Layerwise Theory Research Articles

Effect of orientation of CNTs and piezoelectric fibers on the damping performance of multiscale composite plate

The present work deals with the study of active constrained layer damping treatment of multiscale carbon nanotube-based hybrid carbon fiber-reinforced composite plates. The distinctive feature of novel multiscale hybrid carbon fiber-reinforced composites is that the wavy/straight carbon nanotubes are distributed uniformly in the matrix phase of hybrid carbon fiber-reinforced composites, and the waviness of carbon nanotubes is considered to be coplanar with two mutually orthogonal planes. Firstly, the effective elastic properties of hybrid carbon fiber-reinforced composites are estimated using the Mori-Tanaka method. The outcomes of the Mori-Tanaka method suggest that the transverse effective elastic properties of hybrid carbon fiber-reinforced composites containing wavy carbon nanotubes are better than those of hybrid carbon fiber-reinforced composites with straight carbon nanotubes. Secondly, a finite element model using the layer-wise first-order shear deformation theory is developed to study the damping performance of hybrid carbon fiber-reinforced composite plates integrated with the active constrained layer damping treatment. The constraining layer of active constrained layer damping treatment is a 1–3 piezoelectric composite layer with vertically/obliquely-oriented piezo-fibers. The piezo-fibers make an angle [Formula: see text] with the vertical plane of a layer coplanar with the xz- or yz-plane. The effect of the orientation of piezo-fibers angle on the control authority of active constrained layer damping treatment patches is investigated. Our results reveal that the performance of multiscale hybrid carbon fiber-reinforced composite plates has improved due to the incorporation of wavy carbon nanotubes, and the orientation angle of piezo-fibers has a major impact on the control authority of active constrained layer damping patches. The proposed multiscale composite with the combination of wavy carbon nanotubes and active constrained layer damping patches can be actively used in the aerospace and transport industries to control the mechanical vibrations of structures.

Progressive failure analysis of open-hole composite laminates using FLWT-SCB prediction model

This paper presents the original incorporation of the smeared crack band (SCB) damage model within the full layerwise theory (FLWT) framework, to contribute to the increase of the computational efficiency of the progressive failure analysis of open-hole laminar composites loaded in tension, simultaneously preserving the accuracy of the conventional 3D finite element models. The developed FLWT-SCB prediction model was implemented into an original FLWTFEM framework allowing for the accurate 3D stress fields and excellent visualisation capacity. The response of damaged lamina, in both fiber and matrix directions, was described by distinct bilinear strain-softening curves. The mesh dependency problem was minimized by scaling the fracture energy using a characteristic element length.Both the failure initiation and failure modes were determined using the Hashin failure criterion. To verify the model effectiveness, the obtained results were compared against the experimental and benchmark data from the literature. Mesh dependency was analysed to confirm the benefits of suggested model, as well. The obtained results agreed with the experimental ones and those from the literature.According to the numerical results, FLWT-SCB allows for coarser meshes than those used in the standard finite element models, leading to improved computational efficiency without compromising the accuracy. The model also demonstrated the weak dependency between the size of the structure and the mesh. The advantages of using FLWT-SCB damage model in achieving significant improvements in computational efficiency are highlighted.

Geometrically nonlinear analysis and vibration of in-plane-loaded variable angle tow composite plates and shells

This work intends to present a novel numerical approach for studying the vibration behaviours of variable angle tow (VAT) composite structures in their quasi-static nonlinear equilibrium states. This methodology is able to predict the buckling load, to investigate the natural frequencies variation for progressively higher loads, and to provide a means for verifying experimental Vibration Correlation Technique results. The use of VAT composites, in which the fibre orientations are allowed to vary along with a curvilinear pattern within each lamina, dramatically increases the design space and provides a significant improvement in buckling performance and benefits in the postbuckling regime. This study has been performed using an innovative methodology based on the well-established Carrera Unified Formulation able to describe several kinematic models for two-dimensional structures. In detail, layerwise theories are employed to characterize the complex phenomena that may appear in VAT composite structures. All Green-Lagrange strain components are employed because far nonlinear regimes are investigated. Furthermore, the geometrical nonlinear equations are written in a total Lagrangian framework and solved with an opportune Newton–Raphson method along with a path-following approach based on the arc-length constraint. Different VAT composite structures have been analyzed to validate the proposed approach and provide some benchmark solutions. The computed equilibrium paths are compared with results obtained using the commercial code ABAQUS. The results document the good accuracy and reliability of the presented methodology and show this numerical tool’s potentialities.

