Shear Deformation Plate Research Articles

Sound Insulation Characteristic Analysis of Corrugated Core Sandwich Panel by Using Differential Quadrature Finite Element Method

This paper proposes a universal vibroacoustic coupling theoretical analysis model for investigating the sound insulation characteristic of corrugated core sandwich panel (CCSP) under different boundary conditions. The vibroacoustic coupling model consists of CCSP (structural field) and two three-dimensional acoustic cavities which simulate the incident sound field and accept the sound field, respectively. Based on first-order shear deformation plate and shell theories and acoustic theory, the dynamic model of CCSP and three-dimensional acoustic cavities are established by employing the differential quadrature finite element method in conjunction with the energy principle. The coupling of CCSP and three-dimensional acoustic cavities is realized by the velocity continuity condition at the acoustic–structure interfaces. The validation of the vibroacoustic coupling model is verified by comparing the results calculated by the established model with the corresponding results calculated by ABAQUS. The influence of model parameters on the vibroacoustic characteristic of vibroacoustic coupling model is investigated systematically for determining the critical structure parameters which have influence on the vibroacoustic behaviors. The effect of critical structure parameters on the sound insulation characteristic of CCSP is analyzed systematically for the optimization of the sound insulation performance of CCSP and provides theoretical basis and technique guidance.

Predicting low-velocity impact on the CNTs-reinforced plate using machine learning models

Purpose The study aims to predict a low-velocity impact on a plate reinforced with carbon nanotubes (CNTs) using machine learning models. Design/methodology/approach The first-order shear deformation plate theory (FSDT) is used to express the plate displacements filed. The Hertz nonlinear contact law is used to predict the contact between impactor and plate. Using the energy method and Hamilton’s principle, the motion equations are extracted. The six main parameters considered as inputs to machine learning models are CNTs percentage, impactor radius, plate thickness, plate length and width, CNTs distribution profile and impactor initial velocity. These input parameters are used to predict two impact targets including contact force and contact time. Findings As the values of the targets are continuous, the machine learning task is considered a regression problem. Therefore, this study uses different regression models to predict the targets. These regression models include linear regression, stochastic gradient descent regressor, Bayesian regression, partial least squares regression, Gaussian process regression, multilayer perceptron regressor, support vector regression and decision tree regression. To validate the effectiveness of the regression models, experiments are designed based on different evaluation metrics. The results of the experiments demonstrate that the machine learning models achieve promising performance in predicting the contact force and contact time based on the input parameters. Originality/value Due to the volume of high numerical calculations of impact mechanics to reach the response, the targets of the impact problem are predicted using a variety of machine learning methods.

First Failure Load of Rectangular Laminated and Sandwich Plates Using Isogeometric Analysis

This paper investigates the first failure load of simply supported and clamped laminate and sandwich plates loaded by a distributed normal traction on the top surface. A third-order shear and normal deformable plate theory, the isogeometric basis functions, and five failure criteria, namely, the maximum stress, the Tsai–Wu, the Tsai–Hill, the Hoffman, and the Hashin for laminated plates, and only the Tsai–Hill criterion for sandwich plates are used in this study. Of these, Hashin’s criteria distinguish between the fiber and the matrix failure. The in-plane stresses are found from the plate displacements and Hooke’s law, and the transverse stresses are recovered by integrating the equilibrium equations through the thickness. Effects of the plate aspect ratio, the fiber angle, the face sheet materials, and the core materials on the first failure load are identified. The computed results are found to agree well with those reported in the literature. Whereas the five failure criteria for laminated plates predict nearly the same value of the first failure load, they do not provide the same location of the failure initiation.

Non-linear bending analysis and control of graphene-platelets-reinforced porous sandwich plates with piezoelectric layer subjected to electromechanical loading

Piezoelectric materials as the controlling element have been widely utilized to produce intelligent engineering structures, while these smart structures may fail to realize effective control of composite structures with large deformations. However, investigations on such issues are less reported in published literature, as an accurate and efficient model is required to well forecast the geometrically nonlinear behaviors of smart sandwich structures. As a result, a novel sinusoidal Legendre global-local higher-order shear deformation plate theory (SLHSDT) has been developed to accurately capture geometrically nonlinear behaviors of piezoelectric sandwich plates. The proposed model can fulfill the compatible conditions of transverse shear stresses and contain transverse normal strain, which can ensure precision in predicting electromechanical behaviors. The multi-patch isogeometric analysis (IGA) method for sandwich plates partially bonded with piezoelectric layers is proposed to overcome C1-continuity between patches for the first time. Moreover, the Newmark-β method and Newton-Raphson technique are attempted to solve the nonlinear equations. The present model has been utilized to investigate electromechanical behaviors of laminated structures with piezoelectric layers, which has been compared with the published results. In addition, experiments on macro fiber composite (MFC) integrated sandwich plates have been also carried out in the present work, which can effectively verify the performance of proposed model. Subsequently, the proposed model is employed to study electromechanical behaviors of the five-layer piezoelectric sandwich plates containing internal pores and graphene platelets. Then, influences of the porosity coefficient and GPLs weight fraction on the nonlinear electromechanical behaviors of sandwich plates are investigated. Eventually, the active control on nonlinear behaviors of piezoelectric porous sandwich plates with GPLs reinforcement is studied by using a closed-loop control system, and an effective approach slowing down large deformation has been proposed by selecting an appropriate distribution of GPLs along the thickness direction.

