Hygrothermal effects on multilayered composite plates using a refined higher order theory

A four-node quadrilateral plate element based on the global–local higher order theory (GLHOT) is proposed to study the response of laminated composite plates due to a variation in temperature and moisture concentrations. C⁰$C^0$ and C¹$C^1$ continuities are required in the transverse displacement functions as the first and the second derivatives are involved in the computation of the strain components in GLHOT [Int J Mech Sci, 2007; 49:1276–1288]. In this paper, a displacement function satisfying C⁰$C^0$ continuity is constructed by using the refined element method, and the discrete Kirchhoff quadrilateral thin plate element DKQ is employed for satisfying the requirement of C¹$C^1$ continuity. The effects of temperature and moisture concentrations on the material properties and the hygrothermal response of multilayered plates are studied, in contrast to most of the previous investigations in which the material properties are assumed to be independent of temperature. Hygrothermal response due to a variation in temperature and moisture concentrations has been studied for different material types sensitive to changing hygrothermal environment conditions. Numerical results suggest that temperature-dependent material properties ought to be used in the analysis of laminated plates subjected to hygrothermal loads.     

压电复合材料正交层板的精确理论

基于一个六自由度的位移场和电势场, 建立了压电复合材料层板的控制方程。在简支边界条件下, 得到了正交矩形压电复合材料层板的解析解。该理论是一个等效单层理论, 控制方程的变量仅六个, 且不随层数变化, 使解的数学过程简洁。在该理论中, 决定精度的位移分布函数和电势分布函数由三维应力和静电平衡方程的特解来确定, 使之满足压电层板界面连续条件与板面力及电条件。算例验证了本文中等效单层理论的高精度。     

Analytical solutions using a higher-order refined theory for the static analysis of antisymmetric angle-ply composite and sandwich plates

Analytical formulations and solutions to the static analysis of simply supported anti-symmetric angle-ply composite and sandwich plates hitherto not reported in the literature based on a higher-order refined theory already reported in the literature are presented. The theoretical model presented herein incorporates laminate deformations, which account for the effect of transverse shear deformation and a non-linear variation of in-plane displacements with respect to the thickness coordinate. The transverse displacement is assumed to be constant throughout the thickness. The equations of equilibrium are obtained using principle of minimum potential energy. Solutions are obtained in closed form using Navier's technique by solving the boundary value problem. Accuracy of the theoretical formulations and the solution method is first ascertained by comparing the results with that already reported in the literature. After establishing the accuracy of the solutions, numerical results with real properties are presented for the multilayer antisymmetric angle-ply composite and sandwich plates, which will serve as a benchmark for future investigations.     

Transient dynamic and damping analysis of laminated anisotropic plates using a refined plate theory

A refined model is presented for the linear transient dynamic and damping analysis of laminated anisotropic composite plates. Experimental measurements of specific damping capacity of unidirectional composite beams are used to predict the specific damping capacity of laminated composite plates in various modes of vibration. A finite element idealization is adopted, and the quadratic Lagrangian element is used together with selective/reduced integration. A viscous damping approximation is then employed to calculate the damped transient response of laminated plates. The effects of transverse shear deformation, symmetry condition, boundary conditions, anisotropy, aspect ratio, fibre orientation and the lamination scheme on specific damping capacity and damped transient response are investigated. Realistic examples illustrate the importance of these parameters. The present results agree very closely with experimental results available in the literature and can serve as a benchmark for future comparison by other investigators.     

Non-linear bending of antisymmetric cross-ply plates

The bending of antisymmetric cross-ply plates, based on Von-Karman plate theory, is investigated in this paper with one term approximations for the in-plane and transverse displacements. Rayleigh-Ritz solutions are presented for the non-linear response of cross-ply laminates with various modular and aspect ratios and subjected to sinusoidal transverse loading.     

A refined beam theory based on the refined plate theory

Summary Based on the refined plate theory, a refined theory of rectangular beams is derived by using the Papkovich-Neuber solution and Lur’e method without ad hoc assumptions. It is shown that the displacements and stresses of the beam can be represented by the angle of rotation and the deflection of the neutral surface. The solutions based on the new theory are the same as the exact solutions of elasticity theory. In three examples it is shown that the new theory provides as good or better results than Levinson’s beam theory when compared to those obtained from the linear theory of elasticity.     

