Delamination in sandwich panels due to local water slamming loads

We study delamination in a sandwich panel due to transient finite plane strain elastic deformations caused by local water slamming loads and use the boundary element method to analyze motion of water and the finite element method to determine deformations of the panel. The cohesive zone model is used to study delamination initiation and propagation. The fluid is assumed to be incompressible and inviscid, and undergo irrotational motion. A layer-wise third order shear and normal deformable plate/shell theory is employed to simulate deformations of the panel by considering all geometric nonlinearities (i.e., all non-linear terms in strain–displacement relations) and taking the panel material to be St. Venant–Kirchhoff (i.e., the second Piola–Kirchhoff stress tensor is a linear function of the Green–St. Venant strain tensor). The Rayleigh damping is introduced to account for structural damping that reduces oscillations in the pressure acting on the panel/water interface. Results have been computed for water entry of (i) straight and circular sandwich panels made of Hookean materials with and without consideration of delamination failure, and (ii) flat sandwich panels made of the St. Venant–Kirchhoff materials. The face sheets and the core of sandwich panels are made, respectively, of fiber reinforced composites and soft materials. It is found that for the same entry speed (i) the peak pressure for a curved panel is less than that for a straight panel, (ii) the consideration of geometric nonlinearities significantly increases the peak hydrodynamic pressure, (iii) delamination occurs in mode-II, and (iv) the delamination reduces the hydroelastic pressure acting on the panel surface and hence alters deformations of the panel.     

The complex variable boundary element method for solving sandwich plate problems

The objective of this paper is to develop a new complex variable boundary element method for sandwich plates of Reissner's type and Hoff's type. The general solution of Helmhotz equation in complex field is given. Based on the Vekua's complex integral representation of the analytic function, the new boundary integral equations are formulated. The density function in the integral equation is determined directly by boundary element method. Some standard examples are presented, and the results of numerical solutions are accurate everywhere in the plate. The approach presented is only applicable for bounded simply connected regions. The project is supported by the National Science Foundation of China.     

Nonlinear analysis of skewed sandwich plates

Nonlinear static and dynamic behaviours of freely supported Rhombic sandwich plates have been studied following Banerjee's hypothesis. Numerical results for 0° skew angle are compared with other known results. Results for other skew angles are believed to be new.

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Sommario Si studia, seguendo l'ipotesi di Banerjee, il comportamento nonlineare statico e dinamico di piastre rombiche semplicemente appoggiate. Si presentano risultati numerici relativi a piastre rombiche e rettangolari: questi ultimi vengono paragonati a risultati già noti, mentre i primi si ritengono nuovi.

     

Postbuckling behavior of rectangular moderately thick plates and sandwich plates

ＰＯＳＴＢＵＣＫＬＩＮＧＢＥＨＡＶｉＯＲＯＦＲＥＣＴＡＮＧＵＬＡＲＭＯＤＥＲＡＴＥＬＹＴＨＩＣＫＰＬＡＴＥＳＡＮＤＳＡＮＤＷＩＣＨＰＬＡＴＥＳＣｈｅｎｇＺｈｅｎ－ｑｉａｎｇ（成振强）ＷａｎｇＸｉｕ－ｘｉ（王秀喜）ＨｕａｎｇＭａｏ－ｇｕａｎｇ（黄茂光）...     

Non-linear dynamics of the sandwich double circular plate system

Multi-frequency vibrations of a system of two isotropic circular plates interconnected by a visco-elastic layer that has non-linear characteristics are considered. The considered physical system should be of interest to many researches from mechanical and civil engineering. The first asymptotic approximation of the solutions describing stationary and no stationary behavior, in the regions around the two coupled resonances, is the principal result of the authors. A series of the amplitude-frequency and phase-frequency curves of the two frequency like vibration regimes are presented. That curves present the evolution of the first asymptotic approximation of solutions for different non-linear harmonics obtained by changing external excitation frequencies through discrete as well as continuous values. System of the partial differential equations of the transversal oscillations of the sandwich double circular plate system with visco-non-linear elastic layer, excited by external, distributed, along plate surfaces, excitation are derived and approximately solved for various initial conditions and external excitation properties. System of differential equations of the first order with respect to the amplitudes and the corresponding number of the phases in the first asymptotic averaged approximation are derived for different corresponding multi-frequency non-linear vibration regimes. These equations are analytically and numerically considered in the light of the stationary and no stationary resonant regimes, as well as the multi-non-linear free and forced mode mutual interactions, number of the resonant jumps.     

A new approach to large deflection analysis of heated sandwich plates

This paper represents non-linear analysis of sandwich plates under thermal loading in which a new approach is followed. Analysis of rectangular sandwich plates has been carried out in detail. Numerical results have been computed and compared with other known results.

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Sommario Questo lavoro illustra l'analisi non lineare delle piastre sandwich sotto carico termico seguendo un nuovo approccio. Si è svolta in dettaglio l'analisi delle piastre rettangolari calcolando valori numerici e paragonandoli con risultati precedentemente noti.

