A generalized global-local high-order theory for bending and vibration analyses of sandwich plates subjected to thermo-mechanical loads

Although the global higher-order shear deformation theories may predict the gross responses of the sandwich plates sufficiently accurate, their results may show considerable errors in predicting the local effects. Layerwise and mixed layerwise theories are computationally expensive and generally, the interlaminar transverse stresses continuity conditions are not enforced in the former category of theories. Majority of the available zigzag and global-local theories suffer from the point that the transverse normal stress continuity that influences the transverse deformation significantly, especially in sandwich plates with soft-cores, is not satisfied at the layer interfaces.In the present paper, a generalized global-local theory that guarantees the continuity condition of all of the displacement and transverse stress components and considers the transverse flexibility under thermo-mechanical loads is introduced. One of the advantages of the present theory is that the number of unknown parameters is independent of the number of the layers. Furthermore, all stress components are considered in the formulations. Therefore, in contrast to the available works, the theory may be used for sandwich plates with stiff or soft cores. In contrast to the available global-local formulations, the present formulation is developed in a compact matrix form that makes it more desirable for computerized solutions. The present theory may be considered as a generalized layerwise theory with an optimized computational time. Compatible quadrilateral Hermitian elements are employed to further enhance the accuracy of the results. Validity, advantages, and efficiency of the present theory are investigated for different local and global behaviors of the layered composite and sandwich plates. Comparison of the present results with those of the three-dimensional theory of elasticity and the available plate theories confirms the efficiency and accuracy of the proposed theory. Results reveal that the global theories (e.g. the higher-order shear deformation theories) may encounter serious accuracy problems even in predicting the gross responses of the sandwich plates.     

Polyharmonic (thin-plate) splines in the analysis of composite plates

In the present study a layerwise theory for composite and sandwich laminated plates is discretized by polyharmonic (thin-plates) splines. A composite and a sandwich plate examples are presented and discussed. The combination of adequate shear deformation theory and thin-plate splines allows a very accurate prediction of displacements and stresses.     

Free-edge stresses in general composite laminates

In the present study, by starting from the reduced form of elasticity displacement field for a long flat laminate, an analytical method is developed in order to accurately calculate the interlaminar stresses near the free edges of generally laminated composite plates under extension. The constant parameter appearing in the reduced displacement field, which describes the global rotational deformation of a laminate, is appropriately obtained by employing an improved first-order shear deformation theory. The accuracy and effectiveness of the proposed first-order theory are verified by means of comparison with the results of Reddy's layerwise theory as a three-dimensional benchmark. Reddy's layerwise theory is then utilized for analytical and numerical investigations of the boundary-layer stresses within arbitrarily laminated composite plates. Various numerical examples are presented for the interlaminar normal and shear stresses along the interfaces and through the thickness of laminates in the vicinity of the free edges. The effects of end conditions of laminates, fibers orientation angles as well as the stacking sequences of the layers within laminates, and geometric parameters on the boundary-layer stresses are presented and discussed.     

基于等效理论的多夹心层蜂窝板模态分析

研究蜂窝板的三明治等效理论,应用该等效理论对蜂窝板夹芯进行等效计算得其等效参数,建立多夹心层蜂窝板的有限元模型,完成不同算例在不同边界条件下的模态分析,解决了通用有限元程序如NASTRAN等不能直接计算蜂窝板的动、静力学性能问题.将计算结果与解析解对比,说明等效方法是合理的,适用于多夹心层蜂窝板结构的有限元分析.     

Static electromechanical response of smart composite/sandwich plates using an efficient finite element with physical and electric nodes

An efficient quadrilateral element, recently developed by the authors, based on an improved zigzag theory is assessed for the static electromechanical response of hybrid plates with electroded piezoelectric sensors and actuators. The theory accounts for the transverse normal strain due to the electric field in the approximation of deflection. The electric potential is approximated as layerwise quadratic across the thickness. By introducing an electric node in the element for the electric potentials of the electroded piezoelectric surfaces, the equipotential condition of such surfaces is modelled very efficiently. The electric potential degrees of freedom (DOF) corresponding to the quadratic component of the electric potential distribution are associated with the four physical nodes to allow for the inplane electric field induced due to direct piezoelectric effect. The requirement of C¹ continuity of interpolation functions of the deflection is circumvented by employing the improved discrete Kirchhoff constraint technique. The finite element (FE) formulation is validated by comparing the results with other available results in the literature. Comparison of the present results for static response of a variety of piezoelectric bimorph, hybrid composite and sandwich plates, with 3D analytical and FE solutions and those of other available elements establishes that the present element is accurate, robust and computationally efficient.     

Interlaminar stress analysis of general composite laminates

In this study, based on the reduced from of elasticity displacement field for a long laminate, an analytical method is established to exactly obtain the interlaminar stresses near the free edges of generally laminated composite plates under the extension and bending. The constant parameters, which describe the global deformation of a laminate, are properly computed by means of the improved first-order shear deformation theory. Reddy's layerwise theory is subsequently utilized for analytical and numerical examinations of the boundary layer stresses within arbitrary laminated composite plates. A variety of numerical results are obtained for the interlaminar normal and shear stresses along the interfaces and through the thickness of laminates near the free edges. Finally the effects of end conditions of laminates on the boundary-layer stress are examined.     

