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This paper presents the time-domain viscoelastic formulation based on the Carrera unified formulation (CUF) to obtain the response of composite structures submitted to bending loads. The governing equations are obtained through a modified form of the principle of virtual displacement (PVD) for a viscoelastic analysis. The problem is solved using the Laplace transform instead of direct integration to reduce the computational cost. The results demonstrate the strong capability of the time-domain viscoelastic formulation. Overall, the proposed methodology allows the direct implementation of new optimized high order deformation theories including the thickness stretching effect that may be implemented in futures works. [ABSTRACT FROM AUTHOR]

In this paper, for reducing the number of independent generalized displacements of the traditional piecewise model to decrease the number of vibration equations, a refined piecewise shear deformation model considering the effect of rotary inertias and shear deformation for vibration analysis of laminated composite and sandwich plates is presented. Unlike the conventional piecewise model, the significant novelty of the proposed theory is that the new proposed piecewise theory reduces the number of independent generalized displacements from 9 to 8. Some relevant assumptions, dividing the transverse displacement into bending and shear parts, are introduced into the traditional piecewise model, and the displacement fields of the refined piecewise shear deformation theory are obtained. Next, the governing equations are derived by employing Hamilton's principle and solved by the closed-form Navier method. Then, the present solutions are compared with those available in the previous literature for confirming their validity. Finally, the variations of frequencies and loss factors with system parameters are evaluated and presented graphically. [ABSTRACT FROM AUTHOR]

Although various simplified models can capture size effects of composite laminated micro beam and plate by combining new modified couple stress theory, there is no benchmark to access the accuracy of predicting size effects in those models. Therefore this paper develops a quasi-3D model based on new modified couple stress as a benchmark for analyzing thermal size effects of composite laminated micro plate, and also proposes two simplified quasi-3D models with assumptions out of computational cost at the same time. By a classical example of simply-supported micro laminated square plate, several conclusions can be got from numerical results. For the present quasi-3D model under non-uniform temperature loading, (i): the model is capable to capture size effects of composite laminated micro plate, (ii): discovering a law to define the boundary size between micro and macro laminated plate, which is important for the engineering applications; For the simplified quasi-3D models under uniform temperature loading, (i): As the material length parameter l decreases, the accuracy of both of models is rising gradually, (ii): The first simplified quasi-3D model may substitute the present quasi-3D model to predict thermal size-dependent behaviors of composite laminated micro plate, whereas the second simplified quasi-3D model is suitable to laminated micro plate for which span-to-thickness ratio is no less than 14. [ABSTRACT FROM AUTHOR]

AbstractThis paper presents an analytical model for the free vibration of composite laminated plates with arbitrary biaxial symmetric geometry under elastic boundary conditions, applicable to cross-ply fiber-reinforced composites. In this model, the domain segmentation integral method proposed by the authors is extended to the first-order shear deformation theory (FSDT) and the laminated plate theory. The energy integrals pertaining to the FSDT are analytically simplified by segmenting the integration domains and synthesizing orthogonal polynomial displacement functions over the plate domain coordinate intervals. This synthesis is achieved through the amalgamation of the penalty function method and the Gram-Schmidt orthogonalization process. Then, using the Rayleigh-Ritz procedure, a series solution for the free vibration problem of cross-ply fiber-reinforced composite laminated plates is obtained. The model provides an analytical mathematical relationship between the profile curve of composite laminated plates with arbitrary biaxial symmetric geometry and the strain energy, kinetic energy, and boundary potential energy during vibrational processes. The correctness and applicability of the method are validated by comparing the obtained results with those from the literatures. New results for laminated plates, such as hexagonal and astroid-shaped plates, were presented as references for future research. Taking a track shaped plate as an example, the effect of the number of layers on the vibration characteristics of cross-ply fiber-reinforced composite laminated plates with a certain thickness is studied. [ABSTRACT FROM AUTHOR]

AbstractThis paper studies the free vibration and harmonic response of Functionally Graded Graphene/Epoxy composite plates, considering the First Order Shear Deformation Plate Theory. The weight fraction of graphene variation along the thickness direction with graphene homogeneous dispersed in a polymer matrix. The effective Young Modulus of the plate is predicted by a new micro-mechanical model. The model includes the aspect ratio and weight fraction of nanoplatelets embedded into the matrix. The modal and harmonic of Graphene/Epoxy plates are obtained by the Boundary Element Method formulation for composite plates. The Young modulus calculated from the proposed micro-mechanical model highly agrees with those obtained from experimental results reported in the literature. Results demonstrate a high correlation of the micromechanical model with experimental results and other analytical models. Graphene weight fraction and ratio aspect increase the effective Young modulus of the composite. Boundary Element results show high agreement with Finite Element solutions. Numerical results for modal and harmonic analysis show concentrating graphene near the top and bottom surfaces of the plate is the most effective way to reinforce the plate for increased natural frequencies. The results demonstrate the BEM formulation and micromechanical model can be used as reliable engineering tools for the vibrational analysis of functionally grade graphene composite plates. [ABSTRACT FROM AUTHOR]

