C0 FE model based on HOZT for the analysis of laminated soft core skew sandwich plates: Bending and vibration

Bending and free vibration behaviour of laminated soft core skew sandwich plate with stiff laminate face sheets is investigated using a recently developed C₀ finite element (FE) model based on higher order zigzag theory (HOZT) in this paper. The in-plane displacement fields are assumed as a combination of a linear zigzag function with different slopes at each layer and a cubically varying function over the entire thickness. The out of plane displacement is considered to be quadratic within the core and constant in the face sheets. The plate theory ensures a shear stress-free condition at the top and bottom surfaces of the plate. Thus, the plate theory has all of the features required for accurate modelling of laminated skew sandwich plates. As very few element model based on this plate theory (HOZT) exist and they possess certain disadvantages, an attempt has been made to check the applicability of the refined element model. The nodal field variables are chosen in such a manner that there is no need to impose any penalty stiffness in the formulation. Refined C₀ finite element model has been utilized to study some interesting problems on static and free vibration analysis of laminated skew sandwich plates.     

Electro-dynamic analysis of smart nanoclay-reinforced plates with integrated piezoelectric layers

Integrating engineering structures with piezoelectric layers as actuator and/or sensor offers smart sandwich structures with controllable static and dynamic deflections. In this paper, a smart sandwich plate consisting of a light nanoclay-reinforced composite core and two piezoelectric face sheets is considered. The static and dynamic behaviors of the proposed smart plate are obtained using their governing coupled electro-mechanical system of equations. In order to facilitate the governing equations, a mesh-free method based on moving least square (MLS) shape function and first order shear deformation (FSDT) is developed and implemented. Two morphologies of intercalated stack and exfoliated nanoclay dispersions are considered in the distribution of the nanoclay into the polymeric matrix. The effects of morphology and volume fraction of the nanoclay, time-dependent loading, and essential boundary condition on the static and dynamic behavior of the smart piezoelectric-integrated nanocomposite plates are examined. In the dynamic analysis, resonance and amplitude modulation phenomena are studied. It is observed that the use of nanoclay, especially with exfoliated morphology, improves the static and the free vibration responses of the smart sandwich plates. Moreover, the frequency of the applied mechanical load has a significant effect on the electro-dynamic response of the proposed smart sandwich plates.     

Experimental characterization of dynamic properties of honeycomb sandwich joints and plates

In lots of lightweight applications, constructions are also made by honeycomb sandwiches but little is known about failure and dynamic behavior of sandwich plate connections. In this research, an experimental and simulation study of the mechanical and failure behavior of honeycomb sandwich plates and joints are performed. In detail, series of tensile test have been conducted under quasi static conditions and failure behavior and resistance of the specimens are investigated. The specimens are made by phenolic resin-impregnated aramid paper as core and two different layers of glass fiber reinforced plastic as face sheets in each side. In addition to the experimental tests, numerical simulation with finite element models are performed in Abaqus. Failure modes are investigated and finally a good agreement between test data and simulation results is achieved. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Free-edge effects in a cylindrical sandwich panel with a flexible core and laminated composite face sheets

In the present study, the static response of cylindrical sandwich panels with a flexible core is investigated. The face sheets are considered as composite laminates with a cross-ply lay-up and the core as a flexible elastic medium. The flexibility of the low-strength core leads to high stress concentrations in terms of peeling stresses between the face sheets and the core at edges of the sandwich panel. To take into account the compressibility of the core and to determine the free-edge stresses of sandwich structures accurately, the Reddy layerwise theory (LWT) is used in this paper. The paper outlines the mathematical formulation, along with a numerical study, of a cylindrical sandwich panel with two simply supported and two free edges under a transverse load. The formulation includes the derivation of field equations along with boundary conditions. A Levy-type solution procedure is performed to determine the distributions of stresses and strains. In the numerical study, first a comparison is made with results from the commercial finite-element software ANSYS to verify the LWT results. Finally, a parametric study is conducted, and the effect caused by varying different parameters, such as the radii of curvature and the core to face sheet thickness ratio, on the results are investigated. The results obtained demonstrate a good agreement between LWT and FEM solutions and show increasing interlaminar stresses in the free edge of the sandwich panel     