A non-uniform compound strip method for effective buckling analysis of stiffened structures

In this paper, a versatile compound strip method (CSM) with non-uniform spline functions is developed for buckling analysis of stiffened structures. The proposed method further extends the existing CSM by permitting the flexible modification of local knots to place the stiffeners along the strip arbitrarily. In addition, a reasonable knot arrangement can achieve an accurate solving procedure with improved convergence. The displacements of stiffeners are expressed compatibly by the fundamental parameters of skin according to the beam-plate model. Consequently, the reinforcement of stiffeners is naturally incorporated by adding the beam stiffness matrix to the corresponding strips. Based on the first-order shear deformation plate theory and non-uniform spline functions, the semi-analytical formulations of stiffened structures are established. The present method provides the possibility to achieve the local mesh refinement in the finite strip methods. The convergence and validation study is demonstrated through the comparisons with the results of the existing literature solution and finite element method. In conclusion, a more efficient and applicable CSM is proposed to analyze the buckling behaviors of stiffened structures.

Finite element approach for free vibration and transient response of bi-directional functionally graded sandwich porous skew-plates with variable thickness subjected to blast load

At the first time, the finite element method was used to model and analyze the free vibration and transient response of non-uniform thickness bi-directional functionally graded sandwich porous (BFGSP) skew plates. The whole BFGSP skew-plates is placed on a variable visco-elastic foundation (VEF) in the hygro-thermal environment and subjected to the blast load. The BFGSP skew-plate thickness is permitted to vary non-linearly over both the length and width of the skew-plate, thereby faithfully representing the real behavior of the structure itself. The analysis is based on a four-node planar quadrilateral element with eight degrees of freedom per node, which is approximated using Lagrange Q4 shape function and C1 level non-conforming Hermite shape function based on refined higher-order shear deformation plate theory. The forced vibration parameters of the non-uniform thickness BFGSP skew-plate are fully determined using Hamilton's principle and the Newmark-β direct integration technique. Accuracy of the calculation program is validated by comparing its numerical results with those from reputable sources. Furthermore, a thorough assessment is conducted to determine the impact of various parameters on the free and forced vibration responses of the non-uniform thickness BFGSP skew-plate. The findings of the paper may be used in the development of civil and military structures in situations that are prone to exceptional forces, such as explosions and impacts load.

Tunable Bending and Buckling Behaviors of Circular Plates Made of FG Graphene Origami-Enabled Auxetic Metamaterials

Based on the variational differential quadrature (VDQ) method, the bending and buckling characteristics of circular plates made of functionally graded graphene origami-enabled auxetic metamaterials (FG-GOEAMs) are numerically studied in this paper. It is considered that the plate is composed of multiple GOEAM layers with graphene origami (GOri) content that changes in layer-wise patterns. The results from genetic programming-assisted micromechanical models are also employed in order to estimate the material properties. The plate is modeled according to the first-order shear deformation plate theory whose governing equations are obtained using an energy approach in the context of VDQ technique. The governing equations are given in a new vector-matrix form which can be easily utilized in coding process of numerical methods. By means of VDQ matrix differential and integral operators, the governing equations are discretized and solved to calculate the lateral deflection and critical buckling load of plates under various boundary conditions. Selected numerical results are presented to investigate the influences of boundary conditions, GOri content, folding degree and distribution pattern on the buckling and bending behaviors of FG-GOEAM plates.