In recent years, the use of hybrid composites, in which natural fibers combine with synthetic fibers, in place of composite structures consisting only of synthetic fibers has become increasingly popular due to growing environmental concerns and the need to develop sustainable, more lightweight, recyclable materials required for engineering applications. In this regard, the present paper is an attempt to show the usage of sitka spruce as an alternative to synthetic E-glass fiber and natural flax fiber in design of interply hybrid composite structures in terms of fundamental frequency, buckling resistance and weight. The single-objective and multi-objective approaches are considered to acquire optimum design for non-hybrid and hybrid structures. The modified versions of the optimization methods Differential Evolution (MDE), Nelder Mead (MNM) and Simulated Annealing (MSA) algorithms are considered to solve problems. The results show that the optimum design of the hybrid graphite/epoxy-sitka spruce laminated plate to obtain the structure having a more lightweight (e.g., 53%), higher frequency (e.g., 65%) and buckling resistance (e.g., 90%) was computed and compared with those of the hybrid graphite-flax/epoxy, neat sitka spruce, neat flax/epoxy and neat glass/epoxy laminated composite plates. [ABSTRACT FROM AUTHOR]

Due to their simplification and efficiency, five-variable higher-order models have been widely developed for static and dynamic analysis of multilayered composite and sandwich plates. Nevertheless, the existing five-variable higher-order models will encounter difficulty to produce accurately natural frequencies of sandwich plates. Thereby, this paper proposes a five-variable sine-type higher-order model, which can predict reasonably natural frequencies of sandwich plates. To broaden the scope of application, the finite element formulation in the light of the proposed model is presented. In order to verify the reliability of the proposed model, experiments including two groups of samples have been carried out to test natural frequencies of sandwich plates with diverse holes. After the proposed model is evaluated by experiments, natural frequencies of sandwich plates with different boundary conditions and cutout shapes have been investigated in detail by utilizing the proposed model, which will be further assessed by employing the three-dimensional finite element method (3D-FEM). In addition, the typical five-variable higher-order models published from 1980s to 2020s have been also selected to assess the proposed model. Numerical results show that the proposed model can yield more accurate results than the previous five-variable models. Furthermore, variation of natural frequencies of sandwich plates is also explored by changing the material properties of face sheets, which can provide a consultation for design of dynamic characteristics of sandwich plates. [ABSTRACT FROM AUTHOR]

In this paper, the first attempt has been made to investigate the performance of the active constrained layer damping system in the thermal environment. For such investigation, a skew laminated composite sandwich plate with carbon nanotube-reinforced composite core is considered. The nonlinear strain-displacement relations are employed to generate the initial-stress stiffness matrix and the mechanical stiffness matrices using linear strain-displacement relations. The negative velocity feedback control-law is used to control the first few modes of the vibrating sandwich plate. Comprehensive investigation has been carried out to understand influence of geometric and material parameters on the damping performance of the system. [ABSTRACT FROM AUTHOR]

This paper proposed a virtual testing method combining finite element procedure with heterogeneity weak bonding model to analyze the macroscopic responses of composite plates. Results show that weak bonding can induce out-of-plane displacement fluctuation when plates subjected to tension or shearing loads. However, it is less sensitive to transverse load. Further, much more distorted displacement map means more serious weak bonding interface. The fluctuated displacements can be used to measure and evaluate weak bonding under some specified loading modes. Since the computational framework considers the heterogeneity weak bonding, the statistical characteristics of results can be obtained by multiple computations. [ABSTRACT FROM AUTHOR]

In this paper, we present the dispersion relation of Lamb waves propagating along one-dimensional phononic and along nesting Fibonacci superlattices, using the plane wave expansion and stiffness matrix methods. More band gaps of Lamb wave appear in nesting Fibonacci superlattices plates than in phononic composite plates. Effect of substrate on band gap structures of nesting Fibonacci composite model is analyzed. In addition, the influence of widths of the materials' strips on the band structure is discussed. Finds could be relevant to understand the intrinsic physical properties of quasi-periodic composites piezoelectric and provide flexible choices to meet real engineering applications. [ABSTRACT FROM AUTHOR]

The paper aims to develop a finite element methodology to deal with vibrations and buckling of laminated thin plates subjected to thermal and hygroscopic effects, once a second-order strain gradient theory is included to overcome the limitations of conventional elasticity and to capture nonlocal phenomena. The numerical scheme takes advantage of Hermite approximation for both membrane and bending primary variables, since the strain gradient introduces higher-order derivatives of the nodal displacements. Its versatility is proven by dealing with general lamination schemes and arbitrary boundary conditions. The analyzed configurations cannot be solved analytically. [ABSTRACT FROM AUTHOR]

This paper addresses the effects of uncertainties on the optimal design of trusses and laminated composite plates. Uncertainties are considered in the design variables and material properties. Structural optimization is performed using the failure theory as a constraint, coupled with particle swarm optimization (PSO). Three different optimization approaches are utilized: (i) Deterministic optimization (ii) Reliability-based design optimization and (iii) Robust design optimization. A comparison is conducted between the aforementioned approaches based on the probability of failure. Monte Carlo simulation is performed to obtain the probability of failure. [ABSTRACT FROM AUTHOR]

This paper addresses the influence of material and fabrication uncertainties on natural frequencies of curvilinear fiber laminate. Material properties and fiber orientation are considered uncertain. The sensitivity of input parameters to natural frequencies is obtained using high-dimensional model representation tool, and the results are compared with Monte Carlo simulation. This sensitivity pattern is established through various parametric studies. Highly sensitive parameters are identified and analyzed. Further stochastic analysis of natural frequencies of curvilinear fiber laminate is performed using polynomial neural network. The accuracy and efficiency of polynomial neural network are compared and conclusions are drawn. [ABSTRACT FROM AUTHOR]

