Vibration characteristics of sandwich plates with an auxetic honeycomb core and laminated three-phase skin layers under blast load

In this article,vibration characteristics of sandwich plates with an auxetic honeycomb core and laminated three-phase skin layers subjected to blast load are studied.Higher-order ES-MITC3 element based on higher-order shear deformation theory(HSDT)to achieve the governing equations.The sandwich plates with the ultra-light feature of the auxetic honeycomb core layer(negative Poisson’s ratio)and reinforced by two laminated three-phase skin layers.The obtained results in our work are compared with other previously published to confirm accuracy and reliability.In addition,the effects of parameters such as geometrical and material parameters on the vibration characteristics of sandwich plates with an auxetic honeycomb core and laminated three-phase skin layers are fully investigated.

Finite element analysis of functionally graded sandwich plates with porosity via a new hyperbolic shear deformation theory

This study focusses on establishing the finite element model based on a new hyperbolic sheareformation theory to investigate the static bending,free vibration,and buckling of the functionally graded sandwich plates with porosity.The novel sandwich plate consists of one homogenous ceramic core and two different functionally graded face sheets which can be widely applied in many fields of engineering and defence technology.The discrete governing equations of motion are carried out via Hamilton’s principle and finite element method.The computation program is coded in MATLAB software and used to study the mechanical behavior of the functionally graded sandwich plate with porosity.The present finite element algorithm can be employed to study the plates with arbitrary shape and boundary conditions.The obtained results are compared with available results in the literature to confirm the reliability of the present algorithm.Also,a comprehensive investigation of the effects of several parameters on the bending,free vibration,and buckling response of functionally graded sandwich plates is presented.The numerical results shows that the distribution of porosity plays significant role on the mechanical behavior of the functionally graded sandwich plates。

NATURAL FREQUENCY FOR RECTANGULAR ORTHOTROPIC CORRUGATED-CORE SANDWICH PLATES WITH ALL EDGES SIMPLY-SUPPORTED

A simple approach to reduce the governing equations for orthotropic corrugated core sandwich plates to a single equation containing only one displacement function is presented, and the exact solution of the natural frequencies for rectangular corrugated-core sandwich plates with all edges simply-supported is obtained. Furthermore, two special cases of practical interests are discussed in details.

FURTHER STUDY ON LARGE DEFLECTION OF CIRCULAR SANDWICH PLATES

In this paper, a nonlinear solution is first presented for a circular sandwich plate with the flexure rigidity of the face layers taken into account. In solving the nonlinear bending equations, a modified power series method is proposed. The uniformly distributed loading and the clamped but sliding boundary condition are also assumed. Then our results are compared with those from Liu Ren-huai and Shi-Yun-fang[15]. The present solution can be used ax a more accurate basis in engineering applications.

NONLINEAR BUCKLING BEHAVIOR OF DAMAGED COMPOSITE SANDWICH PLATES CONSIDERING THE EFFECT OF TEMPERATURE-DEPENDENT THERMAL AND MECHANICAL PROPERTIES

On the basis of the first-order shear deformation plate theory andthe zig-zag deformation as- sumption, an incremental finite elementformulation for nonlinear buckling analysis of the composite sandwichplate is deduced and the temperature-dependent thermal and mechanicalproperties of composite is consid- ered. A finite element method forthermal or thermo-mechanical coupling nonlinear buckling analysis ofthe composite sandwich plate with an interfacial crack damage betweenface and core is also developed.

Free vibration of functionally graded sandwich plates using four-variable refined plate theory

This paper uses the four-variable refined plate theory （RPT） for the free vibration analysis of functionally graded material （FGM） sandwich rectangular plates. Unlike other theories, there are only four unknown functions involved, as compared to five in other shear deformation theories. The theory presented is variationally consistent and strongly similar to the classical plate theory in many aspects. It does not require the shear correction factor, and gives rise to the transverse shear stress variation so that the transverse shear stresses vary parabolically across the thickness to satisfy free surface conditions for the shear stress. Two common types of FGM sandwich plates are considered, namely, the sandwich with the FGM facesheet and the homogeneous core and the sandwich with the homogeneous facesheet and the FGM core. The equation of motion for the FGM sandwich plates is obtained based on Hamilton＇s principle. The closed form solutions are obtained by using the Navier technique. The fundamental frequencies are found by solving the eigenvalue problems. The validity of the theory is shown by comparing the present results with those of the classical, the first-order, and the other higher-order theories. The proposed theory is accurate and simple in solving the free vibration behavior of the FGM sandwich plates.

