a new layerwise method

This research work presents a comparison of the dynamic response of the functionally graded sandwich cylindrical shell panels (FGSCS) using a new layerwise method. The layerwise method developed assumes a first-order shear deformation theory (FSDT) for top and bottom facesheets and a third-order shear deformation theory for the core. The strain-displacement relation for FGSCS panels is obtained using Sander's first approximation. Two different sandwich configurations are considered, one having a pure metallic core with top and bottom facesheets made of functionally graded material (FGM) and the other one having an FGM core with top and bottom facesheets made of pure ceramic and pure metal, respectively. Material properties of the FGM layers for the two configurations are varied along the thickness direction according to the power-law (P-FGM) and the sigmoid models (S-FGM) respectively. The newly developed layerwise finite element model in conjunction with Hamilton's principle is employed to obtain the governing differential equation. Subsequently, the Newmark-Beta time integration scheme is used to obtain the dynamic response of P and S functionally graded sandwich cylindrical shell (P and S-FGSCS) panels for two configurations. The results obtained are first compared with the exact analytical results available in the literature. Numerical results are presented to investigate the effect of volume fraction index, loading conditions, core-to-facesheet thickness ratio, curvature ratio and boundary conditions on the transient response of P and S-FGSCS panels. The analysis reveals by selecting optimum parameters and gradation model, the amplitude and frequency of dynamic response of P and S-FGSCS panels can be controlled substantially.

A coupled efficient layerwise finite element model for free vibration analysis of smart piezo-bonded laminated shells featuring delaminations and transducer debonding

This paper presents a computationally efficient multifield finite element (FE) model for accurate analysis of smart composite and sandwich shells equipped with piezoelectric patch actuators and sensors, featuring multiple delaminations and transducer debonding. It employs a facet shell element with four physical nodes and one electric node, based on the third order zigzag theory approximations for displacements and a piecewise quadratic through-thickness variation for the electric potential. A hybrid point-least squares method recently proposed by the authors is extended to impose the condition of continuity of the nonlinear displacement field at the delamination, debonding, and patch fronts. The methodology is generic for multiple patch transducers, delaminations, and debonding, occurring at any arbitrary interface and in-plane locations. The model shows excellent accuracy in comparison with the coupled full-field 3D FE solutions, for the natural frequencies and complex global, local and hybrid mode shapes of delaminated smart composite shells and soft-core sandwich plates, with partially debonded actuators and sensors. The developed model will be of immense use for the design of active vibration control and structural health monitoring strategies for smart laminated shell-type structures featuring such damages.

Aeroelastic analysis of foam-filled composite corrugated sandwich plates using a higher-order layerwise model

Due to the versatility of load bearing and heat insulation, foam-filled composite corrugated sandwich plates have a broad application in aerospace industry as thermal insulation structures for hypersonic vehicles. In this paper, a C0 higher-order layerwise finite element model is presented for aeroelastic analysis of foam-filled composite corrugated sandwich plates in supersonic flow with equivalent properties. The homogenization method for the foam-filled corrugated core is formulated by force and energy equivalence under different assumptions of force or moment distributions. In the proposed layerwise model, the composite sandwich plate is divided into three sections through thickness, while a higher-order displacement field is assumed for the single-layer orthotropic core section and a first-order displacement field for the two face-sheet sections made of multi-layer laminates. The effect of transverse normal strain is also taken into consideration. The unsteady aerodynamic pressure is evaluated by the first-order Piston theory. An eight-noded isoparametric element with 16 degrees of freedom per node is used for finite element method. The accuracy of the present model is verified with existing results in the literature. The influence of geometric parameters and material properties on critical dynamic pressure are discussed.