The paper proposes a multi-scale uncertainty quantification framework of composite laminated plates. The micro and macro uncertainty parameters are represented by random and interval variables according to available uncertainty information. The data-driven Polynomial Chaos Expansion model is constructed, where polynomial coefficients of random variables are determined based on their high-dimensional statistical information, and coefficients of interval variables are calculated using sampling analysis method. The proposed framework is applied for multi-scale buckling analysis, natural frequency calculation and reliability estimation. The comparison results with Monte Carlo Sampling method demonstrate the computational superiority of the proposed algorithm to achieve high accuracy in multiple conditions. [ABSTRACT FROM AUTHOR]

This paper defines in-plane displacement functions of a composite lattice rectangular plate, which is assumed to be a Kirchhoff-Love plate. It presents an approximate method based on the continuous model of conducting a progressive failure analysis for predicting material failure and post-failure behavior of the composite lattice rectangular plate with various boundary and load conditions. To define the approximate method, we use the Ritz method and Hashin's failure criteria. The validity of the present method is verified by comparing the results of the finite element analysis. Finally, we perform parametric and sensitivity analyses to investigate the effects of the design parameters on the failure characteristics of the composite lattice rectangular plates based on the present method. The results allow a database to be obtained on the structural characteristics of composite lattice rectangular plates. Consequently, it is concluded that the present method is well suited to progressive failure analysis of composite lattice rectangular plates due to their relative simplicity and computational efficiency. [ABSTRACT FROM AUTHOR]

This paper proposes a new zig-zag function to develop the refined sinusoidal theory. A refined sinusoidal shear deformation theory can be obtained by including the proposed zig-zag function and meeting the traction-free boundary conditions on the top and the bottom surfaces. Governing equations and boundary conditions are obtained by using the principle of virtual displacement. Using Navier's method, analytical solutions are presented by solving the boundary value problem. By investigating the typical bending problems of laminated composite and sandwich plates, the effect of various parameters like aspect ratio, thickness ratio and material properties on the bending response of plate is studied in detail. Comparison of the present results with the three-dimensional elasticity solutions and the results calculated using other models published recently in the literature shows that the proposed theory can yield accurately the displacements and stresses of multilayered composite and sandwich plates. Moreover, the accuracy of the displacement and stresses are not impacted by the number of layers and the material properties. [ABSTRACT FROM AUTHOR]

This paper presents the free vibration analysis of a variable stiffness laminated composite sandwich plates. The fiber orientation angle of the face sheets (Skin) is assumed to vary linearly with the x-axis. The problem formulation is based on the higher-order shear deformation plate theory HDST C0 coupled with p-version of finite element method. The elements of the stiffness and mass matrices are calculated analytically. The sandwich plate is presented with a uniform mesh of four p-elements and the convergence properties are achieved by increasing the degree p of the hierarchical shape functions. A calculation program is developed to determine the fundamental frequencies for different physical and mechanical parameters such as plate thickness, core to face sheets thickness ratio, orientation angle of curvilinear fibers and boundary conditions. The results obtained show a good agreement with the available solutions in the literature. New comparison study of vibration response of laminated sandwich plate between the straight and curvilinear fibers is presented. [ABSTRACT FROM AUTHOR]

The second-order statistics of critical stress intensity factor (SIF) of single edge notched fiber reinforced composite plates with random system properties and subjected to uniaxial tensile loadings is investigated. This paper is an extension of reference (Lal and Kapania, 2013) by the present authors by considering more number of input random system parameters for higher accuracy. A C0 finite element method based on a higher-order shear deformation plate theory using displacement correlation method via isoparametric quarter point element is proposed for basic formulation. A stochastic finite element method using first-order perturbation technique and Monte Carlo simulation (MCS) is employed to examine the mean, coefficient of variance, and probability density faction of critical first mode SIF. The effect of different fiber orientations, crack length, plate thickness, a number of layers, and the lamination schemes with random system properties on the statistics of SIF of single edge crack laminated composite plate is evaluated. The tensile failure load is predicted using Hashin's failure criteria. The present approach is validated with results available in literature and by employing independent MCS. [ABSTRACT FROM AUTHOR]

In this paper, finite element method is employed to study the free vibration response of the rotating pretwisted carbon nanotube-reinforced composite cylindrical shell in thermal environment. The shells are reinforced by single walled carbon nanotubes (SWCNTs) and the material properties of SWCNTs are considered to be temperature dependent. The dynamic equilibrium equation is derived from Lagrange's equation for moderate rotational speeds for which the Coriolis effect is neglected. Parametric study is performed to investigate the effects of pretwist angles, temperature rise, rotational speed, and volume fraction of CNTs. In addition to this, the representative mode shapes are also presented. [ABSTRACT FROM AUTHOR]

Shape memory alloys as a kind of smart materials, have two unique characteristics entitled shape memory and pseudoelastic effects. In this paper, a nonlinear dynamic analysis of multilayered composite plate embedded with pre-strained SMA wires under thermal condition is implemented considering both effects of SMAs simultaneously, for the first time. The constitutive equation proposed by Brinson is used for modelling the behaviors of SMA wires. In this work, equations of motion are derived in the framework of Carrera's Unified Formulation, for robust analysis of the problem. In this regard, the nonlinear strains are employed for modelling the thermal effects and also the effect of recovery stresses in the SMA wires. In this study not only the material properties are instantaneous variable with respect to the time and location, but they are also unknown, which make the problem more complicated. For this aim, a transient nonlinear finite element in conjunction with incremental iterative algorithm proposed by the author is employed, in order to solve the equations. Results show that upon the thermal condition, the recovery stress is generated in the SMA wires and therefore reduce the amplitude of a damped response of the plate. One conclusion from this study is that, in contrast with many studies reported before, it cannot be always say that the stress recovery in SMA wires is increased with increasing the pre-strain of SMA wires. In other words, for a specified increasing in temperature, only a limit amount of pre-strain comes back to its original shape and not more. Also, several numerical examples upon effect of different thermal condition, different volume fraction of SMA wires and different boundary conditions have been analyzed. [ABSTRACT FROM AUTHOR]