Thermomechanical buckling of laminated composite and sandwich plates using global–local higher order theory

In this paper, a global–local higher order theory has been used to study buckling response of the laminated composite and sandwich plates subjected to thermal/mechanical compressive loads. The present global–local theory satisfies the free surface conditions and the geometric and stress continuity conditions at interfaces, and the number of unknowns is independent of the layer numbers of the laminate. Based on this higher-order theory, a refined three-noded triangular element satisfying C¹ weak-continuity conditions has been also proposed. The present theory not only predicts accurately the buckling response of general laminated composite plates but also calculates the critical buckling loads of the soft-core sandwich plates. However, numerical results show that the global higher-order theories as well as first order theories encounter some difficulties and overestimate the critical buckling loads for the sandwich plates with a soft core.     

约束阻尼板的主被动一体化振动控制

基于虚功原理,提出了一种新的建立主动约束阻尼板动力学模型的方法。该方法采用层合理论推导出约束阻尼板结构的动力方程,用GHM(Golla Hughes McTavish)方法引入辅助的耗散坐标,来描述粘弹性材料随频率变化的特性,并采用LQR方法控制结构的振动。其有效性通过算例进行了验证。同传统的有限元建模理论比较,采用层合理论,减少了结构自由度,并且具有良好的计算精度。     

Metal sandwich plates optimized for pressure impulses

Survival of a plate against an intense, short duration impulsive loading requires the circumvention of failure modes, including those associated with excessive overall deflection and shear-off at supports and webs. All-metal sandwich plates have distinct advantages over comparable weight monolithic plates, especially for intense water loadings. A recently developed mechanics of dynamically loaded sandwich plates by N. A. Fleck and V. S. Deshpande is extended and modified to address the problem of the minimum weight design of plates of given span that must sustain a uniformly distributed impulsive wave in air or water environments. Requirements for core crushing strength and energy absorption are discussed, as are conditions governing shear-off of the face sheet. Dimensionless parameters governing optimal designs are identified. Specific results are presented for plates with square honeycomb cores outlining trends for the best performance that can be achieved and the optimal distribution of mass between faces and core. Optimally designed sandwich plates can sustain water shocks that are two to three times as large monolithic plates of the same mass and material. The model is used to discuss a number of issues relevant to the design of effective metal sandwich plates, including differing requirements for air and water environments, face sheet shear-off resistance, the role of core strength, and the relation between small-scale tests and full-scale behavior.     

Modified stiffness formulation of unbalanced anisotropic sandwich plates

An approximate formulation is presented for the analysis of sandwich plates consisting of an orthotropic core and two unequal thickness anisotropic face plates. The method uncouples the membrane and bending actions, thereby significantly reducing the effort involved in accurately predicting displacements and stresses. Defining modified stiffnesses, the formulation is valid for relatively thick anisotropic laminated face plates and can be combined with a variety of analysis techniques. Using a series solution, results are generated herein for simply supported sandwich plates with unbalanced cross-ply and angle-ply faces.     

2A12铝合金圆波纹夹芯板抗平头弹冲击特性的试验研究

为研究铝合金圆波纹夹芯板对平头弹体的抗冲击性能,通过一级气炮系统开展弹体冲击铝合金圆波纹夹芯板以及等面密度单层均质板的试验.基于冲击试验数据,分析圆波纹夹芯板对弹体冲击的防护性能、失效模式和能量吸收情况,并与单层板进行对比,以获得两种靶板抗冲击性能的差异及原因.研究结果表明:弹体冲击圆波纹夹芯板的弹道极限速度低于单层板...     

铝褶皱夹层板的抗低速冲击性能

通过有限元方法对比研究了两种常见提高铝褶皱夹层板抗冲击特性的方法。增大面板厚度和芯层壁厚均可提高夹层板的抗冲击性能,而增大芯层壁厚可使结构的吸能特性和吸能效率更优。在实际应用中,夹层板受到的外来冲击是随机的,因此对夹层板不同角度冲击的损伤进行了仿真分析。发现随着冲击角度的增大,夹层板损伤减轻,褶皱芯层的损伤程度逐渐小于上面板,夹层板总体吸能降低。     

Maximizing the fundamental frequency of laminated cylindrical panels using layerwise optimization

A method of analysis is presented for determining the free vibration frequencies of cylindrically curved laminated panels under general edge conditions, and is implemented in a layerwise optimization (LO) scheme to determine the optimum fiber orientation angles for the maximum fundamental frequency. Based on the classical lamination theory applicable to thin panels, a method of Ritz is used to derive a frequency equation wherein the displacement functions are modified to accommodate arbitrary sets of edge conditions for both in-plane and out-of-plane motions. The LO approach, a recently developed scheme for laminated plates, is extended for the first time to the optimum design of curved panels. In a number of numerical examples, the accuracy of the analysis and the effectiveness of the LO approach are demonstrated.     