Effect of plastic deformation on diffusion-rolling bonding of steel sandwich plates

Diffusion bonding is one of the most important techniques for composite materials, while bonding temperature, holding time,and rolling reduction are the key parameters that affect the bonding strength of sandwich plates. To study the effect of plastic deformation on the bonding strength, laboratory experiments were carried on a Gleeble Thermal Simulator to imitate the diffusion-rolling bonding under different reductions for steel sandwich plates. The bonding strength and interlayer film thickness were measured, and the element diffusion was analyzed using line scanning. The relationship between the bonding strength and “diffused interlayer” thickness was investigated. It has been found that the bonding strength increases with reduction, whereas the interlayer film thickness decreases gradually as the reduction increases. The diffusion under plastic deformation is obviously enhanced in comparison with that of nil reduction. The mechanism of plastic deformation effect on the diffusion bonding and related models have been discussed.

FURTHER STUDY ON LARGE AMPLITUDE VIBRATION OF CIRCULAR SANDWICH PLATES

In this paper, a solution of axisymmetric large amplitude vibration is presented for a circular sandwich plate with the flexure rigidity of the face layers taken into account . In solving the problem , the modified iteration method is proposed. Then our results are compared with those from paper [1].

Static and free vibration analysis of four-parameter continuous grading elliptical sandwich plates

In the present study,the static and dynamic analyses of elliptical functionally graded sandwich(FGS)plates are investigated.The constituent materials of the sandwich plates are ceramic and metal so that the core is made of pure metal,while the face sheets consist of a combination of metal and ceramic according to a four-parameter power-law distribution.Different material profiles such as classic,symmetric,and asymmetric can be obtained using the applied generalized power-law distribution relation.The analysis is performed based on the classical laminated plate theory(CLPT)and the Ritz method.The effects of four parameters in the material distribution relation as well as different geometric parameters on the deflection and natural frequencies of elliptical FGS plates are studied.The results of this study show that with a proper distribution of materials,the optimal static and dynamic behavior can be achieved.The results also indicate that the generalized power-law distribution has significant effects on the natural frequencies of elliptical FGS plates.For example,although the frequency parameter of a plate with ceramic face sheets is more than the one with metal face sheets,the use of larger amounts of ceramic does not necessarily increase the natural frequency of the structure.

NONLINEAR VIBRATION OF CIRCULAR SANDWICH PLATES UNDER CIRCUMJACENT LOAD

Based on von Karman plate theory, the issue about nonlinear vibration for circular sandwich plates under circumjacent load with the loosely clamped boundary condition was researched. Nonlinear differential eigenvalue equations and boundary conditions of the problem were formulated by variational method and then their exact static solution can be got. The solution was derived by modified iteration method, so the analytic relations between amplitude and nonlinear oscillating frequency for circular sandwich plates were obtained. When circumjacent load makes the lowest natural frequency zero, critical load is obtained.

CUBLIC SPLINE SOLUTIONS OF AXISYMMETRICALNONLINEAR BENDING AND BUCKLING OFCIRCULAR SANDWICH PLATES

Cubic B-spline taken as trial function, the nonlinear bending of a circular sandwich plate was calculated by the method of point collocation. The support could be elastic. A sandwich plate was assumed to be Reissner model. The formulae were developed for the calculation of a circular sandwich plate subjected to polynomial distributed loads, uniformly distributed moments, radial pressure or radial prestress along the edge and their combination. Buckling load was calculated for the first time by nonlinear theory. Under action of uniformly distributed loads, results were compared with that obtained by the power series method. Excellences of the program written by the spline collocation method are wide convergent range, high precision and universal.

THE BUCKLED STATES OF ANNULAR SANDWICH PLATES

In this paper, the axisymmetric buckled states of an annular sandwich plate ( Reissner-type sandwich plate) with the clamped inner edge which is subjected to a uniform radial compressive thrust at the clamped outer edge are studied. Firstly, the basic equation of the buckled problem is derived. Secondly, the critical loads for some parameters are obtained by using the shooting method. Finally, we discuss the existence of the buckled slates in the vicinity of the critical loads and obtain the asymptotic expansions of the buckled states.