PHOTO (COLOR) This Special Issue in the Mechanics of Advanced Materials and Structures (MAMS) presents a collection of 12 original journal articles and 1 review article to honor our dear colleague and friend, Dr. Junuthula N. Reddy of Texas A & M University for receiving the 2019 ASME Timoshenko Medal. The review article of Romanoff et al. ( I A review on non-classical continuum mechanics with applications in marine engineering i ) discusses representative problems from different length scales of ship structural design from a non-classical continuum mechanics approach. [Extracted from the article]

In this paper, a new analytical model for behavior of carbon nanotubes reinforced composite plates under low velocity impact has been presented. Nanotubes aligned, straight and randomly oriented are distributed on rectangular simply supported composite plate. The Mori–Tanaka model is used to obtain effective mechanical properties of composites reinforced with nanotubes consisting of aligned, straight and randomly oriented carbon nanotubes embedded in a polymer matrix. The analytical model based on the first-order shear deformation theory and spring-mass model. The results of analytical model are compared with the results of low velocity impact on fiber-reinforced polymer composites. The results show that the deflection and energy absorption of plate in a randomly oriented distribution is more than aligned straight of carbon nanotubes in the composite layers. [ABSTRACT FROM AUTHOR]

In this paper, a nonlinear analysis for large amplitude free vibration of laminated composite plates is developed using higher-order shear deformation theory. The effect of all higher-order terms arising from nonlinear strain-displacement relations are included in the formulation and present plate theory exhibits traction-free surface of the laminated plate in von-Karman sense. A finite element procedure considering a C° continuous isoparametric nine-node rectangular element is implemented for nonlinear model. The accuracy of the theory is validated with some available theory for different aspect ratio, modular ratio, number of layers, ply orientations, etc. through some numerical examples. [ABSTRACT FROM AUTHOR]

This paper is concerned with the static analysis of simply supported cross-ply substrate plates integrated with a layer of piezoelectric fiber reinforced composite material undergoing nonlinear deformations. The von Kármán type nonlinear strain displacement relations and first order shear deformation theory are used to formulate the variational model of this electromechanical coupled problem. Subsequently, Galerkin procedure is employed to derive the nonlinear algebraic governing equations which are solved by usingNewton-Raphson method. The results suggest the potential use of PFRC material for distributed control of nonlinear deformations of smart composite structures. The effect of variation of piezoelectric fiber orientation on the actuating capability of the PFRC actuator for counteracting the nonlinear deformations of the smart composite plates has also been investigated. [ABSTRACT FROM AUTHOR]

This paper deals with the analysis of vertically reinforced 1-3 piezoelectric composite materials as the material for the distributed actuator of smart laminated composite plates. A simple micromechanics model has been derived to predict the effective elastic and piezoelectric coefficients of these piezoelectric composites which are useful for the three dimensional analysis of smart structures. The main concern of this study is to investigate the performance of a layer of this vertically reinforced 1-3 piezoelectric composite material as the constraining layer of the active constrained layer damping (ACLD) treatment. A finite element model has been developed for analyzing the active constrained layer damping of laminated symmetric and antisymmetric cross-ply and angle-ply composite plates integrated with the patches of such ACLD treatment. Both in-plane and out-of-plane actuation of the constraining layer of the ACLD treatment have been utilized for deriving the finite element model. The analysis revealed that the vertical actuation dominates over the in-plane actuation. Particular emphasis has been placed on investigating the performance of the patches when the orientation angle of the piezoelectric fibers of the constraining layer is varied in the two mutually orthogonal vertical planes. Also, the effect of different boundary conditions on the performance of the patches has been studied. The analysis revealed that the vertically reinforced 1-3 piezoelectric composites which are in general being used for the distributed sensors can be potentially used for the distributed actuators of high performance light-weight smart structures. [ABSTRACT FROM AUTHOR]

The effect of boundary conditions on the vibrations of variable stiffness composite laminates (VSCL) with curvilinear fibers is particularly interesting because fiber orientations at the plate edges and in the plate's domain can differ. Since real boundaries are not the ideal limit cases usually assumed in the literature, a more correct model can be achieved by representing boundaries as elastically restrained edges. This approach is followed in this work, which investigates the combined effect of fiber orientation and boundary stiffness on the geometrically non-linear forced vibrations of rectangular VSCL plates. The boundary stiffness is adjusted using experimental data. [ABSTRACT FROM AUTHOR]

The non-linear dynamic response of a randomly distributed carbon nanotube fiber-reinforced laminated composite (CNTFRLC) plate subjected to various in-plane pulse localized loadings and transverse patch loading is presented semi-analytically. Implementing higher-order shear deformation theory (HSDT) along with von-Kármán non-linearity, the non-linear kinematics of the CNTFRLC plate are modeled. The nonuniform pre-buckling stresses ( σ x x , σ y y , and τ x y ) were developed implementing Airy's stress equilibrium approach, and subsequently utilized while deriving the non-linear partial differential equations (PDEs) of the plate through Hamilton's principle and solved via. Galerkin's method. Finally, the non-linear dynamic responses of the CNTFRLC plate are traced using Newmark's method. [ABSTRACT FROM AUTHOR]

