Higher-order Layerwise Theories Research Articles

Coupled higher-order layerwise mechanics and finite element formulations for laminated composite beams with active SMA layers

This study proposes a thermo-elastic coupled nonlinear finite element (FE) model for laminated composite beams with active SMA layers based on a higher-order layerwise theory and Brinson's model of SMA's phase transformation constitutive relations. The developed FE Model is further discretized by using the Newton-Raphson time integration scheme to update SMA's phase transformation progress step by step. This new model can be used for thermal-mechanical behavior analysis of hybrid SMA-composite laminated beams, which especially enables accurate prediction for static response of moderately thick to thick beams, large deformation analysis, through-thickness variations of interlaminar stresses and strains. The accuracy and effectiveness of the proposed approach are verified by several numerical examples, and the results are compared with those obtained from corresponding alternative solutions and experimental tests. Using the developed FEM, the effects of temperature, geometrical nonlinearity, pre-strain of SMA, and stacking sequence of composite laminates on the static response of hybrid SMA-composite beams are studied.

Dynamics of rectangular laminated composite plates with selective layer-wise fillering rested on elastic foundation using higher-order layer-wise theory

A laminated composite plate designed is supposed to be used under different end supports. The elastic foundation is one of such conditions. The strength of the laminated composite plates can be enhanced by altering constituents or by the addition of filler materials. For localized strengthening of laminated composite plates, such as at particular layers, it is not cost-effective to strengthen the whole structure. So, the laminated composite plates are strengthened at a particular layer by adding the fillering materials, for example, graphene or flyash. The addition of these filler materials in a particular region sometimes causes agglomeration. Agglomeration of filler materials causes adverse effects such as stress concentration or strain aging. In theoretical formulation, Eringen’s nonlocal principle is applied to account for the impact of agglomeration. In the current study, neat epoxy glass laminated composite plates as well as rectangle laminated composite plate variants with outer layer graphene, core layer graphene, functionally graded laminated composite plate, laminated composite plates exclusively rich in graphene, and laminated composite plates only rich in flyash are taken into consideration. Using a layer-wise model, the fifth-order shear deformation theory is applied. The laminated composite plates are assumed to rest on an elastic foundation. The consequence of elastic coefficient of foundation on procured parameters such as fundamental frequencies, stress parameters, center deflections, and buckling performance is determined. For this purpose, computerized programs are developed using MATLAB and validated first for isotropic material. Further, the work is extended to study these effects on the laminated composite plate variants.

Vibration and Uncertainty Analysis of Functionally Graded Sandwich Plate Using Layerwise Theory

In the present study, free vibration analyses of porous functionally graded material (FGM) sandwich plates are carried out in thermal environment. Two types of sandwich plates such as sandwich with FGM face sheets and homogeneous core and sandwich with homogeneous face sheets and FGM core are considered for free vibration analysis with nonlinear temperature variation over the thickness direction. The metal and ceramic components are assumed to be temperature dependent. The higher-order layerwise theory is adopted with an eight-noded rectangular element to build a finite element model for free vibration analysis. A radial basis function network (RBFN) based surrogate model is developed to investigate the stochastic frequency response due to the uncertain material properties. The accuracy and the efficiency of the RBFN model are established by comparing the results with that of Monte Carlo simulation. Further, the developed surrogate model is implemented to perform various parametric studies and sensitivity analyses. The influence of the volume fraction index, types of porosity, and thermal gradient on the stochastic frequency response are analyzed. Though the influence of different stochastic input parameters is strongly dependent on the volume fraction index, the mass density of metal is found to be the most sensitive parameter for the sandwich plate with FGM face sheets and homogeneous core.

Bending and free vibration and analysis of laminated plates on Winkler foundations based on meshless layerwise theory

Free vibration and bending of laminated plates on Winkler foundations are investigated based on a combination of generalized layerwise theory (LW) for higher-order shear deformation theory (HSDT) and the meshless radial point interpolation method (RPIM). The shape function of the meshless radial interpolation method is used to discretize the weak form control equations derived from the principle of virtual work. The shape functions have the properties of Kronecker functions. The slope components associated with the first-order derivatives of the transverse displacements are defined as approximate variables. The transverse shear stresses at each layer interface are continuous. A comparative study with literature solutions verified the numerical stability and applicability of the combined generalized LW-HSDT and meshless RPIM methods. The effect of Winkler modulus parameters on the vibration performance and bending performance of the laminated plate was investigated. The results of bending, vibration frequencies and modes of the laminated plates on different Winkler foundations are presented. It is found that initially, the Winker foundation had a significant effect on the frequency magnitude and bending deformation, but little influence on vibration mode. After the influence of the foundation on the frequency enters the stable period, the influence of foundation on the mode shape will be significant. With the relaxation of the boundary conditions, the vibration mode will still be affected when the foundation parameters are small. Highlights It is for the first time that the laminated plates on Winker foundations were investigated using a combination of higher-order layerwise theory and meshless radial interpolation method. In the proposed model, the slope component related to the first-order derivative of the transverse displacement is defined as an approximate variable and does not require the boundary to be treated by the isogeometric method. The transverse shear stresses at the interface of each layer are continuous for the bending analysis of laminated panels. The meshless results reveal the influence of the Winker foundation parameters on the vibration characteristics of the laminated plate