1/3 SUBHARMONIC SOLUTION OF ELLIPTICAL SANDWICH PLATES

The problem of nonlinear forced oscillations for elliptical sandwich plates is dealt with. Based on the governing equations expressed in terms of five displacement components, the nonlinear dynamic equation of an elliptical sandwich plate under a harmonic force is derived. A superpositive-iterative harmonic balance (SIHB) method is presented for the steady-state analysis of strongly nonlinear oscillators. In a periodic oscillation, the periodic solutions can be expressed in the form of basic harmonics and bifurcate harmonics. Thus, an oscillation system which is described as a second order ordinary differential equation, can be expressed as fundamental differential equation with fundamental harmonics and incremental differential equation with derived harmonics. The 1/3 subharmonic solution of an elliptical sandwich plate is investigated by using the methods of SIHB. The SIHB method is compared with the numerical integration method. Finally, asymptotical stability of the 1/3 subharmonic oscillations is inspected.

Free vibration of functionally graded sandwich plates in thermal environments

This paper presents an analytical solution for the free vibration of functionally graded material(FGM)sandwich plates in a thermal environment.An equivalentsingle‐layer(ESL)plate theory with four variables is used to obtain the solution.Two types of sandwich plates are examined in this study:one with FGM face sheets and a homogeneous core and the other with an FGM core and homogeneous face sheets.The governing equations of motion are derived based on Hamilton's principle and then solved using the Navier method.The results of natural frequencies of simply supported FGM sandwich plates are compared with the available solutions in the literature.The effects of volume fraction distribution,geometrical parameters,and temperature increments on the free vibration characteristics are discussed in detail.

Higher-order vibration of thick composite and sandwich plates based on an alternative higher-order model

The transverse stretching vibration of thick sandwich plates,which is attributed to largely different stiffness at the adjacent layers,is a challenging issue,and efficient approach for such issue is less reported in the published literature.Thus,natural frequencies corresponding to stretching vibration modes are generally neglected in engineering design,which might impact structural safety as frequencies of the exciting force are close to transverse stretching vibration frequencies.This paper proposes an alternative higher-order model for dynamic analysis corresponding to the higher-order vibration modes.The proposed model is classified in the displacement-based equivalent single-layer theory,as the number of displacement parameters in the proposed model is independent of the layer number.The continuity of displacements and transverse shear stresses can be fulfilled at the interfaces between the adjacent layers of structures.To demonstrate the capability of the proposed model,typical examples are analyzed by utilizing the proposed model,the threedimensional finite element method and the chosen higher-order models.By comparing with the exact three-dimensional elasticity solutions,it is found that the proposed model can yield more accurate natural frequencies corresponding to the higher-order displacement modes than the selected models.Moreover,the factors influencing reasonable prediction of the higher-order frequencies are investigated in detail,which can provide a reference for the accurate prediction of the higher-order frequencies.

Least Square Finite Element Model for Analysis of Multilayered Composite Plates under Arbitrary Boundary Conditions

Laminated composites are widely used in many engineering industries such as aircraft, spacecraft, boat hulls, racing car bodies, and storage tanks. We analyze the 3D deformations of a multilayered, linear elastic, anisotropic rectangular plate subjected to arbitrary boundary conditions on one edge and simply supported on other edge. The rectangular laminate consists of anisotropic and homogeneous laminae of arbitrary thicknesses. This study presents the elastic analysis of laminated composite plates subjected to sinusoidal mechanical loading under arbitrary boundary conditions. Least square finite element solutions for displacements and stresses are investigated using a mathematical model, called a state-space model, which allows us to simultaneously solve for these field variables in the composite structure’s domain and ensure that continuity conditions are satisfied at layer interfaces. The governing equations are derived from this model using a numerical technique called the least-squares finite element method (LSFEM). These LSFEMs seek to minimize the squares of the governing equations and the associated side conditions residuals over the computational domain. The model is comprised of layerwise variables such as displacements, out-of-plane stresses, and in- plane strains, treated as independent variables. Numerical results are presented to demonstrate the response of the laminated composite plates under various arbitrary boundary conditions using LSFEM and compared with the 3D elasticity solution available in the literature.

