Laminated Sandwich Plates Research Articles

Non-polynomial zig-zag unified shear deformation formulation solved via boundary discontinuous method for laminated sandwich plates

Analytical solutions of mechanical problems with refined theories and challenge boundary conditions are still a topic of research due to intrinsic complexity. In this paper, a generalized refined theory is formulated to obtain analytical solutions for the static problem of cross-ply laminated and sandwich plates with several boundary conditions. These theories are implemented in the framework of the Carrera unified formulation (CUF) based on the equivalent-single-layer (ESL) approach. The displacement field of ESL-based models are expanded over the thickness direction by using non-polynomial terms, e.g. trigonometric, hyperbolic and the so-called zig-zag (ZZ) Murakami’s functions. The principle of virtual displacements (PVD) statement is used to derive the strong form of the governing equations in terms of displacements variables. These equations are solved by the boundary-discontinuous double Fourier series approach which provides highly accurate analytical solutions. This work gives a detailed comparison of results obtained using the presented ZZ models highlighting the differences with 3D FEM results. Furthermore, the influence of non-polynomial and ZZ terms in each ESL model is investigated. The superior robustness of the presented methodology compared to past works is demonstrated, making the proposed results suitable as a benchmark for validating new theories and finite elements. The findings can be also useful to train artificial intelligence (AI) models that can allow to the development of faster digital twin structure technology.

A compressible layerwise third-order shear deformation theory with transverse shear stress continuity for laminated sandwich plates

Sandwich structures with a soft core typically exhibit multiple deformation modes such as bending, twisting and compression when subjected to transverse loads. Compressive behavior of soft core significantly affects the structural response, which is usually neglected in conventional plate theories. Additionally, conventional plate theories do not take into account transverse shear stress continuity. In order to address this concern and precisely characterize the characteristics of arbitrary multilayer laminated structures, a novel electromechanical coupled finite element model is developed. This model is based on a compressible layerwise third-order shear deformation theory with a soft core. Notably, the proposed model theory requires only twelve degrees of freedom for each quadratic element node. The accuracy of the model is validated first. Afterwards, several numerical investigations are carried out for piezolaminated sandwich structures with different width-to-thickness ratios, reinforcement angle and skew angle. The results demonstrate the applicability of the current model in predicting the behavior of laminated sandwich plates.

Free Vibration Analysis of Laminated Sandwich Plates Using Wavelet Finite Element Method

The accuracy of a wavelet depends on the choice of the mother wavelet adopted. The present work aims to predict the free vibration behavior of laminated sandwich plates using wavelet finite element (WFE). Different kinds of mother wavelets, namely, B-spline wavelet on the interval (BSWI), Gaussian, Haar, Daubechies 6 (db6), Biorthogonal 3.7 (bior3.7), Coiflet5 (coif5), Symlets (sym8), Morlet, Mexican hat (Mh), and Meyer mother wavelets, are employed in WFE for predicting the frequencies. Both symmetric and unsymmetric laminates are studied using the proposed approaches. A wide range of problems, including the influence of the geometric and material properties and end conditions on the free vibration behavior of the laminated sandwich plates, are solved. The effectiveness of the WFE over the conventional finite element method in terms of computational efficiency is discussed. In conclusion, BSWI-based WFE method (WFEM) is found to be the most accurate and computationally efficient in predicting the free vibration behavior of laminated sandwich plates. The accuracy of the WFEM depends widely on the type of mother wavelet adopted.

Stability and mode shape analysis of doubly- and cross-helicoidal laminated sandwich plates inspired from dactyl’s club

The present work intends to use higher-order zigzag theory to analyze double- and cross-helicoidal laminated sandwich plates under buckling conditions. Geometry and boundary effects on buckling and mode shapes are examined. The behavior of helicoidal sandwich plates is compared with the cross-ply and quasi-isotropic lamination schemes. In the case of plates with free edges, the bio-inspired laminated sandwich plates outperform the more traditional cross-ply and quasi-isotropic laminated schemes. Numerous more findings are provided as well, all of which may be used as a standard by which to measure the success of comparable future research efforts.

Dynamic buckling of active sandwich panels

In this work, a laminated sandwich plate model with external piezoelectric layers is extended for buckling and dynamic stability analysis. In-plane harmonic uniformly distributed loads are considered in the dynamic stability problem, and the Mathieu-type equilibrium equations are solved using Bolotin’s method to obtain the regions of dynamic instability. The model is validated to begin with, using available results in the literature for static and dynamic buckling of laminated soft core sandwich panels. Ultimately, the model is used to simulate the behaviour of laminated composite and sandwich plates with piezoelectric patches, controlled using a closed loop law with proportional and derivative gains, for buckling and dynamic stability analysis. This control system is used to postpone buckling, increase fundamental frequencies and reshape the regions of dynamic instability.