     

Thermoelastic bending of a sandwich ring plate on an elastic foundation

The thermomechanical bending of an elastic sandwich ring plate with light core on an elastic foundation is considered. To describe the kinematics of the plate that is asymmetric across the thickness, broken-normal hypotheses are accepted. The foundation reaction is described by Winkler's model. A system of equilibrium equations is derived and solved for displacements. Numerical results for a sandwich ring plate in a temperature field are presented Translated from Prikladnaya Mekhanika, Vol. 44, No. 9, pp. 94–103, September 2008.     

Thermoelastic bending of a sandwich plate on a deformable foundation

The thermoelastic bending of a circular light-core sandwich plate on a deformable foundation is examined. To describe the kinematics of the plate with asymmetric thickness, the hypothesis of broken normal is adopted. The reaction of the foundation is described by Winkler’s model. The thermomechanical load is local and symmetric. The system of equilibrium equations is derived and solved exactly. Numerical results for three-layer metal-polymer plate are presented __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 2, pp. 96–103, February 2006.     

A blast-tolerant sandwich plate design with a polyurea interlayer

This paper presents a study of both conventional and modified sandwich plate designs subjected to blast loads. The conventional sandwich Design (1) consists of thin outer (loaded side) and inner facesheets made of fibrous laminates, separated by a layer of structural foam core. In the modified Design (2), a thin polyurea interlayer is inserted between the outer facesheet and the foam core. Comparisons of the two designs are made during a long time period of 5.0 ms, initiated by a pressure impulse lasting 0.05 ms applied to a single span of a continuous plate. In the initial response period the overall deflections are limited and significant foam core crushing is caused in the conventional design by the incident compression wave. This type of damage is much reduced in the modified design, by stiffening of the polyurea interlayer under shock compression, which provides support to the outer facesheet and alters propagation of stress waves into the foam core. This benefits the long term, bending response and leads to significant reductions in facesheet strains and overall deflection. The total kinetic energy of the modified sandwich plate is much lower than that of a conventionally designed plate, and so is the stored and dissipated strain energy. Similar reductions are found when the conventional and the enhanced sandwich plates have equal overall thickness or equal total mass.     

Edge effects in a sandwich plate: a plane problem

Edge effects in a rectangular sandwich plate with isotropic components are studied. The mathematical model is represented by the homogeneous equations of linear elasticity, which is indicative of an approximate approach in edge-effect theory. The initial equations are reduced to inhomogeneous ones and an exact problem is formulated. Approximate solutions are found by the mesh method. Discrete problems are based on the concept of base scheme. The mesh equations are written in an explicit form and then solved using a computation optimization procedure. As an example, edge-effect zones in a real composite are analyzed.__________Translated from Prikladnaya Mekhanika, Vol. 40, No. 12, pp. 124–133, December 2004.     

Flexoelectric vibration analysis of nanocomposite sandwich plates

Abstract

In the present study, free vibration of sandwich flexoelectric plates resting on Pasternak foundation is investigated. The top and bottom layers are under applied voltage based on flexoelectricity considerations and core is a nanocomposite plate where reinforced by carbon nanotubes. Based on first-order shear deformation theory, flexoelectricity considerations and Hamilton’s principle, the governing equations are derived for the first time. Navier’s method is used to solve the governing equations analytically in the case of simply supported sandwich plate. Finally, the effects of different parameters are discussed in details. It is found when thickness of flexoelectric face sheets increase, the frequency of nano-sandwich plate decrease. The results of this study can be useful in design and manufacturing of flexoelectric systems as sensor and actuator.     

基于双曲面蜂窝夹层结构等效模型的研究及数值分析

蜂窝夹层结构在轻量化设计领域一直备受关注,相关的理论研究也日趋完善.然而,很多研究主要集中在平面蜂窝夹层结构上,而对于曲面结构的相关研究甚少.本文对双曲面蜂窝夹芯进行了力学分析,建立了曲面蜂窝夹层板的等效力学模型,同时建立了双曲面蜂窝夹层板详细模型和基于三明治夹层板理论以及曲面夹层板理论的等效模型,最后通过有限元方法对...     

Deflection of sandwich plates in terms of corresponding Kirchhoff plate solutions

Summary This study presents exact relationships between the deflections of isotropic sandwich plates and their corresponding Kirchhoff plates. The governing equilibrium equations for the sandwich plates are derived on the basis of the Reissner-Mindlin shear deformation plate theory. The considered plates are either (i) simply supported, of general polygonal shape and under any transverse loading condition or (ii) simply supported and clamped circular plates under axisymmetric loading. As the relationships are exact under the assumptions used in the plate theories, one may obtain exact deflection solutions of sandwich plates if the Kirchhoff plate solutions are exact. The relationships should also be useful for the development of approximate formulas for plates with other shapes, boundary and loading conditions, and may serve to check numerical deflection values computed from sandwich plate analysis software.     