Thermal vibration analysis of bi-directionally stepped porous functionally graded plates with segment-specific material property variation supported by Kerr foundation

This paper presents a comprehensive analysis of the nonlinear dynamic response of stepped rectangular plates made of functionally graded porous material (FGPM), supported by the Kerr foundation, in a thermal environment. A novel analytical framework is developed to explore geometric and material variations. The study investigates structural variations in plate thickness with abrupt changes in uni- or bi-directional orientations, examining both single and double stepped thickness profiles. Material properties vary with thickness, featuring distinct horizontal discontinuities across plate segments. Porosity distributions, both even and uneven, are addressed using modified mixture rules. Nonlinear kinematic relationships are established using Reddy’s third-order shear deformation plate theory and von Kármán’s nonlinear geometric assumptions, with equations of motion solved via Galerkin’s technique. This improved model effectively addresses non-continuous thickness variation through integral calculus, enhancing computational efficiency. Validation is achieved by comparing outcomes with published literature and Finite Element Analysis (FEA). The study investigates the influence of material properties, elastic foundation, boundary conditions, and geometric parameters on the free vibration and nonlinear behaviors of the plates. Some of the key findings include: increasing the thickness of the stepped segment significantly heightens the fundamental frequency while reducing vibrational amplitudes; optimizing the location of the stepped segment directly impacts the plate’s fundamental frequency and vibrational amplitudes; and as the load factor increases, the difference between linear and nonlinear deflection becomes evident. Therefore, accurate FGPM stepped plate design requires incorporating nonlinear terms in the strain–displacement relationships. Suggestions for future model modifications are also discussed, contributing to advancements in structural design and analysis.

DYNAMIC RESPONSE ANALYSIS OF h-FGS PLATES SUBJECTED TO CONSECUTIVE BLAST LOADING

The main aim of this work is to use a finite element method (FEM) based on Shi’s third-order shear deformation plate theory (TSDT) to study the dynamic response of sandwich plates subjected to consecutive blast loading. The sandwich plate has an auxetic honeycomb core and two different functionally graded materials (FGMs) skin layers (so-called h-FGS plates). The honeycomb core helps significantly reduce the weight of the sandwich structures as well as enhance vibration absorption. The governing equation is derived from Hamilton's principle. After verifying the present approach, the effect of input parameters on the dynamic response of h-FGS plates is carried out in detail. The obtained results are expected to be useful for calculating and designing h-FGS plates in practical engineering.

Dynamic Analysis of Hexagon Honeycomb Sandwich Plate Resting on Elastic Foundations

Dynamic analysis of hexagon honeycomb sandwich plate resting on elastic foundations are presented. Modeling is formed by 3 layers, in which core layer is hexagon honeyconb and facesheet layers is isotropic material. The Reddy’s first order shear deformation plate theory and Galerken method are used to investigate the influnce of elastic foundations, geometrical parameters and material properties of hexagon honeycomb on the deflection – time curve. The value of the natural frequency was compared to the results reported in other works forevaluating the acuracy of used method.

Predicting the compressive strength of advanced concrete structures by developed African vulture optimization algorithm-Elman neural networks

ABSTRACT: Concrete plate structures’ compressive strength and natural frequency are connected by the mechanical characteristics of the material and structural dynamics. Concrete’s elastic modulus rises along with its compressive strength, making the structure stiffer. Since the natural frequency is proportional to the square root of the stiffness over the mass, the increased stiffness raises the natural frequency. In this work, the relationship between natural frequency and compressive strength in advanced concrete constructions reinforced with graphene oxide particles is examined. Also, the structure is under applied pressure. By using a trigonometric shear deformation plate theory, we hope to improve compressive strength prediction accuracy. Navier’s technique is used as the analytical solution process in the analysis. This study contributes to the design and assessment of more durable and effective structural systems by offering a reliable framework for estimating the compressive strength of reinforced concrete structures. This paper presents a novel method by combining Elman Neural Networks (ENNs) with the developed African Vulture Optimization Algorithm (DAVOA) to estimate the frequency of the structure. With the help of this integration, researchers and engineers can now more precisely estimate the compressive strength of sophisticated concrete structures, leading to the creation of stronger and more robust structural solutions.

A light gradient boosting machine-based method for predicting the dynamic response of functionally graded plates

The primary objective of this paper is to efficiently predict the dynamic response of functionally graded plates using LightGBM – a light gradient boosting machine, without reliance on supplementary analysis tools. To obtain the optimal LightGBM model, a dataset comprising 1,000 pairs of input and output is generated through iterations using a combination of isogeometric analysis (IGA) and third-order shear deformation plate theory (TSDT). In this model, the input is represented by a power index which governs the material distribution of the plate, and the output comprises 200 values illustrating deflection over time. To demonstrate the effectiveness of LightGBM in terms of accuracy and computational time, the results obtained by the proposed model are compared to those achieved with the optimal ANN, XGBoost models, and IGA. ® 2024 Journal of Science and Technology - NTTU