Free vibration analysis of sandwich plates

Laminated sandwich plates consisting of a soft core bounded by two relatively thin and stiff faces exhibit excellent strength to weight and stiffness to weight ratios. This makes them very suitable for applications where weight saving is a major concern, such as in aerospace and automotive structures. Piezoelectric layers or patches, due to their simple electro-mechanical properties, can easily be integrated with sandwich composites. The objective of integrating piezoelectric patches is to use them as sensors and actuators in order to control the excessive deformations and vibrations of the structure. Such a structure will have self-correcting capabilities against external loads and is called a smart structure. This further reduces the weight of the structure without compromising on strength or stiffness and becomes a very suitable choice for aerospace applications. Since these structures are often subjected to high dynamic loadings, it becomes important to have an insight of their free vibration characteristics. The work presented includes a study of the free vibration response of laminated sandwich plates using different core materials. From the study it was found that the material of the core significantly influences the free vibration behaviour of the plate, the natural frequency increases with the increase in density of the core material and also with an increase in mode number. The investigation will help in acquiring a better insight of the dynamic behaviour of sandwich plates with surface bonded piezoelectric patches. The efficiency and accuracy of the used elements is established by validation of the results with the published literature.

Buckling and free vibration analysis of bio-inspired laminated sandwich plates with helicoidal/Bouligand face sheets containing softcore

Helicoidal laminates inspired by mantis shrimp crustacean can sustain higher loads compared to conventional laminated structures. However, there is still a lack of bending studies on the plates inspired by these helicoidal structures. The buckling and free vibration studies have been undertaken in the present work on the laminated composite and sandwich plates inspired by the helicoidal structures of the biological characters. Investigations are carried out using higher-order zigzag theory. For sandwich plates, the top and bottom face sheets are assumed to be made up of helicoidal layup schemes. Different kinds of helicoidal schemes, namely, recursive, exponential, semicircular, Fibonacci, and linear helicoidal are considered during the analysis. The buckling and free vibration behavior of helicoidal-based laminated sandwich plates are compared with the conventional laminated sandwich plates such as uniform distribution and cross-ply configurations. The influence of the number of layers, helicoidal schemes, geometric properties, and end conditions on the buckling and free vibration analysis of bio-inspired helicoidal laminated composite and sandwich plates is carried out in detail.

Mechanical behaviors of variable stiffness composite laminated sandwich plates using layer-wise model

Mechanical behaviors of variable stiffness composite laminated sandwich plates using layer-wise model

Instability Regions of a laminated Sandwich Plate with MRE Core Under Parametric Excitation Using Finite Element Method

This paper is concerned with the instability regions of a laminated sandwich plate with magneto-rheological elastomer (MRE) core under periodic axial loads. Structures operating under this unstable region cause large response even if the excitation force is small in magnitude. The governing equations of motion of the system are obtained by using finite element method [FEM].The parametric stable and unstable regions of the MRE cored composite sandwich plate for different system parameters and end constraints are found using modified Hsu method for simple parametric resonance condition. This analysis will help to design passive attenuation by using sandwich plates of varied dimensions, material parameters of both skin and core. Further active vibration reduction is possible by applying suitable magnetic field and operating the system outside of the instability region.

Hygrothermal vibration of a laminated sandwich plate with magnetostrictive faces and a homogeneous core

AbstractHygrothermal forced vibration and damping analyses of a simply supported symmetric laminated composite plate with homogeneous core and magnetostrictive layers are examined using the exponential displacement model in this article. Three hygrothermal environment distribution types are investigated: uniform, linear and nonlinear rises in the present analysis. The equations of motion for laminated rectangular plates subjected to hygrothermal loads and in‐plane forces in x and y directions are developed through Hamilton's principle. The closed‐form solution is arrived at based on Navier's technique to analyze the hygrothermal effect on the vibrational behavior of the structure. Some parametric examples are presented to discuss the effects of the smart layer location, lamination schemes, mode number, aspect ratio, thickness ratio, feedback gain control value, in‐plane forces, core thickness‐to‐fiber reinforced layer thickness ratio, magnetostrictive layer thickness to fiber‐reinforced layer thickness ratio, temperature and moisture changes on vibration response of the proposed model. The study results illustrate that the high hygro ratio weakens the plate stiffness, and accordingly, the amplitude of the deflection increases with raising the moisture and/or temperature. The numerical results emphasize the strong role of the feedback control gain values and the smart layer position in controlling the system vibration. The largest deflections and highest damping time interval happen in the uniform temperature distribution and moisture concentration case. Moreover, the vibration frequencies of the thin smart plates are smaller than the thick ones.