Static Analysis of Functionally Graded Sandwich Plates Using an Efficient and Simple Refined Theory

In this paper, a new displacement based high-order shear deformation theory is introduced for the static response of functionally graded sandwich plate. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory presented is variationally consistent, has strong similarity with classical plate theory in many aspects, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. Two common types of functionally graded sandwich plates, namely, the sandwich with fimctionally graded facesheet and homogeneous core and the sandwich with homogeneous facesheet and functionally graded core, are considered. Governing equations are derived from the principle of virtual displacements. The closed-form solution of a simply supported rectangular plate subjected to sinu- soidal loading has been obtained by using the Navier method. The validity of the present theory is investigated by comparing some of the present results with those of the classical, the first-order and the other higher-order theories. It can be concluded that the proposed theory is accurate and simple in solving the static bending behavior of functionally graded sandwich plates.

An advanced five-unknown higher-order theory for free vibration of composite and sandwich plates

Accurate prediction of dynamic characteristics is quite critical to understand the strength of layered structures.Nevertheless,the existing five-unknown higher-order theories encounter difficulties to forecast accurately the dynamic response of sandwich structures.Therefore,a new five-unknown higher-order theory is developed for free vibration analysis of composite and sandwich plates,which possesses the same degree of freedom as those of other five-unknown higherorder theories.The developed model can meet beforehand interlaminar continuity conditions and the free-surface conditions of transverse shear stresses.To assess capability of the proposed model,analytical solution for such composite structures with simply-supported conditions has been presented by employing Hamilton’s principle,which is utilized for analysis of mechanical behaviors of composite and sandwich plates.Compared with the three-dimensional(3 D)elasticity solutions,3 D finite element results and the results obtained from the chosen five-unknown higher-order models,the proposed model can yield accurately natural frequencies of composite and sandwich plates.Even for the thick plates,the higher-order frequencies calculated from the proposed model are in good agreement with the 3 D finite element results.By studying effect of the thickness/length ratios on natural frequencies,it is found that the proposed model is adaptable to predicting natural frequencies of the sandwich plates with the thickness/length ratios between 1/4 and 1/100.In addition,some factors influencing accuracy of five-unknown higher-order models have been investigated in detail.Finally,by means of numerical analysis and discussion,some conclusions have been drawn as well,which can serve as a reference for other investigators.

A novel finite element formulation for static bending analysis of functionally graded porous sandwich plates

This article aims to propose a finite element formulation based on Quasi-3D theory for the static bending analysis of functionally graded porous(FGP)sandwich plates.The FGP sandwich plates consist of three layers including the bottom skin of homogeneous metal,the top skin of fully ceramic and the FGP core layer with uneven porosity distribution.A quadrilateral(Q4)element with nine degrees of freedom(DOFs)per node is derived and employed in analyzing the static bending response of the plate under uniform and/or sinusoidally distributed loads.The accuracy of the present finite element formulation is verified by comparing the obtained numerical results with the published results in the literature.Then,some numerical examples are performed to examine the effects of the parameters including power-law index k and porosity coefficient on the static bending response of rectangular FGP sandwich plates.In addition,a problem with a complicated L-shape model is conducted to illustrate the superiority of the proposed finite element method.

Impact of aperture on dynamic response of sandwich plates with aluminium face-sheets and PMI core based on an alternative finite element formulation and experiments

Apertures generally exist in the sandwich structures attributing to mechanical connection and lightweight, which might induce failure of such structures. Thus, it is required to realize the impact of aperture on mechanical behaviors of sandwich structures. If transverse shear deformations are unable to be described accurately, the reasonable prediction of dynamic behaviors of the form-core sandwich plates with apertures will meet severe challenges due to a large difference of transverse shear modulus at the adjacent layers. Thereby, such issue is less studied by using the efficient models and experimental testing, so an alternative sinusoidal-type finite element formulation is to be proposed to precisely predict dynamic response of the form-core sandwich structures with apertures. The proposed finite element formulation can meet beforehand compatible conditions of transverse shear stresses at the interfaces of adjacent laminates. In order to appraise strictly capability of the proposed model, experimental tests on natural frequencies of three groups of specimens with different apertures have been carried out. Moreover, four specimens in each group are tested to reduce the testing errors, which is less reported in the published literature. In addition,three-dimensional Finite Element Method(3-D FEM) is also selected to account for the good performance of the present model. Finally, the impact of aperture diameter on the natural frequencies of the sandwich structures is both experimentally and numerically investigated, which can serve as a reference for other researchers.