Nonlinear Viscoelastic Response of Unidirectional Polymeric Laminated Composite Plates Under Bending Loads

Nonlinear bending analysis of polymeric laminated composite plate is examined considering material nonlinearity for viscoelastic matrix material through a Micro–macro approach. The micromechanical Simplified Unit Cell Method (SUCM) in three-dimensional closed-form solution is used for the overall behavior of the unidirectional composite in any combination of loading conditions. The elastic fibers are transversely isotropic where Schapery single integral equation in multiaxial stress state describes the matrix material by recursive-iterative formulation. The finite difference Dynamic Relaxation (DR) method is utilized to study the bending behavior of Mindlin annular sector plate including geometric nonlinearity under uniform lateral pressure with clamped and hinged edge constraints. The unsymmetrical laminated plate deflection is predicted for different thicknesses and also various pressures in different time steps and they are compared with elastic finite element results. As a main objective, the deflection results of viscoelastic laminated sector plate are obtained for various fiber volume fractions in the composite system.     

Multiscale analysis of laminated plates with integrated piezoelectric fiber composite actuators

This study is concerned with the detailed analysis of fiber-reinforced composite plates with integrated piezoceramic fiber composite actuators. A multiscale framework based on the asymptotic expansion homogenization method is used to couple the microscale and macroscale field variables. The microscale fluctuations in the mechanical displacement and electric potential are related to the macroscale deformation and electric fields through 36 distinct characteristic functions. The local mechanical and charge equilibrium equations yield a system of partial differential equations for the characteristic functions that are solved using the finite element method. The homogenized electroelastic properties of a representative material element are computed using the characteristic functions and the material properties of the fiber and matrix. The three-dimensional macroscopic equilibrium equations for a laminated piezoelectric plate are solved analytically using the Eshelby-Stroh formalism. The formulation admits different boundary conditions at the edges and is applicable to thick and thin laminated plates. The microscale stresses and electric displacement in the fibers and matrix are computed from the macroscale fields through interscale transfer operators. The multiscale analysis procedure is illustrated using two model problems. In the first model problem, a simply-supported sandwich plate consisting of a piezoceramic fiber composite shear actuator embedded between two graphite/polymer layers is studied. The second model problem concerns a cantilever graphite/polymer substrate with segmented piezoceramic fiber composite extension actuators attached to its top and bottom surfaces. Results are presented for the homogenized material properties, macroscale deformation, macroscale average stresses and microscale stress distributions.     

Micro-Macro Analysis of Viscoelastic Unidirectional Laminated Composite Plates Using DR Method

The Dynamic Relaxation (DR) technique together with finite difference discritization is used to study the bending behavior of Mindlin composite plate including geometric nonlinearity. The overall behavior of the unidirectional composite is obtained from a three-dimensional (3D) micromechanical model, in any combination of normal and shear loading conditions, based on the assumptions of Simplified Unit Cell Method (SUCM). The composite system consists of nonlinear viscoelastic matrix reinforced by transversely isotropic elastic fibers. A recursive formulation for the hereditary integral of the Schapery viscoelastic constitutive equation in multiaxial stress state is used to model the nonlinear viscoelastic matrix material in the material level. The creep tests data is used for verification of the predicted response of the current approach. Under uniform lateral pressure, the laminated plate deformation with clamped and hinged edged constraints is predicted for various time steps.     

复合材料层合板力学性质分析及角铺设层优化设计

基于Kirchhoff经典理论,用样条有限元法以三次B样条函数构成的样条基对反对称多层角铺设层合板的三个独立位移进行插值,推导了复合材料层合板刚度阵,质量阵列式,阻尼阵列式,并由Lagrange方程导出了层合板的动力学方程,通过瑞利一李兹法建立了特征方程。分析了层合板的固有频率及不同层数和不同约束条件下的基频变化等力学特性,在Kirchhoff假设的基础上,对层合板的非线性弯曲的力学特性进行了探讨。基于样条有限元法和遗传算法进行复合材料层合板的角铺设层的优化设计,数值算列验证了算法的有效性。     

Reliability predictions of laminated composite plates with random system parameters

Reliability predictions of laminated composite plates with random system parameters subjected to transverse loads are performed using different methods. System parameters such as material properties, layer thicknesses, and lamina strengths of a laminated composite plate are treated as base-line random variables and an appropriate failure criterion is used to construct the limit state equation of the plate in the reliability analysis. Based on the statistics of the base-line random variables obtained from experiments, different methods, namely, Monte Carlo method, β method, and first-order second moment method, are used to calculate the reliability of the laminated composite plates. In the first-order second moment method, the stochastic finite element method is used to derive for the statistics of the first-ply failure load of the laminated composite plates from those of the base-line random variables. The reliability of the laminated plate is then computed using the theoretically determined statistics together with an assumed probability distribution function of the first-ply failure load. The feasibility and accuracy of the different methods are studied by means of the experimental data of centrally loaded laminated composite plates with different lay-ups. The suitability of several commonly used failure criteria for reliability analysis of laminated composite plates is also investigated by means of several examples.     