Layer-wise solutions for variable stiffness composite laminated sandwich plate using curvilinear fibers

This paper deals with the vibration analysis of variable stiffness composite laminated (VSCL) sandwich plates. The VSCL sandwich plate is composed by soft core and two laminated face sheets, in which the face sheets are considered with curvilinear fiber. The layer-wise plate theory and p-version of finite element method are used to solve the problem formulation. In layer-wise theory, each layer modeled separately as a one p-element and the continuity of displacement fields is based on a linear zig-zag variation of displacements through the thickness of the layers. The obtained results of present model are compared and validated with available solutions, such as equivalent single layer theories, layer-wise theory and three-dimensional theory for sandwich plate with constant stiffness. The frequencies and mode shapes are examined for different physical and mechanical parameters such as plate thickness, core to face sheets thickness ratio, orientation angle of curvilinear fibers, stacking sequence and boundary conditions. New layer-wise solutions for thin and thick VSCL sandwich plate are offered, in which can be used to establish benchmarks for future comparisons.

Nonlinear hygrothermal effects on the vibrations of a magnetostrictive viscoelastic laminated sandwich plate resting on an elastic medium

In engineering applications, composite structures supported by elastic foundations are being vastly utilized in various operating environmental conditions. The nonlinear hygrothermal effect on vibration analysis of a magnetostrictive viscoelastic laminated composite sandwich plate rested on two-parameter Pasternak’s foundations is studied in the present article. The material properties of the viscoelastic plate’s layers are considered based on the Kelvin–Voigt model. The governing equation system is derived according to Hamilton’s principle. The analytical solution is obtained to study influences of the hygrothermal change, half wave number, magnitude of the feedback control gain, aspect ratios, thickness ratio, and structural viscoelastic damping coefficients on vibration damping characteristics of the plate including the frequencies, the damping rate, and the deflection. The obtained results indicate that the natural frequency and deflection reduce with increasing the structural viscoelastic damping value. The plate takes a long time for suppressing its vibration due to increasing the hygrothermal factor.

An efficient eight‐node quadrilateral element for free vibration analysis of multilayer sandwich plates

AbstractThis article presents a free vibration analysis of laminated sandwich plates under various boundary conditions by using an efficient C0 eight‐node quadrilateral element. This new element is formulated based on the recently proposed layerwise model. The present model assumes an improved first‐order shear deformation theory for the face sheets while a higher‐order theory is assumed for the core maintaining an interlaminar displacement continuity. The advantage of this model relies on its number of variables is fixed, does not increase when increasing the number of lamina layers. This is a very important feature compared to the conventional layerwise models and facilitates significantly the engineering analysis. Indeed, the developed finite element is free of the shear locking phenomenon without requiring any shear correction factors. The governing equations of motion of the sandwich plate are derived via the classical Hamilton's principle. Several examples covering the various features such as the effect of modular ratio, aspect ratios, core‐to‐face thickness ratio, boundary conditions, skew angle, number of layers, geometry and ply orientations are solved for laminated composites and sandwich plates. The obtained results are compared with 3D, quasi‐3D, 2D analytical solutions, and those predicted by other advanced finite element models. The comparison studies indicate that the developed finite element model is of fast convergence to the reference and valid for both thick and thin laminated sandwich plates. Finally, it can be concluded that the present model is not only simple and accurate than the conventional ones, but also comparable with refined analytical solutions found in the literature.

Dynamic analysis of hybrid sandwich plate

Laminated sandwich structures exhibit high strength to weight and stiffness to weight ratios and therefore find wide application in aerospace applications where weight saving is a major consideration. Such composite laminates when integrated with piezoelectric layers form a smart structure and may be used for vibration and shape control applications. Since these applications often require the structures to be subjected to dynamic loadings, their vibration response analysis become an important design aspect. A detailed parametric study for the vibration analysis of laminated sandwich plates is presented in this work. The influence of aspect ratio, boundary conditions and thickness ratios on the free vibration response of the sandwich panel is studied. The plate is modelled using commercial FE package ANSYS. An eight-nodded shell-91 element is used to model the composite laminates, solid-5 element is used for modelling the piezoelectric layers and a solid-95 element is used to model the core. The efficiency and accuracy of the used elements is established by validation of the results with the published literature. All the results are presented with a converged mesh size.

Bending analysis of laminated sandwich plates under hygrothermal loadings

Abstract In present work, hygrothermal based analysis of laminated composite and sandwich plates is carried out by using recently proposed finite element based higher-order zigzag theory. Present formulation satisfies transverse shear stress continuity condition at top and bottom surface of the plate. Also, the model satisfies transverse shear stress free condition at the bottom and top surface of the plate. A nine-noded C-0 Lagrangian finite element having eleven degrees of freedom per node is used during study. Proposed model is free from any kind of inclusion of penalty function. Effectiveness of the present model is carried out by comparing the present results with those available in the literature.