Pristup projektiranja ekonomičnih hibridnih CLT podova

There is a growing research and production interest for the application of lower-cost hybrid cross-laminated timber (CLT) panels composed of timber layers of dissimilar quality. Therefore, an approach for the design of cost-effective hybrid CLT panels in bending, based on the existing analytical and novel finite element procedures, is presented in the paper. The gamma-method, the extended gamma method, and the composite theory are applied in the analysis of square panels, while the finite element model based on the Reddy’s full layerwise theory is used for the complex-shape panels in bending. An extensive benchmark technical and economic study is performed for 25 CLT panels, considering various spans, lamination schemes, geometries, and boundary conditions. Cost savings made by using a lower timber class in central zones of CLT panels are highlighted and quantified. This concept shows an economic potential that should be considered during the design and production of CLT panels in structural engineering applications, such as lightweight floor structures.

Nonlocal layerwise theory for bending, buckling and vibration analysis of functionally graded nanobeams

Nonlocal layerwise theory for bending, buckling and vibration analysis of functionally graded nanobeams

Isogeometric buckling analysis of orthotropic thin-walled laminated beams using the Carrera unified formulation

The current work presents the combination of isogeometric approach (IGA) and Carrera unified formulation (CUF) to perform the buckling analysis of isotropic thin-walled and orthotropic beams. Toward this end, the layerwise (LW) theory based CUF and B-spline basis functions in IGA have been used. The LW theory uses Lagrangian expansion (LE) to estimate the displacement field in the cross-section. However, in the present study, B-spline basis functions in both longitudinal direction and cross-section have substituted the corresponding functions. The CUF expresses the 3 D displacement fields as a set of 1 D generalized unknown displacement. Combined model in the present study obliterates the costly use of 3 D finite element analysis with its high accuracy and loyalty to 3 D problems. The principle of virtual displacement (PVD) is used to obtain the fundamental nuclei. One of the features of CUF is that it’s higher-order expansion is free of the Poisson locking phenomenon. Also, there is no need to use the shear correction factor. Some examples of the isogeometric analysis of laminated composite beams with different geometries and boundary conditions are conducted and comparison of the critical buckling load results illustrate the proper validation and formulation of the present study.

Analysis and optimal control of smart damping for porous functionally graded magneto-electro-elastic plate using smoothed FEM and metaheuristic algorithm

This paper proposed an effective numerical approach for free vibration analysis and optimal control of the porous functionally graded magneto-electro-elastic (PFGMEE) plates integrated with the active constrained layer damping (ACLD). Specifically, in order to analyze the free vibration characteristic of the PFGMEE plates based on the layer-wise shear deformation theory, a cell-based smoothed discrete shear gap (CS-DSG3) method is applied. The accuracy and convergence of the CS-DSG3 method are demonstrated by comparing its results with those available in the literature. Additionally, due to the coupling characteristic between magnetic, electric, and elastic fields, the coupled response of the PFGMEE plate is also considered. Furthermore, in order to obtain the optimal performance of the PFGMEE plates with the ACLD treatment, a combination of the CS-DSG3 method with an adaptive elitist differential evolution (aeDE) algorithm is used to determine the optimal placement of ACLD patches and the piezoelectric fiber orientation angle of the PFGMEE plates. The effect of several boundary conditions and porous distribution types on the free vibration response and the optimal control solution of the PFGMEE plates is also examined.

Progressive debonding analysis of sandwich composite strips using a cohesive-layerwise spectral finite element model

This paper presents a novel numerical framework for the simulation of debonding growth in sandwich structures via a layerwise spectral finite element model. A variable kinematic layerwise theory is developed, which employs cubic Hermite splines for the composite facesheets and the core and linear interpolation functions for the thin resin-rich layers in connection with continuum damage mechanics for tracking of debonding propagation. The layerwise mechanics and continuum damage mechanics are integrated into a spectral finite element, termed thereafter as cohesive-layerwise spectral finite element, with integration points collocated to nodes and high-order spatial approximation in the plane of the structure. The developed computational model is applied to global mode I, mode II, and mixed-mode fracture problems and correlated with experimental results and reference high-fidelity finite element models. The evaluation cases of the present method reveal significant enhancements in computational speed and meshing process due to elimination of cohesive layer parameter calibration, alleviation of FE aspect ratio constraints and high-convergence rates.