夹层圆柱壳在移动内压作用下的临界速度研究

基于夹层壳理论和三维弹性动力学理论,研究了无限长夹层圆柱壳在移动内压作用下的临界速度．首先,基于夹层壳理论,考虑夹芯的压缩和剪切变形以及面板的剪切变形,研究了轴对称简谐波在无限长夹层圆柱壳中的传播问题;其次,基于三维弹性动力学理论,将位移变量用Legendre正交多项式系表示,同时引入位置相关函数,将求解导波问题化为简单的特征值问题．利用这两种方法得到了最低模态的频散曲线,最小相速便是内压移动的临界速度．最后,用算例和数值模拟来验证方法的有效性．结果表明,两种理论得到临界速度吻合得较好;当波数较小时,两种理论得到的频散曲线吻合得很好,当k→∞时,夹层壳理论和弹性动力学理论得到的极限相速分别趋于面板和夹芯的剪切波波速．波数较小时,两种理论分析夹层圆柱壳的导波问题是有效的．数值模拟预测的临界速度与理论分析的结果吻合得很好．     

A Nonlinear Sandwich Shell Theory Accounting for Transverse Core Compressibility

The present study is concerned with an advanced theory of sandwich shells with transversely compressible core. The model is based on the standard Kirchhoff‐Love hypothesis for the face sheets and a third‐order displacement expansion for the core. Consistent equations of motion and boundary conditions are derived by means of Hamilton's variational principle. The model is applied to a postbuckling analysis of cylindrical shells under axial compression.     

Weight‐Reduction of Sandwich Structures by an Efficient Topology Optimization Technique

A heuristic algorithm for the weight minimization of sandwich structures by a specific kind of topology optimization is presented. The method employs a preexisting algorithm for the layerwise topology optimization of symmetric laminates under in‐plane loads and expands this method for the case of bending. During the optimization procedure the algorithm adds or subtracts material from the layers of the face sheets and the core of the sandwich plate in regions of high or low stresses respectively. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stress Singularities in Honeycomb Cores for Structural Sandwich Panels

The present study is concerned with stress singularities in the core and face sheet interface of structural sandwich panels caused by an incompatibility in the modes of deformation associated with the homogeneous face sheets and the cellular core. The singularities are studied in a closed form asymptotic analysis and in a pure numerical approach based on the finite element method. It is shown that the singularity is of the pure, non oscillatory power law type with variable order depending on the cell wall angle and the cell wall material.     

严格求解夹层圆柱壳在轴压下的轴对称失稳问题

本文在文献[1]的基础上,用严格的方法求解两端简支的夹层圆柱壳在均匀轴压下的轴对称失稳问题.内、外表层很薄弹性模量又大,按薄壳理论处理;夹心较厚弹性模量又相当小,横向剪切变形的影响必须考虑,在研究夹层壳的整体失稳尤其是局部失稳时,横向的拉伸和压缩变形也不可忽略,用数学弹性力学的方法处理.本文导得了可求解轴对称整体失稳和局部失稳临界载荷的超越方程,用数值计算的方法可算得临界载荷的最小值.对于整体失稳的情况,给出算例,与夹层壳理论的解作了比较.     

Stability of the Face Layer of Sandwich Structures with a Local Interlaminar Damage

The effect of a local interlaminar damage on the stability of the face layer of composite sandwich beams is investigated. Mathematical models are proposed for estimating the critical compressive stresses for two typical types of damage. Experimental and numerical data are obtained for two types of materials (with glass-fiber-reinforced plastics as face layers and Rohacell WF51 and Divinycell H60 foams as the core). The analytical results agree well with the experimental data.     