Delamination of laminated composite plates by p-convergent partial discrete-layer elements with VCCT

The simulation of the delamination process in laminated composite plates is quite complex and requires advanced finite element modeling techniques. Failure analysis tools must be able to predict initiation, size and propagation of delamination process. This paper presents the p-convergent partial discrete-layer elements with the virtual crack closure technique (VCCT) for the delamination analysis of laminated composite plates. The proposed element can be formulated by the suitable dimensional reduction from three-dimensional solid to two-dimensional plate. It is assumed that the piecewise linear variation of in-plane displacements and the constant value of out-of-plane displacements across the thickness. The higher-order approximation based on integrals of Legendre polynomials is used to define displacement fields. The three-dimensional VCCT is also slightly modified to incorporate with the proposed elements to estimate the energy release rate. The initiation of delamination occurs when the energy release rate for a displacement increment is same as the critical energy release rate corresponding to fracture toughness. The approach is to use a fracture mechanics criterion, but to avoid the complex moving mesh technique. At first, the validation and characteristic of the proposed elements are investigated on isotropic plates and orthotropic laminated plates, compared with referenced values. Then for fracture analysis, the efficiency of proposed approach is demonstrated with the help of additionally two problems such as the double-cantilever-beam test and the orthotropic laminated square plate with interior delamination.     

Nonlinear vibration of circular sandwich plate under the uniformed load

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四边简支正交各向异性蜂窝型夹层板固有频率计算

该文以四边简支的方形蜂窝矩形夹层板为例,在经典夹层板理论的基础上,运用离散结构形式的运动控制方程和线性微分算子的可交换性,给出了一种把具有蜂窝型夹心的夹层板的包含三个广义位移的控制方程组化为,仅包含一个广义位移函数的单一方程的简单方法,并给出了四边简支蜂窝型夹层板的固有频率的精确解。研究结果对蜂窝夹层板的结构设计和工程应用具有指导意义。     

复合材料Ⅰ型层间断裂韧性GIC和初始裂纹长度

从经典梁理论和弹性基础上的正交各向异性梁理论出发，分析了梁的弯曲剪切效应和弹性基础对用双悬臂梁试件测得的复合材料层合板Ⅰ型层间断裂韧性Ｇ＿（ＩＣ）的影响，发现当试件的初始裂纹长度较短时，剪切效应和弹性基础对Ｇ＿（ＩＣ）的影响是显著的，建议将初始裂纹长度取５０毫米。实验结果表明，初始裂纹长度由２０毫米增加到５０毫米时，测得的Ｇ＿（ＩＣ）值的离散系数降低２０％～４０％，数据趋于稳定，分散性减小。     

黏弹夹芯板的有限元建模及实验研究

从有限元分析和数值模拟及实验验证的角度研究了黏弹夹芯板的频率依赖振动特性。夹芯板中间层为黏弹性材料,其刚度和阻尼的频率依赖性行为直接影响系统的模态频率和阻尼,并导致振动模式求解的复杂化。采用三阶七参数Biot模型描述黏弹性材料频率相关的黏弹性行为。开发了三层四节点28自由度的夹芯板单元,基于经典板理论和哈密顿原理建立了黏弹夹芯板的有限元动力学方程。通过引入辅助耗散坐标,将Biot模型和黏弹夹芯板的有限元动力学模型结合起来,并将其转化为常规二阶线性系统形式,极大简化了求解非线性振动特性的过程。对一边固定、另三边自由的黏弹夹芯板进行了前三阶固有频率和损耗因子的预测,并与实验结果对比。数值模拟结果和实验结果吻合良好,说明所提有限元方法是正确有效的。     

UNCONVENTIONAL HAMILTON-TYPE VARIATIONAL PRINCIPLES FOR DYNAMICS OF REISSNER SANDWICH PLATE

According to the basic idea of classical yin-yang complementarity and modern dual-complementarity,in a simple and unified way proposed by Luo(1987),some uncon- ventional Hamilton-type variational principles for dynamics of Reissner sandwich plate can be established systematically.The unconventional Hamilton-type variation principle can fully characterize the initial-boundary-value problem of this dynamics.In this pa- per,an important integral relation is given,which can be considered as the generalized principle of virtual work in mechanics.Based on this relation,it is possible not only to obtain the principle of virtual work in dynamics of Reissner sandwich plate,but also to derive systematically the complementary functionals for five-field,two-field and one-field unconventional Hamilton-type variational principles by the generalized Legender trans- formations.Furthermore,with this approach,the intrinsic relationship among the various principles can be explained clearly.     

求解矩形夹层板在集中载荷下的稳定问题

在考虑了横向切应力和横向正应力对夹层板稳定影响的情况下,给出了矩形夹层板结构屈曲失稳的控制方程、基本解以及边界条件。应用功的互等定理求解了在均布载荷作用下的矩形夹层板的屈曲失稳问题。