Lightweight sandwich and composite beam analysis using improved higher-order theory with respect to strain energy fidelity in ply-wise approach

ABSTRACT This approach present improved higher-order layer-wise theory for the investigation of flawlessly wedged sandwich-composite beams with general laminate configurations. Our analysis incorporates the continuity assumption of interlaminar shear stresses and in-plane and flexural displacements between interfaces. In addition, interlaminar shear stresses are constrained using the Lagrange multiplier technique by introducing new unknown variables. These unknown variables are expressed with interlaminar strain energy, assuming that the strain energy is continuous throughout the overall thickness of the beam. To govern the newly introduced and other unknown variables, the total potential energy (TPE) is minimised using variational calculus. The numerical analysis results show that our approach provides enhanced accuracy to examine sandwich-composite beams.

Sound Transmission Analysis of Viscoelastic Composite Multilayered Shells Structures

In the development of aircraft comfort, one of the main issues is the sound transmission analysis to estimate the insulation capability of aeronautical panels. In this work, a higher-order shell finite element is proposed for the passive noise insulation analysis of composite laminated structures embedding viscoelastic layers. Starting from the Principle of Virtual Displacements, the present Finite Elements are obtained by making use of higher-order Layer-Wise theories, employing the Mixed Interpolated Tensorial Components (MITC) method to avoid the shear locking effect and taking into account the frequency dependence of the viscoelastic material through the use of a fractional derivative model. The Rayleigh integral method is considered for the evaluation of the acoustic insulation of the panels. Numerical studies are carried out to demonstrate that the present shell finite element is an efficient and accurate tool for the sound transmission analysis. Different lamination sequences, different boundary conditions and various radius to thickness ratios are taken into account.

Design of a noise reduction passive control system based on viscoelastic multilayered plate using PDSO

Abstract The sound transmission and insulation of aeronautical panels represents one of the major problem of the aircraft comfort. In the present work, a plate finite element with advanced higher-order kinematic field is proposed for the analysis of noise reduction passive control system in laminated structures. A novel Decline Population Swarm Optimization ( P D SO ) procedure is introduced and used to select the optimal parameters for the sound control. The present sound insulation passive control is based on Finite Elements obtained by applying the Principle of Virtual Displacements, taking into account the frequency dependence of the viscoelastic material, making use of higher-order Layer-Wise theories, and employing the Mixed Interpolated Tensorial Components (MITC) method to contrast the shear locking effect. The P D SO procedure is based on a decline demographic model and is characterized by high global search capabilities with reduced computational costs. The acoustic insulation of the panels is evaluated by computing its sound transmission factor using Rayleigh integral method. Several numerical investigations are carried out to validate and demonstrate the accuracy and efficiency of the acoustic optimization procedure for the design of viscoelastic plates.

Analysis of functionally graded sandwich plates using a higher-order layerwise theory

A higher-order layerwise finite element formulation is presented for static and dynamic analyses of functionally graded material (FGM) sandwich plates. A higher-order displacement field is assumed for core and first-order displacement field is assumed for top and bottom facesheets maintaining a continuity of displacement at layer interface. An eight noded isoparametric element using a C0 based finite element formulation with thirteen degrees of freedom per node has been considered in the present work. Two configurations of FGM sandwich plates, one with FGM core and homogenous facesheets and second having top and bottom layers made of FGM and homogenous core are considered. Effective material properties of the FGM are computed using rule of mixture (ROM). In order to establish the correctness of the present finite element formulation for wide range of problems for two configurations of FGM sandwich plates, comparison studies are presented. Next, parametric studies are taken up to investigate the effects of volume fraction index, span to thickness ratio and boundary conditions on static and dynamic behavior of FGM sandwich plate. It is shown here that present formulation is simple, straightforward and accurate for static and dynamic analyses of functionally graded material (FGM) sandwich plates.