传递矩阵法分析复合材料层合板的传声损失

为了得到不同频率下正交各向异性复合材料层合板的传声损失,基于传递矩阵的方法,推导出层合板的传声损失计算公式。通过建立复合材料层合板的传声计算模型,研究了层合板铺设角度、板厚度和板密度等结构参数对层合板的传声损失影响。计算结果表明：复合材料的密度与传声损失之间没有明显的线性关系,而是随着频率的增加而上升;层合板的总厚度越大,传声损失也越大,而且各层之间厚度不同,也会引起传声损失的较大改变;层合板铺层角度越大,传声损失也越大。采用传递矩阵法能充分考虑复合材料层合板的铺设方式和铺层角度等因素的影响,利用层合板层间的速度和应力连续边界条件,准确的反应复合材料层合板隔声性能。     

Non-homogeneous response of cross-ply laminated elastic plates using a higher-order theory

A consistent formulation for the bending of cross-ply laminated composite plates that possess non-homogeneous elastic properties is presented. Based on a third-order shear deformation plate theory, the governing equations are obtained using the principle of virtual work. With the help of the small parameter method, a wide variety of results are presented for the symmetric and antisymmetric analysis of non-homogeneous rectangular laminated plates. The influence of non-homogeneity, lamination schemes, aspect ratio and material anisotropy on the deflections and stresses is investigated. The new results for non-homogeneous response of composite plates should serve as bench marks for future comparisons.     

On the response of MMC laminated plates to non-uniform temperature loading: the effect of temperature-dependent material properties

Thermal response of antisymmetrically laminated metal matrix composite (MMC) plates subjected to non-uniform temperature field is analysed. Temperature dependence of both elastic and viscoplastic properties of the metallic matrix is taken into account; this suggests that a non-uniformly heated plate should be considered as a non-homogeneous structure. A micro-to-macro approach is employed to establish the instantaneous thermo-inelastic constitutive law at each point of the plate and to perform the structural analysis.

Results are presented for simply-supported and clamped graphitealuminium plates. The effects of boundary conditions, lamination angle, length-to-thickness ratio and different types of spatial temperature distributions are illustrated. Comparisons with the results obtained using an approach that treats the effect of temperature-dependent material properties in a simplified manner are shown. Comparisons with the corresponding elastic solutions (which neglect the inelastic effects in the metallic matrix) are given.     

Thermal post-buckling and flutter characteristics of composite plates embedded with shape memory alloy fibers

It is investigated that the composite plate embedded with shape memory alloy (SMA) fibers is subject to the aerodynamic and thermal loading in the supersonic region. The nonlinear finite element equations based on the first-order shear deformation plate theory (FSDT) are formulated for the laminated composite plate embedded with SMA fibers (SMA composite plate). The von Karman strain–displacement relation is used to account for the large deflection. The incremental method considering the influence of the initial deflections and initial stresses is adopted for the temperature-dependent material properties of SMA fibers and composite matrix. The first-order piston theory is used for modeling aerodynamic loads. This study shows the effect of the SMA on the critical temperature, thermal post-buckling deflection, natural frequency and critical dynamic pressure of the SMA composite plate.     

Optimum stacking sequence design of laminated composite circular plates with curvilinear fibres by a layer-wise optimization method

The optimum stacking sequence design for the maximum fundamental frequency of symmetrically laminated composite circular plates with curvilinear fibres is investigated for the first time using a layer-wise optimization method. The design variables are two fibre orientation angles per layer. The fibre paths are constructed using the method of shifted paths. The first-order shear deformation plate theory and a curved square p-element are used to calculate the objective function. The blending function method is used to model accurately the geometry of the circular plate. The equations of motion are derived using Lagrange’s method. The numerical results are validated by means of a convergence test and comparison with published values for symmetrically laminated composite circular plates with rectilinear fibres. The material parameters, boundary conditions, number of layers and thickness are shown to influence the optimum solutions to different extents. The results should serve as a benchmark for optimum stacking sequences of symmetrically laminated composite circular plates with curvilinear fibres.     