A new hyperbolic shear deformation theory for buckling and vibration of functionally graded sandwich plate

A new hyperbolic shear deformation theory taking into account transverse shear deformation effects is presented for the buckling and free vibration analysis of thick functionally graded sandwich plates. Unlike any other theory, the theory presented gives rise to only four governing equations. Number of unknown functions involved is only four, as against five in case of simple shear deformation theories of Mindlin and Reissner (first shear deformation theory). The plate properties are assumed to be varied through the thickness following a simple power law distribution in terms of volume fraction of material constituents. The theory presented is variationally consistent, 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. Equations of motion are derived from Hamilton's principle. The closed-form solutions of functionally graded sandwich plates are obtained using the Navier solution. The results obtained for plate with various thickness ratios using the theory are not only substantially more accurate than those obtained using the classical plate theory, but are almost comparable to those obtained using higher order theories with more number of unknown functions.     

铝合金三角形波纹夹芯板对平头弹抗冲击特性数值模拟研究

为研究铝合金三角形波纹夹芯板对平头弹体的抗冲击性能及损伤特性,利用有限元软件ABAQUS/Explicit建立弹体冲击靶板的数值模拟模型,并结合实验验证了模型及其参数的有效性。基于数值计算结果,分析了三角形波纹夹芯板几何结构对其防护性能、失效模式和能量吸收的影响规律及机理,并与等面密度单层板进行对比分析,研究结果表明,靶体几何结构对其抗冲击性能存在影响,三角形波纹夹芯板抗冲击性能低于单层板抗冲击性能。此外,增加芯体拓扑结构夹角能显著提高三角形波纹夹芯板的抗冲击性能,并且靶板几何形状会对其失效模式及耗能特性存在影响。     

Nonlinear flexural vibration of rectangular moderately thick plates and sandwich plates

Nonlinear flexural vibration is investigated for rectangular Reissner moderately thick plates and sandwich plates. The fundamental equations and boundary conditions are expressed in unified dimensionless form for rectangular moderately thick plates and sandwich plates. Highly accurate solutions of series form with many different movable and immovable boundary conditions, especially with unsymmetrical boundary conditions, are obtained by means of the method of harmonic balance and by developing a new technique of mixed Fourier series in nonlinear analysis. The nonlinear partial differential equations are reduced to an infinite set of simultaneous nonlinear algebraic equations, which are truncated in numerical computations. Solutions of the nonlinear fundamental frequency of rectangular plates are obtained by iteration. The multimode approach includes not only the influences of transverse shearing deformation and rotatory inertia, but also the coupling effect of vibrating modes on the nonlinear fundamental frequency. The present solutions are satisfactory in comparison with other available results.     

Buckling of multi-layer sandwich plates by the finite strip method

This paper presents a finite strip method for the stability analysis of rectangular multi-layer sandwich plates. The method permits freedom of in-plane displacements for all the stiff layers, thus excludes the assumption of common shear angle for all cores as adopted in some previous works. Numerical examples of various multi-layer sandwich plates with different boundary conditions and under different edge loadings are included.     

Analysis of sandwich plates with unbalanced cross-ply faces

The analysis of rectangular sandwich plates constructed of an orthotropic core and unbalanced cross-ply face plates is presented. A double Fourier series approach is used for simply supported sandwich plates under lateral loads. Results are compared to the corresponding sandwich plate results with orthotropic faces. The results indicate that the effect of bending-membrane coupling depends mainly upon the relative thicknesses of the core and faces; other factors include the shear stiffnesses of the core, the degree of anisotropy of the individual plies, the total number and lay-up of plies in the faces and the aspect ratio of the plate.     

Buckling of laminated sandwich plates subjected to partial edge compression

The buckling characteristics of sandwich plates having laminated stiff layers are studied for different types of partial edge loadings using a refined plate theory. With this plate theory, the through thickness variation of transverse shear stresses is represented by piecewise parabolic functions where the continuity of these stresses is satisfied at the layer interfaces by taking jumps in the transverse shear strains at the interfaces. The transverse shear stresses free condition at the plate top and bottom surfaces is also satisfied. It is quite interesting to note that this plate model having all these refined features requires unknown parameters only at the reference plane. To have a generality in the present analysis, finite element technique is adopted and it is carried out with newly developed triangular element, as existing finite elements cannot accommodate this plate model. So far, no solution exists in the literature for the problem of sandwich plate subjected to partial edge loading. The present analysis is first validated for the case of an isotropic plate subjected to partial edge compression and then it is extended to analyze sandwich plates. Few results are presented.     

Analytical models of sandwich plates with piezoelectric strip-stiffeners

A theory of sandwich plates with composite-material facings and piezoelectric strip-stiffeners bonded to the surface or embedded in the facings is developed. The stiffeners bonded to the surfaces are modeled using either the plane stress assumption or a first-order shear deformable theory. The former approach is appropriate if the stiffeners represent thin strips, while the latter method can be used in the case where the stiffeners are relatively deep. The stiffeners embedded in the facings in the form of piezoelectric strips are considered using the plane stress assumption.