Nonlinear transient response of rotating graphene platelets reinforced metal foams blades with initial geometric imperfection

In this paper, a new mechanical model including initial geometric imperfection is developed to investigate the nonlinear transient response of graphene platelets reinforced metal foams (GPLRMF) blades subjected to blast load. Combined with higher-order shear deformation plate theory (HSDT) and von-Karman geometric nonlinearity, the nonlinear motion equations are established, in which the Coriolis force, centrifugal force as well as initial geometric imperfection are simulated. Considering cantilever boundary condition, the partial differential equations are transformed into a series of ordinary differential equations by Galerkin discretization. Using the four order Runge-Kutta algorithm, the nonlinear transient response is numerically researched, and the time histories and phase trajectories are obtained. In addition, the effectiveness of the current research is validated by comparing the results with the existing valuable literatures. The influences of rotating speed, presetting angle, initial geometric imperfection, material property, damping coefficient, and blast load parameter on the dynamic deflection and instantaneous speed are presented. Numerical results reveal that the nonlinear transient dynamics of the composite blades under blast load are significantly influenced by initial geometric imperfection.

Influence of the CNT addition on the mechanical performance of three-phase composite plates

This work has analyzed the bending, free vibration and buckling performance of a three-phase (CNT/Polymer/Carbon fiber) composite plate as a function of the carbon fiber volume fraction and the CNT volume fraction, under several values of the plate aspect ratio (a/b) and the plate slenderness parameter (h/b), and considering the presence of defects due to the poor dispersion on the CNTs. Based on a two-steps homogenization technique, the mechanical properties of the carbon fibers reinforced –CNT enriched– polymeric matrix are computed. Then, the mechanical response of the plate is computed according to the first-order shear deformation plate theory solutions presented in Reddy’s books. The numerical results have revealed the presence, in three-phase (CNT/Polymer/Carbon fiber) composite plates, of a CNT volume fraction threshold above which the bending, free vibration and buckling performance of the plate decay with the carbon fiber volume fraction.

On the transient vibrations of the advanced composite systems under mechanical loading

This work examines the transient nonlinear oscillations of complex composite systems under mechanical pressure utilizing Reddy’s theory of higher-order shear deformation plates. The analysis entails the formulation of nonlinear equations that regulate the stress and displacement fields inside the composite structure. The dynamic behavior is defined by using Hamilton’s idea. The transient response of the composite system under various loading conditions is determined by deriving analytical solutions. The work offers a full knowledge of the dynamic behavior of advanced composite structures by using Reddy’s higher-order shear deformation plate theory, which takes into account the effects of transverse shear deformation and rotating inertia. The intricate interplay of material properties, shape, and external force is elucidated by the nonlinearity inherent in the equations. This provides valuable information on the temporary vibrations that occur in the composite system. The work employs rigorous mathematical analysis and closed-form solutions to clarify the intricate transient dynamics of modern composite structures, providing insights into how they react to mechanical loads over time. The results enhance the overall comprehension of composite material behavior and provide useful insights for the technical design and optimization of composite structures.

A derivative-free phase-field theory for capturing local buckling induced damage in architected plates

Architected plates are commonly used to enhance the load-bearing capacity and stability of structures such as ship hulls and aircraft components. Local buckling-induced damage in these plates are critical events that occur when the plate is subjected to external transverse loading. Performing the analysis to accurately capture this damage and estimation of local buckling load requires explicit 3D- modeling of the architected plate, which is computationally expensive. We address this issue by proposing a derivative-free phase-field theory to capture local buckling-induced damage in architected plates. Here the architected plate is modeled using the shear deformable plate theory and the internal web-core structure is preserved in terms of length scale parameters. The numerical value of the length scale parameter depends on the shape of the webcore structure so that any complicated shape of the webcore is handled based on this parameter. This approach makes the analysis simple to predict the damage behavior with a lesser number of degrees of freedom. The extra energy required to attenuate the zero energy mode-induced oscillations in the solution is estimated from the in-plane buckling analysis of the architected plate. To showcase the efficiency, simulations are conducted based on the proposed approach with different loading cases. The local buckling load and the induced damage behavior of the webcore are compared with the 3D-finite element solution obtained from ABAQUS. The comparison shows that the damage variable is an equivalent estimator of out-of-plane stretch of the webcore in predicting the buckling behavior of the webcore with reduced computational cost and time.

Vibration analysis of functionally graded epoxy/graphene composite plates using the Boundary Element Method and new micromechanical model

This 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.