Refined stability theory for sandwich shells with transversally stiff core. 1. Nonlinear equilibrium equations

A refined version of geometrically nonlinear relationships is proposed for the static thermoelastic response of sandwich shells with face sheets made of composite or homogeneous materials and a transversally stiff core. This theory has primary importance for studying mixed forms of buckling of the bearing sheets, which are mainly realized in the zones of a momentary stress-deformed state of the shell on the whole. An iteration procedure was developed for construction of the model. In the first step, assuming that the core is transversally soft, expressions are derived for the components of the displacement vector after integration of the three-dimensional equilibrium equations. In the second step, the tangential stresses are determined assuming a transversally stiff core to obtain the in-plane stresses and highly accurate transverse normal stresses. The proposed model admits a formal changeover to the model of a shell with a transversely soft core.Center for the Study of Dynamics and Stability. A. N. Tupolev Kazan State Technical University, Kazan, Tatarstan, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 4, pp. 513–524, July–August, 1996.     

Design of axisymmetric sandwich plates for alternative loads

The minimal-weight design of sandwich plates whose rigidplastic face sheets obey the Tresca yield condition and which are subjected to two alternative loads is systematically determined by the method of stress variation. It is shown that, when the loads are unidirectional, the general solution for a certain class of edge conditions consists of five fundamentally different designs. The totality of optimal design solutions is depicted in the form of a design chart. A comprehensive example is presented to illustrate the method.This paper is based in part upon a dissertation submitted by the first author to The University of Iowa in partial fulfillment of requirements for the PhD Degree.     

Electro-thermo-mechanical vibration and stability analyses of double-bonded micro composite sandwich piezoelectric tubes conveying fluid flow

New sandwich panels and tubes have widely applications in nanotechnology such as transportation, naval, aerospace industries, micro and nanoelectromechanical systems and fluid storage. For example, carotid arteries play an important role to high blood rate control that they have a similar structure with flow conveying cylindrical shells. In the current study, stability and free vibration analyses of double-bonded micro composite sandwich piezoelectric tubes conveying fluid flow embedded in an orthotropic foundation under electro-thermo-mechanical loadings are presented. In fact, this work can be provided a valuable background for more research and further experimental investigation. It is assumed that the micro tubes are made of flexible material and smart piezoelectric composites reinforced by carbon nanotubes as core and face sheets, respectively. Energy method and Hamilton's principle are applied to derive the governing equations of motions based on Euler–Bernoulli beam model and using modified strain gradient theory. Moreover, generalized differential quadrature method is used to discretize and solve the governing equations of motions. Numerical results are investigated to predict the influences of length-to-radius, thickness of face sheets-to-thickness of core ratio, temperature changes, orthotropic elastic medium, Knudsen number, and carbon nanotubes volume fraction on the dimensionless natural frequencies and critical flow velocity of sandwich double-bonded piezoelectric micro composite tubes. The results of this article show that increasing the thickness ratio, volume fraction carbon nanotubes and orthotropic elastic constants lead to enhance the dimensionless natural frequency and stability of system, while decrease these parameters with increasing the temperature and length-to-radius ratio.     

Plane finite element for static and free vibration analysis of sandwich plates

Conclusions Triangular sandwich finite elements (MPLW30) with 30 DOF have been developed for the static and free vibration analysis of sandwich plates with thin faces and low core shear modules. The results of numerical examples presented here demonstrate the accuracy and suitability of the formulations for the analysis of sandwich plates with k_H > 25 and k_E > 200.Published in Mekhanika Kompozitnykh Materialov, Vol. 30, No. 2, pp 238–248, March–April, 1994.     

Stability and free vibration analyses of double-bonded micro composite sandwich cylindrical shells conveying fluid flow