Nonlocal vibration of functionally graded nanoplates using a layerwise theory

This work studies the size-dependent free vibration response of functionally graded (FG) nanoplates using a layerwise theory. The proposed model supposes not only a higher-order displacement field for the core but also the first-order displacement field for the two face sheets, thereby maintaining an interlaminar displacement continuity among layers. Unlike the conventional layerwise models, the number of variables is kept fixed and does not increase for an increased number of layers. This is a very important feature compared to conventional layerwise models and facilitates significantly the engineering analyses. The material properties of the FG nanoplate are graded continuously through the thickness direction in accordance with a power-law function. The Eringen’s nonlocal elasticity theory is here adopted to relax the continuum axiom required in classical continuum mechanics and hence hopeful to capture the small size effects of naturally discrete nanoplates. The equations of motion of the problem are obtained via a classical Hamilton’s principle. The present layerwise model is implemented with a computationally efficient C0- continuous isoparametric serendipity elements and applied to solve a large-scale discrete numerical problem. The robustness and reliability of the developed finite element model are demonstrated by a comparative evaluation of results against predictions from literature. The comparative studies show that the proposed finite element model is: (a) free of shear locking, (b) accurate with a fast rate convergence for both thin and thick FG nanoplates, and (c) excellent in terms of numerical stability. Moreover, a detailed parametric analysis checks for the sensitivity of the vibration response of FG nanoplates to the aspect ratio, length-to-thickness ratio, nonlocal parameter, boundary conditions, power-law index, and modes shapes. Referential results are also reported, for the first time, for natural frequencies of FGM nanoplates which will serve as benchmarks for further computational investigations.

Modeling of partially delaminated composite plates resting on two-parameter elastic foundation with improved layerwise theory

In this work, we aim to build the mathematical model for delaminated composite plates resting on elastic foundation by means of improved layerwise theory and finite element implementation for free vibration analysis. The proposed model takes into account the transverse normal and shear deformation of the elastic foundation so as to investigate their effect on the dynamic characteristics of delaminated plates. The four-node plate element is used for the finite element formulations with Langrage interpolation functions for in-plane structural unknowns and Hermite cubic interpolation functions for out-of-plane structural unknowns. The delamination is simulated by means of Heaviside unit step functions allowing for the discontinuity of displacement fields. The effects of both longitudinal locations and interfacial locations of delamination are investigated. The results show that when the delamination located closer to the clamped end and at the middle plane, it has much more severe influence on its natural frequencies. The foundation parameters also have significant effect on the natural frequencies and frequency shift due to delamination. Different layup stacking sequences are also considered in this study.

Stress distribution of a cylindrical sandwich sector with FG-CNT core and piezoelectric face sheets subjected to low-velocity impact

A new theoretical solution based on Layerwise theory is presented to determine the stress distribution in a simply-supported cylindrical sandwich sector with a functionally graded carbon nanotube core and piezoelectric face sheets subjected to low-velocity impact. The spherical elastic ball hits the top face sheet of the sector at an initial velocity of 50 m/s. The classical non-adhesive elastic contact theory and Hunter's relationship were used to determine the normal contact pressure distribution in terms of time and distance of the contact location. Moreover, Hamilton's principle and Maxwell's static equation were used to obtain the nineteen equations of motion. The numerical code was written to solve these nonlinear equations and the stress components in each layer were calculated in terms of time. In addition, it was assumed that the out-of-shell displacement of the sector at each layer is a quadratic polynomial function of the radial component in addition to a function of the coordinate components within the shell. Due to this assumption, the normal out-of-shell strain is not only zero, or not even a constant, but it changes in the form of a linear function along with the thickness of each layer.

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.