Quasi-3D theory for the vibration of a magnetostrictive laminated plate on elastic medium with viscoelastic core and faces

The vibration of a magnetostrictive laminated composite sandwich plate with a viscoelastic core and faces rested on the two-parameter elastic medium is analyzed in the present article. The laminated sandwich plates are designed wherein consist of three kinds of composite materials: magnetostrictive material, fiber-reinforced material, and viscoelastic material in the core and faces. The viscoelastic core and faces are modeled as a Kelvin-Voigt viscoelastic model. The partial differential equations of motion are derived by implementing Hamilton’s principle. The analytical Navier’s solution type is obtained to analyze the behavior of the damping coefficient and the damped natural frequency coefficient. The influence of significant parameters is examined on vibration characteristics of the plate and discussed in detail, especially, location of smart layers, lamination schemes, elastic foundation coefficients, modes, the magnitude of the feedback coefficient, viscoelastic structural damping, thickness ratio, the aspect ratio, and viscoelastic layer thickness-to-magnetostrictive layer thickness ratio. Numerical results illustrate that the location of smart layers is an important element in the design of the plate to be more stable. It is anticipated that the findings reported in the study can be utilized to develop the adaptive structural applications and the solutions to future smart structure problems.

Analysis of non-skew and skew laminated composite and sandwich plates under hygro-thermo-mechanical conditions including transverse stress variations

A new fourth-order in-plane displacement field based refined higher-order zigzag theory is proposed for analysis of laminated sandwich plate (for both skew and non-skew shaped) subjected to hygro-thermal conditions. In order to predict behavior of thick laminated sandwich plates, third-order transverse displacement field is taken. Zig-zag effects are introduced using linear unit Heaviside step function. The theory satisfies zeros transverse normal and shear stress condition at the bottom and top surface of the plate along with continuity condition at interface. The proposed model is free from any kind of C-1 or penalty function requirements. Nine-noded isoparametric finite element having twelve degrees of freedom per node is used during analysis. Since, the present theory incorporates transverse displacement field along with continuity conditions, is able to predict the behavior of thick sandwich plates more efficiently. In literature no results are present for skew laminated composite and sandwich plates therefore, present results for skew plates are entirely new and will serve as benchmark for future studies.

Free vibration analysis of laminated sandwich plates under thermal loading

In present work, free vibration analysis of laminated sandwich plates is carried out under thermal loading. C-0 finite element based higher-order zigzag theory is used during analysis. Third-order variation of in-plane displacement field is assumed while for transverse displacement field, quadratic variation is used for core region and is taken constant for the face layers. Present model is free from any kind of penalty requirements. Also, the proposed model satisfies transverse shear stress continuity condition at interface and same is zero at top and bottom faces. Present results are compared with those available in literature. New results for sandwich plates are proposed in the present work which will serve as benchmark for future studies.

Multiobjective optimization solutions for noise reduction in composite sandwich panels using active control

In this paper, optimal solutions for noise reduction in laminated viscoelastic soft core sandwich plates are obtained, using active control with surface bonded piezoelectric sensors and actuators. An in–house finite element implementation of the active laminated sandwich plate is used to obtain the frequency response of the panels. Since the structural/acoustic problem is lightly coupled, the sound transmission characteristics of the panels are evaluated by computing their radiated sound power, using the Rayleigh integral method. A negative velocity feedback control law has been used to implement the active damping. The optimal location of the surface co-located pairs of piezoelectric patches is then obtained, using the Direct MultiSearch (DMS) optimization algorithm to minimize simultaneously the added weight, the number of controllers and noise radiation. The minimization of noise radiation is accomplished by minimizing the total length of the radiated sound power frequency response curve. Trade-off Pareto fronts and the respective optimal active patch configurations are obtained and discussed.

Optimal passive shunted damping configurations for noise reduction in sandwich panels

This article addresses the issue of vibration and noise reduction in laminated sandwich plates using piezoelectric patches with passive shunted damping. A finite element implementation of a laminated sandwich plate with viscoelastic core and surface bonded piezoelectric patches is used to obtain the frequency response of the panels. The sound transmission characteristics of the panels are evaluated by computing their radiated sound power using the Rayleigh integral method. Resistor and inductor shunt damping circuits are used to add damping to the sandwich panels. The optimal location of the surface-bonded piezoelectric patches is then obtained, along with the resistor and inductor circuits resistance and inductance, using direct multisearch optimization to minimize added weight, number of patches, and noise radiation. Trade-off Pareto optimal fronts and the respective optimal patch configurations are obtained.