The high temperature environment makes the buckling of composite laminated plate happen earlier. Further weight savings can be achieved once the plate has a favorable postbuckling stiffness. This study aims to address this issue by developing a ROM-driven lamination optimization to maximize the buckling and postbuckling performance of compressed plates under initial temperature field. The reduced-order model(ROM) constructed using the improved Koiter theory is reformulated to be suitable for thermal-mechanical buckling problems. A linear subspace of the force space is represented to be the span of the mechanical load, the thermal load and a set of predefined perturbation loads. The thermal load related to the initial temperature field is constant during the increase of in-plane compressive load. An independently additional degree of freedom corresponding to the thermal load is implemented into the construction of the reduced-order model. The buckling and postbuckling performance can be extracted from the solution of reduced-order model, and then subsequently selected as inputs to achieve the optimal laminate. The main novelty of this work is to achieve the thermal-mechanical buckling and postbuckling optimization, benefitting from the highly efficient single run of thermoelastic geometrically nonlinear analysis. Various numerical examples have been selected to validate the performance of the proposed method, considering the influences of length-to-width ratio, α1/α2, ply number and nonuniform temperature field. [ABSTRACT FROM AUTHOR]

In this article, the Carrera Unified Formulation and full Green–Lagrange nonlinear relations are employed to investigate the postbuckling behavior of laminated composite panels subjected to in-plane shear and combined loadings. The layerwise refined plate models are implemented by the efficient Lagrange expansion functions through the laminate thickness. An artificial surrounding area is assumed to model shear conditions. The accuracy of the presented model is validated based on the available literature. Then, the effects of stiffeners on the nonlinear response of panels are evaluated, and comprehensive assessments are provided for the equilibrium curves and stress distributions. [ABSTRACT FROM AUTHOR]

In this work, a comprehensive investigation of curvilinear fiber reinforcement on damping of rectangular and skew composite plates is computationally estimated using higher-order shear flexible model. A set of governing equilibrium equations developed here in form of eigenvalue analysis is solved by adopting the Q-R algorithm. The damping factors associated with different vibrational modes are evaluated from the complex eigenvalues. The proposed model is validated against the available analytical and experimental results. The damping capability of laminated rectangular/skew composite plates is thoroughly analyzed by varying the curvilinear fiber path angles in the layers, lay-up orientations, structural boundary conditions, skew angle of the laminate, and nature of the material. Results reveal that the damping pretending to the curvilinear fibers plate is better than the conventional composite laminate; it varies significantly according to the variation in center and edge of the curvilinear fiber angles. It is also noted that the damping increases with the skew angle of the plate. The study conducted here shows the suitability of such variable stiffness composite structure for safe design under dynamic/impact loading situation. [ABSTRACT FROM AUTHOR]

The 3D state space approach (SSA) allows accurate description of composite plate behavior, regardless of plate thickness. A new formulation of the SSA is proposed here for the hitherto unexplored case of an asymmetrically supported plate. This solution takes into account all independent elastic constants and satisfies all governing equations and boundary conditions. The new formulation is first derived and then compared to predictions by alternative analytical solutions including classical plate theory as well as the finite element method (FEM) for a number of case studies. Globally, the SSA solution compared well and produced greater accuracy than the FEM model. [ABSTRACT FROM AUTHOR]

A novel method for predicting effective stiffnesses of composite plates with in-plane periodicity is proposed according to two-scale strain energy equivalence. The macroscale energy is reached with the Reissner-Mindlin plate theory, while the microscale energy is obtained through the newly constructed displacement functions of a unit cell within the framework of the three-dimensional elasticity theory. The new displacement functions consist of homogenized displacements, two decoupled expansion terms, and a higher-order perturbed displacement term. The elaborate finite element formulations are presented for realizing the present method in Comsol Multiphysics. Several numerical experiments demonstrate the effectiveness of the new stiffness prediction method. [ABSTRACT FROM AUTHOR]

In this article, the Carrera unified formulation (CUF) is developed for the buckling analysis of multilayered functionally graded carbon nanotube (MFG-CNT) reinforced cylinders. For this purpose, the CUF is obtained in the cylindrical coordinate system as a first step. Then, the displacement-based CUF is derived from the principle of virtual work in each individual layer in the framework of the element free Galerkin (EFG) method. The mechanical properties of each CNTs-reinforced layer are estimated using the modified Halpin–Tsai (H-T) micromechanical model and rule of mixture. In this model, the waviness, interphase, and agglomeration of CNTs are accounted using influencing factors in terms of CNTs geometric and processing characteristics. Four types of laminates, which are composed of several reinforced layers with different arrangements (distributions) along the radial direction, are taken into account to examine the effect of the layers' arrangement on the buckling capacity of the cylinder. The proposed CUF-EFG formulations and solution method are validated by comparing the present buckling loads with those obtained by theoretical formula for the homogeneous slender cylinders. A parametric study is conducted to investigate the effects of CNTs weight fraction, waviness, agglomeration and interphase of CNT, distribution of layers, power-law index, radius-to-thickness ratio, length-to-radius ratio, and boundary conditions (BCs) on the critical buckling loads of MFG-CNT reinforced cylinder. The results show the high performance of the proposed CUF-EFG method for buckling analysis of MFG-CNT reinforced cylinders with a wide range of aspect ratios. [ABSTRACT FROM AUTHOR]