Effect of porosity and skew edges on transient response of functionally graded sandwich plates

This work for the first time presents the effect of porosity and skew edges on the transient response of functionally graded material (FGM) sandwich plates using a layerwise finite element formulation. Two configurations of FGM sandwich plates are considered. In the first configuration, the top and the bottom layers are made of the FGM and the core is made of pure metal, whereas in the second configuration, the bottom, core and the top layers are made of pure metal, FGM and pure ceramic, respectively. Four micromechanics models based on the rule of mixture are used to model porosity for these two configurations of FGM sandwich plates. A layerwise theory based on a first-order shear deformation theory for each layer that maintains the displacement continuity at the layer interface is used for the present investigation. An eight-noded isoparametric element with nine degrees of freedom per node is used to develop the finite element model (FEM). The governing equations for the present investigation are derived using Hamilton’s principle. A wide range of comparison studies are presented to establish the accuracy of the present FEM formulation. It has been shown here that the parameters like skew angle, porosity coefficient, volume fraction index, core to facesheet thickness ratio and boundary conditions have a significant effect on the transient response of FGM sandwich plates. Also, the present finite element formulation is simple and accurate.

GA Optimization of Variable Angle Tow Composites in Buckling and Free Vibration Analysis through Layerwise Theory

In the current research, variable angle tow composites are used to improve the buckling and free vibration behavior of a structure. A one-dimensional (1D) Carrera Unified Formulation (CUF) is employed to determine the buckling loads and natural frequencies in Variable Angle Tow (VAT) square plates by taking advantage of the layerwise theory (LW). Subsequently, the Genetic Algorithm (GA) optimization method is applied to maximize the first critical buckling load and first natural frequency using the definition of linear fiber orientation angles. To show the power of the genetic algorithm for the VAT structure, a surrogate model using Response Surface (RS) method was used to demonstrate the convergence of the GA approach. The results showed the cost reduction for optimized VAT performance through GA optimization in combination with the 1D CUF procedure. Additionally, a Latin hypercube sampling (LHS) method with RS was used for buckling analysis. The capability of LHS sampling confirmed that it could be employed for the next stages of research along with GA.

Damping analysis of sandwich beams with the viscoelastic particulate composite core using fractional order derivation viscoelastic constitutive model

This article deals with the passive damping analysis of the symmetric/asymmetric sandwich beam with viscoelastic particulate composite (VEPC) core, where solid particles are incorporated in a soft viscoelastic matrix to form VEPC. The theoretical study is performed by considering the symmetric/asymmetric beam, where top/bottom stiff layers constrain a viscoelastic core for the passive control of vibration of the overall sandwich beam. Initially, the fractional-order derivative (FOD) parameters of the VEPC are obtained for the viscoelastic constitutive model. Subsequently, an analytical model of the overall beam is developed according to FOD constitutive model and layer-wise first-order shear deformation theory (FSDT). The transient responses of the symmetric/asymmetric sandwich beam are evaluated through this analytical model to explore the change in the passive damping characteristics due to the incorporation of solid particles in a soft viscoelastic matrix. The results reveal a significant reduction in vibration amplitude or improvement in the damping ratio of the symmetric/asymmetric sandwich beam with the incorporation of solid particles in the viscoelastic matrix. The results also illustrate the optimal VEPC for enhanced passive damping of the vibration of symmetric/asymmetric sandwich beam.

Investigation of delamination effect on nonlinear vibration behaviors of a composite plate resting on nonlinear elastic foundation

The aim of the present work is to investigate the delamination effect on nonlinear vibration behaviors of composite plate resting on nonlinear elastic foundation. The composite plate is assumed to be pre-delaminated with various delamination locations and modeled with an improved layerwise theory and finite element method. The delamination is simulated by the Heaviside unit step function allowing for the discontinuity of displacement fields. By means of the variational principle, the nonlinear governing equations can be obtained and further solved by the direct iterative method. The model takes into account three foundation parameters so as to investigate their effect on the nonlinear vibration characteristics. Three longitudinal locations and three interfacial locations are considered, and both clamped-free and clamped–clamped boundary conditions are considered to investigate the nonlinear vibration behaviors. The results show that different from the linear vibration, with the existence of delamination, the nonlinear fundamental frequencies may exceed the fundamental frequency of the healthy plate when the vibration amplitude ratio reaches a certain value. This finding may help engineers understand the nonlinear vibration behaviors and further detect the delamination in composite plate resting on nonlinear foundations in presence of delamination.