Optimal location and geometry of sensors and actuators for active vibration control of smart composite beams

ABSTRACT This work investigates the problem of optimal placement and geometry of piezoelectric sensors and actuators (S/A) to improve active vibration control performance of smart laminated beam. Theoretical formulation is based on efficient layer-wise finite element model along with an optimal control theory. Control theory is implemented in state space format considering a reduced order model. A laminated beam with collocated piezoelectric S/A placed at the top and bottom surfaces has been considered. A series of simulation based on Taguchi design of experiment has been carried out to determine the optimal placement and geometry of the S/A to achieve best control performance that is maximum modal active damping ratio /minimum settling time with minimum actuator voltage. A multi-criteria optimisation has been performed using Proximity Indexed Value (PIV) integrated with entropy methods. Further, the analysis of mean (ANOM) and analysis of variance (ANOVA) are performed to identify the most significant input parameter based on their percentage contribution. For the smart cantilever beam considered in the analysis, the location of the S/A is the most significant having maximum percentage contribution (35.69%) followed by its length (33.04%) and thickness (24.55%).

Mechanical Stability of Hybrid Corrugated Sandwich Plates under Fluid-Structure-Thermal Coupling for Novel Thermal Protection Systems

Hybrid corrugated sandwich (HCS) plates have become a promising candidate for novel thermal protection systems (TPS) due to their multi-functionality of load bearing and thermal protection. For hypersonic vehicles, the novel TPS that performs some structural functions is a potential method of saving weight, which is significant in reducing expensive design/manufacture cost. Considering the novel TPS exposed to severe thermal and aerodynamic environments, the mechanical stability of the HCS plates under fluid-structure-thermal coupling is crucial for preliminary design of the TPS. In this paper, an innovative layerwise finite element model of the HCS plates is presented, and coupled fluid-structure-thermal analysis is performed with a parameter study. The proposed method is validated to be accurate and efficient against commercial software simulation. Results have shown that the mechanical instability of the HCS plates can be induced by fluid-structure coupling and further accelerated by thermal effect. The influences of geometric parameters on thermal buckling and dynamic stability present opposite tendencies, indicating a tradeoff is required for the TPS design. The present analytical model and numerical results provide design guidance in the practical application of the novel TPS.

Performance analysis of composite ply orientation in aeronautical application of unmanned aerial vehicle (UAV) NACA4415 wing

The advancement in today's material science has driven composite materials to globally use in aircraft design with its superiority in high structural stiffness and significant weight reduction. Composite structures ordinarily comprise of laminates with various fiber orientation angles offers unique outcome, hence lead to optimized design for composite structure. The paper deals with the layerwise finite element model for static structural analysis of a CFRP laminated composite of unmanned aerial vehicle (UAV) wing. The objective of this study is to compare the results for different orientation of ply combinations which contributed to the high performance of composite materials that exhibit both orthotropic strength and stiffness properties. Both properties present unique challenges for analysis and design. The study is further up to determine the optimum design for selected ply combination on a wing with a tubercle design at the leading edge of the wing. Tubercles mimicking the protuberances on the leading edge of a Humpback whale pectoral flipper, offering great performance from an aerodynamic perspective. Hence, optimum design of composite is found from the tabulated stress and displacement for each ply combination, where the tubercles design at the leading edge of UAV wing showed better performance with a reduction in 38.75% of deformation and 46.83% of stress, compared to normal leading edge of NACA4415 airfoil.

Effect of Thickness Stretching on the Natural Frequencies of Laminate-Faced Sandwich Plates Using a New Layerwise Model

The current work investigates the effect of thickness stretching on the natural frequencies of laminate-faced sandwich plates using new layerwise finite element model. The proposed model assumes higher-order displacement field for the core and first-order displacement field for the face sheets. Thanks for enforcing the continuity of the interlaminar displacement, the number of variables is independent of the number of layers. The consistent mass matrix and the element stiffness matrix are derived using the Hamilton’s principle. The performance and reliability of the proposed formulation are demonstrated by comparing the author’s results with those obtained using the three-dimensional elasticity theory, analytical solutions and other advanced finite element models.

A layerwise finite element formulation of laminated composite cylindrical shells with piezoelectric layers

We present a finite element model of laminated composite cylindrical shells with piezoelectric layers by using layerwise theory. The formulation, which is based on Reddy’s layerwise displacement theory, involves the coupling between mechanical deformations and electric displacements. The full layerwise theory is used to represent the total displacement field and electric potential, and then a finite element model has been formulated based on the developed mechanics by employing Hamilton’s principle and variational method. This layerwise finite element model can give an accurate description of displacement field at the ply level and can model complex boundary conditions. Numerical example of a simply-supported laminated piezoelectric composite shell for static response and free vibration analysis was implemented to evaluate the efficiency and accuracy of the present method. Numerical results obtained with the present method are in excellent agreement with other similar solutions.