Aided by the scaled boundary finite element method (SBFEM), analytical precise integration solutions to the transverse free vibration responses of functionally graded piezoelectric composite plates are provided for the first time. Distributions of the functionally graded piezoelectric materials follow arbitrary mathematical formulae as concerns the in-plane unidirectional or bidirectional coordinates. The vibration behaviors of piezoelectric composite plates with various geometrical shapes, multifarious boundary constraints and any number of laminae can be explored by the introduced technique. Additionally, the shear correction factors and assumptions on the changing patterns of mechanical and electrical variables are not needed to be offered in the employed methodology. The proposed approach regards only four quantities containing three elastic displacement components and the electric potential as the primary unknowns, which can be denoted as an analytical matrix exponent in terms of the thickness coordinate. Only two-dimensional high-order spectral elements are adopted to discretize the in-plane surface of the plate with less nodes and degree of freedoms, which promotes to lowering the calculative expense and advancing the computational efficiency. The introduced scaled boundary coordinate system and the dual vector technology are helpful to simplify the basic partial differential equations of piezoelectric materials into the first order ordinary differential SBFEM governing equation, from which the highly accurate global stiffness matrix are constructed by dine of the precise integration technique (PIT). With the aid of the kinetic energy scheme and compatibility conditions between neighboring layers, the whole mass matrix for the laminated piezoelectric plates can be built. According to solving the eigenvalue equation, the precise integration solutions to free vibration frequencies can be acquired. Finally, numerical experiments are afforded to elucidate the high precision and fast convergence of the present method. Moreover, the effect of different boundary constraints, gradation parameters and aspect ratios on the transverse vibration responses of in-plane-wise functionally graded piezoelectric composite plates is revealed. [ABSTRACT FROM AUTHOR]

The lay-ups of symmetric variable stiffness composite laminated elliptical plates with curvilinear fibers are optimized for the maximum frequencies of the lowest three modes using the layer-wise optimization method. Two design variables and three constraints are considered. The fiber paths are constructed using the method of shifted paths. The laminate is modeled as one curved hierarchical finite element. The formulation is based on the first-order shear deformation theory. The blending function method is used to model accurately the geometry. New results for the optimal lay-ups that maximize the natural frequencies of the lowest three modes are obtained. The method is validated based on convergence test and comparison with published results for symmetric constant stiffness composite laminated elliptical plates with rectilinear fibers. A parametric study is performed showing the effects of aspect ratio, thickness ratio, modulus ratio, number of layers, and boundary constraint on the optimal solutions. [ABSTRACT FROM AUTHOR]

The anti-penetration performance of the composite armor structures, which are composed of steel, Kevlar composite, and ultra-high molecular weight polyethylene (UHMWPE) composite, were investigated numerically. The effects of composite armor configurations, the thickness of back plates, the shapes and incident angles of projectile on the anti-penetration performance were analyzed. The results indicate that the configuration with steel, Kevlar and UHMWPE on the first, second and third layers of the composite armor have the better anti-penetration performance. As the thickness of the composites back plate increases, the specific energy absorption of the composite armor decreases while the anti-penetration performance of the composite armor increases. In addition, it can be also found that the ball-headed projectile has stronger penetration ability than the flat-headed projectile of the same weight, and the penetration ability of projectile decreases with the increase in the impact angle of projectile. [ABSTRACT FROM AUTHOR]

SBFEM is used for three-dimensional modeling of thick laminated composite plates, where plate theories fail to provide the accurate results. SBFEM is a semi-analytical tool and have various advantages over finite element method. It allows for a coarse mesh and refinement over the boundaries only. This improves the computational efficiency by minimizing the number of nodes. Two different meshing structures are considered, and a comparison has been made in terms of various attributes for computational cost such as memory requirements, computational time, and solver complexity. Various numerical examples are considered to assess the suitability of SBFEM for the purpose. [ABSTRACT FROM AUTHOR]

The dynamic analysis is carried out of a laminated composite plate coupled with a piezoelectric energy harvester under the action of a moving vehicle. The finite element method along with Newmark's method are applied to solve the discretized equations. Results are presented for two main cases: (i) free and forced vibrations of the laminated composite plate with no harvester and (ii) forced vibrations of the plate coupled with the energy harvester. Several parameters – such as the symmetric and anti-symmetric layups, length of the harvester, and piezoelectric material parameters – are considered to study their effects on the electrical output. [ABSTRACT FROM AUTHOR]

In this research, a nonlinear dynamic analysis of micro plate containing micro shape memory alloy (SMA) wires, taking into account the material and geometric nonlinear effects and also considering the instantaneous changes of martensitic volume fraction (MVF) in different points of the micro plate, has been investigated. In this study, using the first-order shear deformation theory (FSDT) and applying Hamilton's principle, the governing equations of micro plate are extracted such the kinematic equations of micro SMA wires are coupled with governing equations. In this regard, von Karman nonlinear strain-displacement relation is used to consider large displacements and the model proposed by Hernandez and Lagoudas is employed to model the pseudoelastic behavior and also to capture the size effect of the SMA wires at micro scale. The modified couple stress theory is also employed to consider the size effect on the matrix material of micro plate. In addition, it is assumed that the micro wires are arranged in FG forms in the direction of the thickness of the micro plate. Using the return mapping algorithm and nonlinear finite element method, the governing equations of motion, are solved. In the results section, the study of parameters such as size effects, different boundary conditions, taking into account nonlinear strain field, diameter change and type of arrangement of micro SMA wires, length scale factor and thickness of micro plate, have been implemented. To evaluate the validity of the present work, some of the results are compared with the articles available in the literature. New results show that the bigger diameter of the micro SMA wires (considering the total volume fraction constant) and the smaller length scale factor, the higher damping ratio of the micro plate is obtained. Also, the vibration damping ratio increases when more micro SMA wires are arranged in F G – X form. [ABSTRACT FROM AUTHOR]