对称层合板复合材料的屈曲变形解析

提出了如何利用2 元多项式位移函数来分析层合板复合材料的屈曲问题。在解析中同时 考虑到层合板的面外剪切变形。解析表明屈曲载荷在多项式项数大于20 以上时趋于稳定, 可得到 高精度的解。本文并对对称角铺设层合板进行了系统地数值解析, 明确了在各种边界拘束条件下 材料的工程弹性系数, 层合板长宽比, 铺层数, 层合角对屈曲载荷的影响, 从而以达到优化设计。同 时, 验证了本解析法对任意边界条件下的层合板的屈曲解析是非常有效的。      

Elastic response of a carbon nanotube fiber reinforced polymeric composite: A numerical and experimental study

Premature failure due to low mechanical properties in the transverse direction to the fiber constitutes a fundamental weakness of fiber reinforced polymeric composites. A solution to this problem is being addressed through the creation of nanoreinforced laminated composites where carbon nanotubes are grown on the surface of fiber filaments to improve the matrix-dominated composite properties. The carbon nanotubes increase the effective diameter of the fiber and provide a larger interface area for the polymeric matrix to wet the fiber. A study was conducted to numerically predict the elastic properties of the nanoreinforced composites. A multiscale modeling approach and the Finite Element Method were used to evaluate the effective mechanical properties of the nanoreinforced laminated composite. The cohesive zone approach was used to model the interface between the nanotubes and the polymer matrix. The elastic properties of the nanoreinforced laminated composites including the elastic moduli, the shear modulus, and the Poisson’s ratios were predicted and correlated with iso-strain and iso-stress models. An experimental program was also conducted to determine the elastic moduli of the nanoreinforced laminated composite and correlate them with the numerical values.     

Active aeroelastic flutter analysis and vibration control of supersonic composite laminated plate

The active aeroelastic flutter analysis and vibration control at the flutter bounds of the supersonic composite laminated plates with the piezoelectric patches are studied. The piezoelectric patches are bonded on the top and bottom surfaces of the composite laminated plate to act as the sensor and actuator so that the active aeroelastic flutter suppression and vibration control for the supersonic laminated plate can be conducted. The unsteady aerodynamic pressure in supersonic flow is computed by using the supersonic piston theory. Hamilton’s principle with the assumed mode method is used to develop the governing equation of the structural system. The controller is designed by the velocity feedback and proportional feedback control algorithm, and the active damping and stiffness are obtained. The solutions for the complex eigenvalue problem are obtained by using the generalized eigenvalue methodology. The natural frequencies and damping ratios are also gotten. The aeroelastic flutter bounds of the supersonic composite laminated plate are calculated to investigate the characteristics of the aeroelastic flutter. The impulse responses of the structural system are calculated by using the Houbolt numerical algorithm to study the active aeroelastic vibration control. The influences of ply angle of the laminated plate and the control method on the characteristic of flutter and active vibration control are analyzed. From the numerical results it is observed that the aeroelastic flutter characteristics of the supersonic composite laminated plate can be improved and that the aeroelastic vibration response amplitudes can be reduced, especially at the flutter points, by the proportional feedback or the velocity feedback control algorithm using the piezoelectric actuator/sensor pairs. The effectiveness of the flutter control by the two control algorithms is also compared. The results of this study are of great significance to the flutter analysis and aeroelastic design of the aircraft.     

Bending Analysis of Classical Symmetric Laminated Composite Plates by the Strip Element Method

A new formulation of strip element method based on classical laminated plate theory is derived for the bending analysis of laminated composite plates. In this method, an infinite-length plate is first considered and is discretized into a set of strip elements in the width direction. The principle of minimum potential energy is applied to obtain the ordinary differential equations, which are functions of only the coordinate in the length direction. These differential equations can then be solved analytically. The boundary conditions on the length coordinate direction are finally used to determine the deflection distribution in the plate. The strip element solutions are presented for a rectangular laminated composite plate with various boundary conditions and load cases. The solutions are compared with those of the Rayleigh-Ritz method, and very good agreement is obtained.     

A design of laminated composite plates using graded orthotropic fiber-reinforced composite plies

A new lamination scheme is proposed through the design of a graded orthotropic fiber-reinforced composite ply for achieving continuous variations of material properties along the thickness direction of laminated composite plates. First, a micro-structure of graded unidirectional fiber-reinforced composite ply is designed and its effective graded elastic properties are estimated using finite element procedure. Next, the new lamination scheme is demonstrated through the conversion of a conventional laminated composite plate (CLCP) into a conventional-graded laminated composite plate (CGLCP) utilizing presently designed graded orthotropic composite ply. The suitability of this conversion/proposed lamination scheme is substantiated through the bending analysis of both the plates (CLCP and CGLCP).     