An approach for bending and transient dynamic analysis of integrated thermal protection system with temperature-dependent material properties

A C0 higher-order layerwise finite element model combined with homogenization techniques for bending and transient dynamic analysis of integrated thermal protection system (ITPS) panel is presented. The ITPS panel is homogenized as an equivalent sandwich plate, and a reduced temperature field for the entire panel is derived. An advanced analytical equivalent model based on energy approach and Castigliano’s theorem for the mechanical properties of the trapezoidal corrugated core is presented, which considers the effects of temperature-dependent material properties. The proposed layerwise theory which is developed for a sandwich plate, assumes linear, quadratic and cubic polynomial distributions of displacements for middle layer and linear polynomial distributions of displacements for top and bottom layers. And the effect of transverse normal strains is taken into account in the layerwise theory. A four-noded isoparametric element with 16 degrees of freedom per node is employed to model the equivalent sandwich plate. The accuracy of the proposed method is verified by comparison with the results by three-dimensional (3D) finite element analysis. It has been shown that the proposed method requires significantly less computational effort and agrees well with the finite element results.

Damping properties of bi-dimensional sandwich structures with multi-layered frequency-dependent visco-elastic cores

The aim of this paper is to present a finite element model based on first order shear theory (zig-zag approach) to compute the damping characteristics of sandwich structures with multi-layered frequency-dependent viscoelastic cores. The model is validated versus a layerwise finite element model and used to study damping and rigidity of a laminated glass configuration with a multi-layered visco-elastic core composed of acoustic PVB and PVB. It is shown that the rigidity index of the structure (defined as the adimensionalized inverse of the maximal transverse displacement under a static load) evolves linearly with the viscoelastic layers’ thicknesses and quadratically versus elastic layer’s thickness. The first mode damping and resonant frequency show a non monotonous behaviour. In particular, the existence of an optimal faces thickness for damping is shown while a quadratic behaviour of frequency versus acoustic PVB layer thickness is reported.

Mixed integer multi-objective optimization of composite structures with frequency-dependent interleaved viscoelastic damping layers

The optimal design of composite structures with frequency-dependent interleaved viscoelastic damping layers is addressed in this paper. The design objective of simultaneously maximizing structural modal damping and frequency and minimizing weight is considered. The design problem is formulated as a mixed integer multi-objective optimization problem and solved by evolutionary algorithm. A layerwise finite element model is used. The Pareto-optimal solutions are obtained for two applications. The results show that the approach is quite useful in integrally designing such kind of composite structures. In particular, it is shown that the inserting position and the material type are two important design parameters.

Effect of Orientation Angle on Acoustic Radiation Mode Amplitudes of Laminated Composite Plates

In this paper, the acoustic radiation mode’s amplitudes of laminated composite plates are studied. The layer wise finite element model is imposed to determine velocity distributions of laminated composite plates. Based on the acoustic radiation mode, the effects of the panel orientation angle on the first three orders acoustic radiation mode’s amplitude of the laminated composite plates are then discussed. A twelve-layer laminated plate was used as an example, and the numerical simulations results show that the effects of the panel orientation angle on the acoustic radiation amplitude of the laminated composite plates are significant.

The Research of Structural Parameters on Natural Frequency of Laminated Composite Plates

In this paper, natural frequencies of laminated composite plates were studied. The layerwise finite element model is imposed to determine the natural frequencies of laminated composite plates. The effects of panel orientation angle, elastic modulus ratio and width-depth ratio on the natural frequencies of the laminated composite are then discussed. With an example of a sixteen-laying laminated plate, the numerical simulations show that the factor of key structural parameters to the natural frequencies of the laminated composite plate is panel orientation angle and width-depth ratio.