In the present work, nonlinear free vibration analysis of composite laminated plates and shallow cylindrical/spherical/hyperboloid shell panels considering geometric nonlinearity is carried out using non-polynomial inverse trigonometric higher-order shear deformation theory with seven degrees of freedo (DOFs). The present theory assumes parabolic variation of out-of-plane stresses and satisfies traction-free boundary conditions on the top and bottom surfaces of the composite as a priori. A nonlinear finite element model is developed and applied to obtain discretized nonlinear equations. The geometric nonlinearity in sense of Green-Lagrange considering von-Kármán assumptions is incorporated in formulation. An eight noded efficient C0 continuous isoparametric rectangular finite element is implemented in the present nonlinear analysis. The efficacy and accuracy of the present theory and finite element model is validated with the available literature results. For the analysis, various types of plates and shell panels with different material properties, lamination schemes, thickness ratios, aspect ratios, modular ratios, curvature ratios, and boundary conditions are considered. The effects of these different geometric and material properties on nonlinear frequency ratios at various amplitude ratios are examined in detail. [ABSTRACT FROM AUTHOR]

Due to the classical thin plate theory based governing equations of composite rectangular plates for dynamic problems are linear homogeneous equations on bending stiffness coefficients, a general sequential permutation search (SPS) algorithm is presented to optimize stacking sequences of composite laminates by exploiting convexity of lamination parameters, sensitivity of bending stiffness, and bending-twisting coupling stiffness feature. Numerical examples are conducted for 8-layer composite rectangular plates with different boundaries to maximize the fundamental frequency evaluated by the Rayleigh–Ritz method, and the results are compared with those of layerwise optimization approach and genetic algorithm, demonstrating robustness and efficiency of SPS. [ABSTRACT FROM AUTHOR]

Nowadays, graphene is considered as one of the most ideal reinforcements for composite materials due to the outstanding mechanical properties. From the literature survey, it is found that the researches on interlaminar stress analysis of functionally graded graphene reinforced composite (FG-GRC) laminated structures are scarce in literature. If transverse shear deformations are unable to be described accurately, the reasonable design of FG-GRC laminated structures will meet severe challenges due to the differentiation of material properties at the adjacent layers. Thereby, such issue is less studied by using the efficient models, so an advanced mixed-form plate theory is to be proposed for transverse shear stress analysis of FG-GRC laminated plates. The proposed theory can meet beforehand compatible conditions of transverse shear stresses at the interfaces of adjacent laminates and only contains seven independent displacement variables. By applying the three- dimensional (3D) equilibrium equations and the Reissner mixed variational theorem (RMVT), the accurate transverse shear stresses are obtained. The 3D elasticity solutions and the results computed by using the chosen models are selected to appraise the capability of the proposed model. Numerical results show that the proposed plate model can yield accurately transverse shear stresses without any post-processing procedure. In addition, the effects of graphene volume fraction, graphene distribution pattern, lamination sequence, span-to-thickness ratio and aspect ratio on the displacements and stresses of the FG-GRC laminated plates are thoroughly investigated. [ABSTRACT FROM AUTHOR]

The great potential of variable stiffness laminates in maximizing buckling load is obvious over straight fiber laminates, however the optimum design of such VAT laminates which has much more design variables and larger computational efforts, is still a challenge even for the modern computational method and capability. In addition, the postbuckling performance and the correlations with buckling resistance still need to be further studied for VAT laminates. This work proposes an enhanced reduced-order model based on the improved Koiter perturbation theory for buckling and postbuckling analysis of variable stiffness composite plates. The VAT laminas composed by "two-segment" fibers and "four-segment" fibers are considered, respectively, in construction of the reduced-order finite element model. The nonlinear prediction for initial postbuckling response of VAT laminate can be achieved, by solving the small-scaled reduced-order model. The nonlinear buckling load, postbuckling stiffness and postbuckling stiffness residual factor, are accurately and efficiently extracted from the initial postbuckling predictor, and then subsequently to be selected as inputs to the GA based optimization process for the design of VAT laminates. Extensive numerical investigations validate that the proposed method can find a combination of several varied angle fiber layers with constant thicknesses such that the combination results in an optimal stiffness distribution and provides a more favorable structural performance in both buckling and postbuckling regime for different demands of structure design. [ABSTRACT FROM AUTHOR]

In light of the limited number of available literature on Abaqus user-elements implementation, this work presents two layerwise electro-elastic user-elements for static and free vibration analysis of piezoelectric composite plates. Three discrete layers are considered, each one described by a first-order shear deformation displacement field along with a linear or quadratic z-expansion of the electric potential. The models predictive capabilities are assessed by a comparison with three-dimensional exact solutions for simply supported plates. Numerical results demonstrate an advantage of the electric potential quadratic z-expansion for static analysis, with negligible improvements on the evaluation of the first 12 natural frequencies. [ABSTRACT FROM AUTHOR]