Three-dimensional thermal buckling analysis of piezoelectric antisymmetric angle-ply laminates using finite layer method

Finite layer method is the most efficient numerical method for 3D analysis of simply supported rectangular plates. Using this method, the 3D analysis is transformed into one dimensional analysis by virtue of the orthogonal properties of trigonometric interpolation functions. In the present study, the finite layer method is extended to the thermal buckling analysis of piezoelectric antisymmetric angle-ply laminates, which may be combined with some symmetrical cross-plies. Full coupling between the thermal, electrical and mechanical fields is taken into consideration. Pre-buckling state is assumed to be steady, and initial thermal stresses are computed accordingly. The geometrical stiffness matrix is then formed, and the critical temperature and buckling mode are obtained. Numerical examples are presented to verify the proposed method. The critical temperature is determined for both the adiabatic and isothermal buckling processes. The thermal buckling behaviours of some piezoelectric laminates and the effects of the thermo-electro-mechanical coupling are investigated.     

An accurate determination of stresses in thick laminates using a generalized plate theory

Analytical solutions for displacements and stresses in composite laminates are developed using the laminate plate theory of Reddy. The theory accounts for a desired degree of approximation of the displacements through the laminate thickness, allowing for piecewise approximation of the inplane deformation through individual laminae. The solutions are compared with the 3-D elasticity solutions for the simply supported case and excellent agreement is found. Analytical solutions are also presented for other boundary conditions. The results indicate that the generalized shear deformation plate theory predicts accurate stress distributions in thick composite laminates.     

A simplified analysis of transverse ply cracking in cross-ply laminates

This paper presents a method of analyzing transverse crack initiation and multiplication in symmetric cross-ply laminates. The method is based on the concept of a through-the-thickness inherent flaw and the energy balance principle. With a second-order polynomial assumed for the crack opening displacement, the perturbed stress field due to the presence of ply cracks is determined from the equilibrium conditions. The energy released as a result of ply cracking is then calculated and used to predict the increase in crack density. Based on an experimental correlation of the analytical result, a resistance curve is proposed to be used as a measure of the resistance to crack multiplication. The resistance to crack multiplication is shown to increase with the increasing crack density.     

反对称角铺设复合材料层合板热后屈曲和模态跃迁分析

为有效分析反对称角铺设复合材料层压板热后屈曲性能,由渐近修正几何非线性理论推导双耦合四阶偏微分方程（即协调方程和动态控制方程）,通过双Fourier级数将耦合非线性控制偏微分方程转换为系列非线性常微分方程,从而获得相对简单的求解方法。使用广义Galerkin方法求解与角交铺设复合层合板相关的边界值问题,研究了模态跃迁前后不同复杂程度的后屈曲模式。通过四边简支、面内不可移边界下复合层合板的数值计算表明：该解析法与有限元方法在主后屈曲区域的计算结果有很好的吻合性;有限元方法在解靠近二次分岔点时失去收敛性,而解析法仍具有深入探索后屈曲区域和准确捕捉模态跃迁现象的能力。     

Post‐buckling analysis of imperfect laminates using finite strips based on a higher‐order plate theory

A finite strip procedure has been developed for the post‐buckling analysis of composite laminates when subjected to progressive end shortening. The finite strips are developed based on a higher‐order shear deformation plate theory and there are nine variables at each nodal line. Initial imperfection expressed in the form of suitable trigonometric function is allowed. Examples including isotropic plates and laminates with arbitrary lay‐up arrangement are presented. Numerical results for laminates with and without initial imperfection are used to illustrate the effect of imperfection. Copyright © 2003 John Wiley & Sons, Ltd.     

Hygrothermal aging of polyimide matrix composite laminates

Two polyimide-matrix systems (Avimid^® K3B/IM7 and PETI-5/IM7) were subjected to a series of hygrothermal aging experiments at various temperatures and relative humidities. For each aging condition, we measured the water absorption rate and the microcracking toughness as a function of aging time. The toughness decreased with time. The rate of decrease increased with temperature and relative humidity. All experimental results could be fit to a simple first-order kinetics analysis where the degradation rate was assumed to be proportional to the total exposure to water above a threshold water level. Below the water threshold, no degradation occurred. The kinetics analysis was used to construct a hygrothermal aging master plot that can be used to make predictions of toughness degradation due to arbitrary hygrothermal environments. The master plot can be constructed from a few experiments on specimens immersed in water and thus is a potential accelerated test method for characterizing hygrothermal stability of composite laminates.     