A nonlinear efficient layerwise finite element model for smart piezolaminated composites under strong applied electric field

In this work, we present an electromechanically coupled efficient layerwise finite element model for the static response of piezoelectric laminated composite and sandwich plates, considering the nonlinear behavior of piezoelectric materials under strong electric field. The nonlinear model is developed consistently using a variational principle, considering a rotationally invariant second order nonlinear constitutive relationship, and full electromechanical coupling. In the piezoelectric layer, the electric potential is approximated to have a quadratic variation across the thickness, as observed from exact three dimensional solutions, and the equipotential condition of electroded piezoelectric surfaces is modeled using the novel concept of an electric node. The results predicted by the nonlinear model compare very well with the experimental data available in the literature. The effect of the piezoelectric nonlinearity on the static response and deflection/stress control is studied for piezoelectric bimorph as well as hybrid laminated plates with isotropic, angle-ply composite and sandwich substrates. For high electric fields, the difference between the nonlinear and linear predictions is large, and cannot be neglected. The error in the prediction of the smeared counterpart of the present theory with the same number of primary displacement unknowns is also examined.

Natural Frequencies and Acoustic Radiation Mode Amplitudes of Laminated Composite Plates Based on the Layerwise FEM

In this paper, the natural frequencies and acoustic radiation mode amplitudes of laminated composite plates are studied. The layerwise finite element model is imposed to determine the natural frequencies and velocity distributions of laminated composite plates. The amplitude of the laminated composite plates are then discussed based on the acoustic radiation mode, the effects of the panel orientation angle, the elastic modulus ratio, the widthdepth ratio, and the damping ratio on the first acoustic radiation mode. A sixteen-layer laminated plate was used as an example, and the numerical simulations and experimental results show that the natural frequencies of the laminated composite plate can be analysed accurately using the proposed model. Furthermore, it is found that the effects of the panel orientation angle and width-depth ratio on the acoustic radiation mode amplitude of the laminated composite plates are significant.

A finite element model using a unified formulation for the analysis of viscoelastic sandwich laminates

In this paper we present a layerwise finite element model for the analysis of sandwich laminated plates with a viscoelastic core and laminated anisotropic face layers. The stiffness and mass matrices of the element are obtained by Carrera’s Unified Formulation (CUF). The dynamic problem is solved in the frequency domain with viscoelastic frequency-dependent material properties for the core. The dynamic behaviour of the model is compared with solutions found in the literature, including experimental data.

A layerwise mixed least-squares finite element model for static analysis of multilayered composite plates

A layerwise finite element model is developed in a mixed least-squares formulation for static analysis of multilayered composite plates. The model assumes a layerwise variable description of displacements, transverse stresses and in-plane strains, taken as independent variables. The mixed formulation allows to completely and a priori fulfil the known C z 0 requirements, which refer to the zig-zag form of displacements in the thickness direction and the interlaminar continuity of transverse stresses, due to compatibility and equilibrium reasons, respectively. This contrasts with layerwise displacement-based models that usually cannot a priori account for the interlaminar continuity of transverse stresses. In addition, the benefit of mixed least-squares formulation, as opposed to mixed weak form models, is that it leads to a variational unconstrained minimization problem, where the finite element approximating spaces can be chosen independently. Numerical examples are shown to assess the layerwise mixed least-squares model predictive capabilities compared to three-dimensional elasticity solutions and also other finite element results available in literature. Most notably, the present model is able to achieve accurate results in very good agreement with three-dimensional solutions and is shown to be insensitive to shear-locking.

Damping optimisation of hybrid active–passive sandwich composite structures

Optimisation of active and passive damping is presented in this paper, using a new mixed layerwise finite element model developed for the analysis and optimisation of hybrid active-passive laminated sandwich plates. Optimisation is conducted through maximisation of modal loss factors, using as design variables the viscoelastic core thickness, the constraining elastic layers ply thicknesses and orientation angles, as well as the position of co-located sensor and actuator pairs. Optimal results for passive damping are compared with an alternative optimisation model, based on 3D finite elements included in commercial package ABAQUS. Optimal location for sensor-actuator pairs is also presented and results are discussed.