双稳态复合材料层合结构的黏弹性模型

为探明双稳态复合材料层合结构在复杂环境条件下的应用,对双稳态复合材料层合结构的黏弹性行为进行了研究。首先,将纤维简化为弹性材料,考虑基底材料的黏弹性行为。然后,根据纤维和基底的材料属性,通过理论分析得到了双稳态复合材料层合结构的黏弹性材料属性;根据经典层合板理论、最小应变能原理和Maxwell黏弹性模型建立了双稳态复合材料层合结构的黏弹性模型,通过理论分析得到其第二稳态主曲率与扭曲率随加载时间和温度的变化关系。同时,利用有限元软件ABAQUS及其子程序UMAT建立了相应的有限元模型,研究了加载时间和温度对层合结构第二稳态性能的影响。理论与模拟结果均表明:层合结构第二稳态主曲率随加载时间的延长和温度的升高而增大;扭曲率随加载时间的延长而减小,一般情况下随温度的升高而增大,但在加载时间较长且温度较高时,可能会出现扭曲率随温度升高而减小的情况。理论计算结果与有限元模拟结果的比较显示两者吻合较好,可以通过有限元模拟对双稳态复合材料层合结构的黏弹性行为进行研究。      

Multi-pulse chaotic dynamics of non-autonomous nonlinear system for a laminated composite piezoelectric rectangular plate

The global bifurcations and multi-pulse chaotic dynamics of a simply supported laminated composite piezoelectric rectangular thin plate under combined parametric and transverse excitations are investigated in this paper for the first time. The formulas of the laminated composite piezoelectric rectangular plate are derived by using the von Karman-type equation, the Reddy’s third-order shear deformation plate theory and the Galerkin’s approach. The extended Melnikov method is improved to enable us to analyze directly the non-autonomous nonlinear dynamical system, which is applied to the non-autonomous governing equations of motion for the laminated composite piezoelectric rectangular thin plate. The results obtained here indicate that multi-pulse chaotic motions can occur in the laminated composite piezoelectric rectangular thin plate. Numerical simulation is also employed to find the multi-pulse chaotic motions of the laminated composite piezoelectric rectangular thin plate.     

Stochastic post buckling analysis of laminated composite cylindrical shell panel subjected to hygrothermomechanical loading

In this paper, the effect of random system properties on the post buckling load of geometrically nonlinear laminated composite cylindrical shell panel subjected to hygrothermomechanical loading is investigated. System parameters are assumed as independent random variables. The higher order shear deformation theory and von-Karman nonlinear kinematics are used for basic formulation. The elastic and hygrothermal properties of the composite material are considered to be dependent on temperature and moisture concentration using micromechanical approach. A direct iterative based C⁰ nonlinear finite element method in conjunction with first-order perturbation technique proposed by present author for the plate is extended for shell panel subjected to hygrothermomechanical loading to compute the second-order statistics (mean and variances) of laminated composite cylindrical shell panel. The effect of random system properties, plate geometry, stacking sequences, support conditions, fiber volume fractions and temperature and moisture distributions on hygrothermomechanical post-buckling load of the laminated cylindrical shell panel are presented. The performance of outlined stochastic approach has been validated by comparing the present results with those available in the literature and independent Monte Carlo simulation.     

层合板螺栓连接的渐进失效分析

以三维渐进损伤理论为基础,采用ANSYS的二次开发语言,建立了复合材料层合板螺栓连接模型,在拉伸栽荷下对含孔复合材料板进行数值失效模拟计算．分析各铺层的失效过程和失效形式特点,得到层合板的初始失效栽荷和最终失效栽荷,为复合材料含孔板强化结构的研究提供一定参考．     

抗破片侵彻钢/芳纶纤维叠层复合结构优化设计方法

针对抗破片侵彻用新型钢/芳纶纤维叠层复合结构优化设计,基于4 mm钢板+12 mm芳纶纤维叠层复合结构、5 mm钢板+10 mm芳纶纤维叠层复合结构抗7.5 g FSP型破片弹道极限速度试验分析,进行了同工况下破片侵彻叠层复合结构的数值仿真计算;在验证数值仿真模型基础上,开展了7.5 g与10.0 g破片对4 mm、5 mm钢板叠加6~16mm芳纶纤维板组合成复合结构侵彻数值仿真,获得了相应的弹道极限速度;根据试验现象和数值仿真结果进行了钢/芳纶纤维叠层复合结构抗破片侵彻机理分析;根据此类复合结构的防护特点,以结构最小面密度为目标函数,建立了适用一定破片质量和撞击速度范围的结构参数优化设计模型;采用所提方法进行了抗撞击速度为1100 m/s的10.0 g破片侵彻的钢/芳纶纤维复合结构实例设计,通过试验验证了优化设计方法的合理性和实用性。