Transient stress analysis of sandwich plate and shell panels with functionally graded material core under thermal shock

ABSTRACTA finite element formulation for stress analysis of functionally graded material (FGM) sandwich plates and shell panels under thermal shock is presented in this work. A higher-order layerwise theory in conjunction with Sanders’ approximation for shells is used to develop the finite element formulation for transient stress analysis of FGM sandwich panels. The top and the bottom surfaces of FGM sandwich panels are made of pure ceramic and metal, respectively, and core of the sandwich is assumed to be made of FGM. The temperature profile in the thickness direction of the panels is considered to be varying as per the Fourier’s law of heat conduction equation for unsteady state. The heat conduction equations are solved using the central difference method in conjunction with the Crank–Nicolson approach. Transient thermal displacements of the sandwich panels are obtained using Newmark average acceleration method and the transient thermal stresses are obtained using stress–strain relations, subsequently. Results obtained from the present layerwise finite element formulations are first validated with available solutions in literature. Parametric studies are taken up to study the effects of volume fraction index, temperature dependency of material properties, core thickness, panel configuration, geometric and thermal boundary conditions on transient thermal stresses of FGM sandwich plates and shells.

Vibration and buckling of laminated beams by a multi-layer finite element model

This paper presents a multi-layer finite element for buckling and free vibration analyses of laminated beams based on a higher-order layer-wise theory. An N-layer beam element with (9N + 7) degrees-of-freedom is proposed for analyses. Delamination and slip between the layers are not allowed. Element matrices for the single- and multi-layer beam elements are derived by Lagrange's equations. Buckling loads and natural frequencies are calculated for different end conditions and lamina stacking. Comparisons are made to show the accuracy of proposed element.

A finite element formulation for thermally induced vibrations of functionally graded material sandwich plates and shell panels

A finite element formulation based on a higher-order layerwise theory is presented for the first time to investigate thermally induced vibrations of functionally graded material (FGM) sandwich plates and shell panels. The properties of FGM sandwich are assumed to be position and temperature dependent. The upper and lower layers of the sandwich panel are considered to be made of pure ceramic and metal, respectively and the elastic properties of FGM core are varied according to a power-law function. The top surface is exposed to a thermal shock and the bottom surface of the panel is either kept at a reference temperature or thermally insulated. The one-dimensional transient heat conduction equation is solved using a central difference scheme in conjunction with the Crank-Nicolson method. A higher-order layerwise theory is used for FGM sandwich panels, in which a higher-order displacement field for the FGM core and a first-order displacement field for the facesheets are assumed. The governing equations are solved using Newmark average acceleration method. It is shown that the proposed layerwise finite element formulation is simple and can easily be applied to investigate FGM sandwich plates and shell panels subjected to rapid heating.

General higher-order layer-wise theory for free vibrations of doubly-curved laminated composite shells and panels

ABSTRACTThe present article illustrates a general formulation for a higher-order layer-wise theory related to the analysis of the free vibrations of thick doubly-curved laminated composite shells and panels. The theoretical framework relates to the dynamic analysis of shell structures by using a general displacement field based on the Carrera Unified Formulation (CUF), including the stretching effect for each layer. The order of the expansion along the thickness direction is taken as a free parameter. The starting point of the present general higher-order layer-wise formulation is to propose a kinematic assumption, with an arbitrary number of degrees of freedom. The main aim of this work is to determine the explicit fundamental operators that can be used for the layer-wise (LW) approach. These fundamental operators are obtained for the first time by the author and are related to motion equations of doubly-curved shells described in an orthogonal curvilinear co-ordinate system. The free vibration shell and panel problems are computationally solved using the generalized differential quadrature (GDQ) and generalized integral quadrature (GIQ) techniques. The numerical results are compared with recent papers in the literature and commercial finite element codes.

A simple thermopiezoelastic model for smart composite plates with accurate stress recovery**Presented at the 44th Structures, Structural Dynamics and Materials Conference, Norfolk,VA, 7–10 April 2003.

A Reissner–Mindlin model for analyzing laminated composite plates including piezoelectriclayers under mechanical, thermal and electric loads has been constructed using thevariational-asymptotic method. The present work formulates the original nonlinear,three-dimensional, one-way coupled, thermopiezoelasticity problem allowing for arbitrarydeformation of the normal line and using a set of intrinsic variables defined on the referenceplane. The variational-asymptotic method is used to rigorously split the three-dimensionalproblem into two problems: a nonlinear, two-dimensional, plate analysis over the referenceplane to obtain the global deformation, and a linear analysis through the thickness toprovide both the two-dimensional generalized constitutive model and recovery relations toapproximate the original three-dimensional results. The obtained asymptoticallycorrect second-order electric enthalpy is cast into the form of the commonly usedReissner–Mindlin model to account for transverse shear deformation. The present theory isimplemented into the computer program VAPAS (variational-asymptotic plate and shellanalysis). Results for several cases obtained from VAPAS are compared with theexact thermopiezoelasticity solutions, classical lamination theory and first-ordershear–deformation theory for the purpose of demonstrating the advantages of the presenttheory and the use of VAPAS. The proposed theory can achieve an accuracy comparableto higher-order layerwise theories at the cost of a first-order shear–deformationtheory.