In this study, based on Reddy cylindrical double-shell theory, the free vibration and stability analyses of double-bonded micro composite sandwich cylindrical shells reinforced by carbon nanotubes conveying fluid flow under magneto-thermo-mechanical loadings using modified couple stress theory are investigated. It is assumed that the cylindrical shells with foam core rested in an orthotropic elastic medium and the face sheets are made of composites with temperature-dependent material properties. Also, the Lorentz functions are applied to simulation of magnetic field in the thickness direction of each face sheets. Then, the governing equations of motions are obtained using Hamilton's principle. Moreover, the generalized differential quadrature method is used to discretize the equations of motions and solve them. There are a good agreement between the obtained results from this method and the previous studies. Numerical results are presented to predict the effects of size-dependent length scale parameter, third order shear deformation theory, magnetic intensity, length-to-radius and thickness ratios, Knudsen number, orthotropic foundation, temperature changes and carbon nanotubes volume fraction on the natural frequencies and critical flow velocity of cylindrical shells. Also, it is demonstrated that the magnetic intensity, temperature changes and carbon nanotubes volume fraction have important effects on the behavior of micro composite sandwich cylindrical shells. So that, increasing the magnetic intensity, volume fraction and Winkler spring constant lead to increase the dimensionless natural frequency and stability of micro shells, while this parameter reduce by increasing the temperature changes. It is noted that sandwich structures conveying fluid flow are used as sensors and actuators in smart devices and aerospace industries. Moreover, carotid arteries play an important role to high blood rate control that they have a similar structure with flow conveying cylindrical shells. In fact, the present study can be provided a valuable background for more research and further experimental investigation.     

Elastic impact of spheres on sandwich plates

An integro-differential equation for the elastic impact of spheres on soft core sandwich plates is analytically derived. The impact equation is numerically integrated and the displacement of the sandwich plate underneath the point of impact is calculated as a function of time. Fairly good agreement with experimental results obtained by the author was found. It is emphasized that, physically, the impact response of a sandwich plate is fundamentally different from the response of an isotropic plate.

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Zusammenfassung Die vorliegende Arbeit behandelt den elastischen Stoß von Kugeln auf Sandwichplatten mit weichem Kern. Eine Integro-Differentialgleichung für den Stoßprozeß wird analytisch hergeleitet und numerisch integriert. Die Auslenkung der Platte unter der Aufprallstelle wird als Funktion der Zeit berechnet; es ergibt sich eine befriedigende Übereinstimmung mit experimentellen Werten. -Im Vordergrund steht das Resultat, daß dünne isotrope Platten und Sandwichplatten grundsätzlich verschieden auf einen Stoß reagieren.

     

Accurate stress analysis of sandwich panels by the differential quadrature method

Sandwich structures are widely used in many engineering fields. It is possible but not easy for an engineering theory to recover all stresses accurately. In this paper, a modeling strategy is proposed to simplify the formulation. A classical sandwich panel is firstly divided into three parts, equations of the top and bottom face sheets are used as the boundary conditions of the two-dimensional core and then only the core needs to be analyzed by the differential quadrature method (DQM). In this way, both displacement and stress can be accurately obtained. Detailed formulations are worked out. Three boundary conditions and three types of loading, including the concentrated load regarded as a challenging problem for point discrete methods such as the DQM, are considered to investigate the effect of boundary conditions and loading on the distributions of displacement and stress. For verification, results are compared with theoretical solutions or/and numerical data. Presented data may be a reference for other investigators to develop more accurate engineering beam theory or new numerical method.     

Elastoplastic stability of sandwich plates with a light core

The elastoplastic stability of sandwich plates with a light core is theoretically investigated. Certain specific problems are considered.Tashkent Lenin State University. Translated from Mekhanika Polimerov, No. 3, pp. 568–571, May–June, 1971.     

Multi-dimensional deformation tests of sandwich plates

Sandwich-type plates are widely used in present technical structures. A variety of special sandwich theories and composite laminated plate theories (CLT, FSDT, HSDT) are available for calculating plate deflections. Since the problem of assessing these theories still exists, a new test apparatus for multilayered composite and sandwich plates was developed. Different types of sandwich plates were used in quasistatic multidimensional deformation tests. Deflections and thickness reductions are compared with the theoretical results obtained by sandwich theories, CLT-, FSDT-, HSDT-, and 3D-solutions.Submitted to the 10th International Conference on Mechanics of Composite Materials, Riga, April 20–23, 1998.Published in Mekhanika Kompozitnykh Materialov, Vol. 33, No. 5, pp. 612–625, September–October, 1997.     

夹层圆板大幅度振动的进一步研究

本文给出了具有滑动固定边界条件、并计及表板抗弯刚度的夹层圆板轴对称大幅度自由振动问题的解。在求解此问题时,使用了修正迭代法,并把本文结果与文[1]结果作了比较。