TSDT vs CPT and FSDT for Free Vibration Analysis of Functionally Graded Incompressible Plates

This article studies vibrational behavior of incompressible functionally graded plates through utilizing classical, first-order shear, and third-order shear deformation plate theories. Plate material properties are presumed to differ continuously in the thickness direction concurringto a power law function. The motion and continuity equations are produced using three different plate theories, and then they are analytically solved for rectangular plates with simple supports utilizingNavier's method. The results are verified by obtaining the plate natural frequency for the power law index value equals zero and comparing them to those reported in previous works. It is shown that transverse vibrational analysis of the classical and first-order shear deformationplate theories for incompressible plates are not as precise as thecompressible ones. It is shown that this issue is due to the fact that according to those theories, unlike the higher order theories, the hydrostatic pressure cannot participate in carrying the bending loads. Consequently, the equivalent flexural stiffness and as a result flexural frequencies decrease. So, to analyze the vibrational behavior of functionally graded incompressibleplates, whether the plate is either thin or thick, higher order theories should be adopted. Also, it is demonstrated that TSDT is the simplest shear deformation plate theory for which the hydrostatic pressure can contribute to withstandig the bending moments. So, it can be a practical theory for free vibration analysis of functionally graded incompressible plates. Finally, this theory has been taken into consideration to analyze the vibrational behavior of rectangular plates made of functionally graded incompressible materials Also detailed parametric studies have been carried out.

Natural frequencies and modal shapes of folded sandwich plates made of porous core and FG-CNTRC coating layers resting on two parameters elastic foundation

Folded structures hold significant importance in aerospace technology due to their distinct design, effectively reconciling strength with a lightweight framework. Within aerospace applications, these structures fulfill diverse roles, serving as pivotal elements in aircraft wings, fuselage sections, and essential components of spacecraft and satellites. This study delves into the free vibration behavior of folded sandwich plates composed of a porous core and functionally graded carbon nanotube-reinforced composite (FG-CNTRC) coatings, resting on a two-parameter elastic foundation. Leveraging first-order shear deformation plate theory (FSDT), elasto-dynamic equations are established for each individual plate segment. Utilizing the two-dimensional generalized differential quadrature method (2D-GDQM), these equations are discretized. Subsequently, by applying boundary conditions to all six edges, including traditional clamped, simply supported, and free configurations, and incorporating continuity conditions for displacements, forces, and moments at the joint borders, natural frequencies and modal shapes are extracted for the folded plate structure. The validity of the proposed formulation and results is demonstrated by comparing them with numerical examples for both composite flat and folded plates. This comparison provides strong support for the accuracy and reliability of the present study. The study comprehensively examines the influence of various parameters on natural frequencies, including modal shape visualizations under different boundary configurations, plate thickness, crank angle, porosity parameter, core thickness, foundation stiffness, and CNTs distribution type.

Free-Vibration Analysis for Truncated Uflyand–Mindlin Plate Models: An Alternative Theoretical Formulation

Plates are flat structural elements whose thickness is small in relation to the size of the surface. Their use may include engine foundations, reinforced concrete bridge elements or parts of various floating structures. Consequently, knowledge of their mechanical behavior under static and dynamic loads is of primary importance in engineering applications and of interest from a structural point of view. As a result, numerous works existing in the literature have investigated the mechanical properties of plates using various plate models, such as Reissner’s theory, Levinson’s theory, Kirchhoff’s theory and Mindlin’s theory, and their static and dynamic behavior has been examined. In the present paper the truncated Uflyand–Mindlin plate equation is proposed. According to Uflyand–Mindlin theory, an alternative theoretical formulation is presented for the free-vibration analysis of plates, and the equations of motion and the general corresponding boundary conditions are derived. This paper develops the truncated Uflyand–Mindlin plate equation, i.e., without the fourth-order derivative, by means of the direct method and variational formulation. The first-order shear deformable plate theory developed by Elishakoff, which takes into account rotational inertia and shear deformation and does not include a fourth-order time derivative, is variationally derived here. This derivation complements that performed by Mindlin some 70 years ago. The innovative aspect of the suggested strategy is that variational and direct methods for studying plate dynamics are analogous. Finding the third equation of the reduced Uflyand–Mindlin equations, the accompanying boundary conditions and their mathematical resemblance are the goals of the presented formulations. In order to solve the dynamic equilibrium problem of a truncated Uflyand–Mindlin equation via a variational formulation, it is demonstrated that the differential equations and the corresponding boundary conditions have the same form as those found using the direct technique. This paper successfully completes this task. Finally, in order to validate the effectiveness and correctness of the proposed procedure, a numerical example of the case of a plate simply supported at all four ends is proposed.