Improved Electromechanical Response in Laminated Piezoelectric Plates Using a Zigzag Theory

The zigzag theories are a class of the shear deformation theories that combine the accuracy of the layerwise theories and the efficiency of the equivalent single-layer theories. A nine variable zigzag theory is presented in this work for the laminated piezoelectric plates. Unlike any existing zigzag theory, the transverse shear boundary conditions on the lateral surfaces are not imposed. The theory satisfies interlaminar continuity of displacements and transverse shears stresses. A variational principle is used in deriving governing equations. Bending responses have been obtained under sinusoidal and uniformly applied mechanical and electromechanical loads. Three-dimensional (3D) exact elasticity and piezoelasticity solutions have been used to assess the accuracy of the present theory for a number of simply supported rectangular laminated composite and piezoelectric plates. The transverse shear stress relaxation condition at the boundary surfaces has led to improved predictions in the displacements, stresses, and electric field entities. Present theory is also compared with a number of shear deformation theories to illustrate how significantly the responses get improved due to the transverse shear relaxation.

Generalized higher order layerwise theory for the dynamic study of anisotropic doubly -curved shells with a mapped geometry

An innovative generalized Layer-Wise (LW) approach is proposed for the modal analysis of anisotropic doubly-curved shells with an arbitrary shape by employing the Generalized Differential Quadrature (GDQ) method. The geometrical description of shell structures can be traced from both the differential geometry and mapping technique based on a proper definition of the blending functions.The kinematic field is described in each lamina by employing several interpolating polynomials in a generalized setting, while developing a LW theory that involves different orders of kinematic expansion. The Equivalent Single Layer (ESL) generalized formulation is, thus, derived as particular case of the LW theory. Angle-ply generally anisotropic laminated shells are here investigated, as well as layups with a thick foam softcore. Several numerical examples are illustrated, including different boundary conditions of the mapped geometry, different geometric curvatures for both unmapped and mapped paths, along with a variety of interpolating polynomials and expansion orders of the kinematic field. The accuracy of the proposed model is well-established by a comparative evaluation between our solutions in terms of frequencies and mode shapes and predictions based on classical 3D finite elements.

Characterization of delamination effects on free vibration and impact response of composite plates resting on visco-Pasternak foundations

In this study, the free vibration and impact response of composite plates with interfacial delamination are investigated based on the improved layerwise theory with finite element implementation. The interaction between the composite plate and the surrounding medium is simulated by the visco‐Pasternak foundation model. Hamilton's principle is used to derive the equations of motion for the delaminated composite plates. The impact responses of the delaminated composite plates are later solved by the Newmark algorithm for both clamped-free (C-F) and clamped-clamped (CC) boundary conditions. Influence of the foundation parameters, damping parameter, longitudinal and interfacial delamination locations on eigenfrequencies and transient history are investigated and discussed. Numerical results illustrate that delamination reduces the natural frequencies and the middle plane delamination possesses the largest damage effect. With a stiffer foundation, the damped eigenfrequencies increase significantly and the transient responses also converge much faster. Moreover, the existence of delamination affects the higher frequencies dramatically which may further help identify delamination locations in composite plates resting on visco-Pasternak foundations for structural health monitoring.

Thermo-electro-mechanical investigation of the rectangular composite plate with nano-silver coating subjected to the external voltage

In the current study, layerwise theory (LT) was used to calculate thermal stresses in a clamped rectangular composite plate with nano-silver coating subjected to an external voltage. The composite plate was made of four layers of a piezoelectric or a glass layer, nano-silver coating, and two rectangular silver sub-layers. A set of seventeen differential equations was derived by using the energy method, the piezoelectric relationship, and the heat transfer theory. The numerical code based on the finite difference method (FDM) was written and the stress distribution in each layer was calculated. In order to validate the theoretical results, experimental tests were carried out to determine the temperature of the composite plate with glass and nano-silver coating. Furthermore, the results of FDM to determine, temperature, deflection, and stress distribution were compared to those obtained by the finite element method (Ansys software). It was shown that the results of experimental tests to determine temperature are close to those obtained by LT and the difference between them is less than 0.2%. Furthermore, it was shown that increasing voltage leads to an increase in the temperature gradient and consequently leads to an increase in stress distribution in the composite plate spatially on its edges.