A new microstructure-dependent non-classical model for Kirchhoff plates is developed by using a reformulated strain gradient elasticity theory that incorporates both the strain gradient and couple stress effects. The equation of motion and the boundary conditions are simultaneously obtained through a variational formulation based on Hamilton's principle. The new plate model contains one material constant to account for the strain gradient effect and one material length scale parameter to capture the couple stress effect. The newly developed non-classical plate model includes the plate model incorporating the couple stress effect alone and the plate model based on the classical elasticity as two special cases. To illustrate the new model, the buckling, static bending and free vibration problems of a simply supported rectangular plate are analytically solved by directly applying the general formulas derived. The numerical results reveal that the presence of the strain gradient and couple stress effects leads to reduced plate deflections, enlarged critical buckling loads and increased natural frequencies. These microstructure effects are significant when the plate is very thin, but they are diminishing as the plate thickness increases. These predicted trends of the size effects at the micron scale agree with those observed experimentally. [ABSTRACT FROM AUTHOR]

An extended layerwise/solid-element (XLW/SE) method is developed for a stiffened laminated composite plate with piezoelectric patch, taking the debonding, multiple delaminations, and transverse cracks into account. The governing equations of laminated composite plates and piezoelectric patch are established based on the extend layerwise method, while these of stiffeners are modeling by using the three-dimensional solid element. The final governing equations are assembled by using the compatibility conditions and internal force equilibrium conditions at the plate/stiffener and plate/patch interfaces. The results are compared with those of 3D elastic models developed in commercial software, and good agreements are achieved. [ABSTRACT FROM AUTHOR]

Graphene-based reinforcements can enhance mechanical performances of composite structures by altering the distributions of graphene platelets (GPLs), which determines wave propagation characteristics. Dispersion behaviors of elastic waves in the nanocomposite annular plates are investigated in this work. Utilizing the modified micromechanical model and the rule of mixtures, four types of distribution patterns are considered to evaluate the effective material properties of the nanocomposites. Elastodynamic equations of wave motion are expressed and parameterized in the semi-analytical formulation based on Reddy's higher-order shear deformation theory and the isogeometric analysis. Dispersion characteristics of the in-plane and out-of-plane wave modes are studied in detail. The cutoff frequencies are discussed in order to confirm the accuracy of the results. Besides, parametric studies are conducted to analyze the influences of distribution, weight fraction and size parameters of GPLs on phase-velocity and group-velocity curves of waves. The results indicate that the concentration of GPLs on the boundaries of composite plates can improve the propagation characteristics of wave modes. In the case of FG-V, there exists the interesting phenomenon of mode conversion. It is concluded that dispersion characteristics of elastic waves in nanocomposite annular plates can be flexibly modulated by changing significant parameters of the reinforcement GPLs. [ABSTRACT FROM AUTHOR]

In this article, the elastic problem of composite circular plates with rectilinear orthotropic characteristics, in case of in-plane bending and torsional moments applied, is resolved. According to classical lamination plate theory, the analysis makes use of the Ritz method along with the principle of virtual displacements, originally combined in order to obtain displacements components. The procedure represents an important step for the setting-up of a spot joint element able to simulate in FE analyses the structural behavior of point junctions applied to composite components. The accuracy of the procedure has been demonstrated comparing analytical results to FE reference analyses. [ABSTRACT FROM AUTHOR]

This article presents an investigation on the postbuckling behavior of doubly curved graphene-reinforced composite (GRC) laminated panels supported by an elastic foundation and subjected to lateral pressure and in thermal environments. The piece-wise GRC layers are arranged in a functionally graded (FG) pattern along the thickness direction of the panels. The overall mechanical properties of the FG-GRCs are assumed to be temperature dependent and are estimated through the extended Halpin-Tsai micromechanical model. The governing differential equations for the doubly curved panels are based on a higher order shear deformation shell theory with von Kármán strain-displacement relationships and the panel-foundation interaction. The initial deflections caused by lateral pressure and thermal bending stresses are both taken into account. The governing equations are first deduced to a boundary layer type that includes nonlinear prebuckling deformations and initial geometric imperfections of the panel. The postbuckling equilibrium path for the perfect and geometrically imperfect GRC laminated doubly curved panels are obtained by applying a singular perturbation technique along with a two-step perturbation approach. The impacts of material property gradient, temperature variation, panel curvature ratio, as well as foundation stiffness on the postbuckling behavior of FG-GRC laminated doubly curved panels are investigated. [ABSTRACT FROM AUTHOR]

The nonlinear bending behavior of nanocomposite laminated plates with negative Poisson's ratios (NPR) is reported. Each ply of the plate is made of carbon nanotube-reinforced composites (CNTRCs) and may have different CNT volume fractions and the CNTRC plies are arranged in the thickness direction in a piece-wise functionally graded pattern. The plate is supposed to be rested on a two-parameter elastic foundation and is exposed in a thermal environment. The temperature-dependent material properties of the CNTRCs are evaluated using an extended Voigt (rule of mixture) model. The governing equations for the nonlinear bending of FG-CNTRC laminated plates are based on Reddy's third order shear deformation plate theory and solved by using a two-step perturbation approach. Analytical solutions are obtained which include the geometrical nonlinearity in the von Kármán sense, the thermal effects and the plate-foundation interaction. The effect of NPR on the nonlinear bending responses of FG-CNTRC laminated plates under different loading conditions are investigated comparatively according to the graphical results. It is explicitly shown that NPR has a significant effect on the nonlinear bending responses of CNTRC laminated plates. [ABSTRACT FROM AUTHOR]