Nonlocal buckling and vibration analysis of thick rectangular nanoplates using finite strip method based on refined plate theory

The buckling and vibration of thick rectangular nanoplates is analyzed in this article. A graphene sheet is theoretically assumed and modeled as a nanoplate in this study. The two-variable refined plate theory (RPT) is applied to obtain the differential equations of the nanoplate. The theory accounts for parabolic variation of transverse shear stress through the thickness of the plate without using a shear correction factor. Besides, the analysis is based on the nonlocal theory of elasticity to take the small-scale effects into account. For the first time, the finite strip method (FSM) based on RPT is employed to study the vibration and buckling behavior of nanoplates and graphene sheets. Hamilton’s principle is employed to obtain the differential equations of the nanoplate. The stiffness, stability and mass matrices of the nanoplate are formed using the FSM. The displacement functions of the strips are evaluated using continuous harmonic function series which satisfy the boundary conditions in one direction and a piecewise interpolation polynomial in the other direction. A matrix eigenvalue problem is solved to find the free vibration frequency and buckling load of the nanoplates subjected to different types of in-plane loadings including the uniform and nonuniform uni-axial and biaxial compression. Comparison studies are presented to verify the validity and accuracy of the proposed nonlocal refined finite strip method. Furthermore, a number of examples are presented to investigate the effects of various parameters (e.g., boundary conditions, nonlocal parameter, aspect ratio, type of loading) on the results.     

Thermal post buckling behavior of rectangular antisymmetric cross-ply composite plates

Summary The thermal post buckling behavior of simply-supported, antisymmetric cross-ply plates with immovable edges is investigated in this paper. For this purpose, a one term approximation for the inplane and transverse displacements is assumed and Rayleigh-Ritz method is used to obtain the equations of equilibrium. The question, whether the true thermal buckling (bifurcation buckling under thermal loads) exists for such plates is also addressed to. The conditions under which the thermal buckling in the classical sense occurs are derived. It is shown that nonlinear bending stiffness for such plates is direction dependent, because of an extra quadratic nonlinear term in addition to the usual cubic nonlinear term in the governing equilibrium equation. Results are presented for various plate configurations.     

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.     

Exact analysis for three-dimensional free vibrations of cross-ply cylindrical and doubly-curved laminates

Summary The free vibrations of simply-supported cross-ply cylindrical and doubly-curved laminates are investigated. The three-dimensional equations of motion, expressed in terms of displacements, are reduced to a system of coupled ordinary differential equations, which are then solved using the power series method. Numerical results are presented for cylindrical, spherical and saddle-shape laminates having a various number of layers.     

A novel five-variable refined plate theory for vibration analysis of functionally graded sandwich plates

In this article, a new five-variable refined plate theory for the free vibration analysis of functionally graded sandwich plates is developed. By dividing the transverse displacement into bending, shear, and thickness stretching parts, the number of unknowns and governing equations of the present theory is reduced, and hence, makes it simple to use. Indeed, the number of unknown functions involved in the present theory is only five, as opposed to six or more in the case of other shear and normal deformation theories. The theory accounts for hyperbolic distribution of the transverse shear strains, and satisfies the zero traction boundary conditions on the surfaces of the plate without using a shear correction factor. Two common types of functionally graded material (FGM) sandwich plates, namely, the sandwich with FGM facesheet and homogeneous core and the sandwich with homogeneous facesheet and FGM core, are considered. The equations of motion are obtained using Hamilton's principle. Numerical results of the present theory are compared with three-dimensional elasticity solutions and other higher-order theories reported in the literature. It can be concluded that the proposed theory is accurate and efficient in predicting the free-vibration response of functionally graded sandwich plates.     

Fracture behavior of cross-ply graphite/ epoxy laminates

Fracture behavior of cross-ply (0/90)_4s, (0/90)_10s, (0₂/90₂)_2s and (0₄/90₈/0₄)_T laminates of T300/934 graphite/epoxy material was studied using compact tension specimens of several widths and thicknesses, center notched tension and three point bend specimens. The process of damage initiation and propagation was studied and is discussed in detail. The critical stress intensity factor was evaluated and its variation with specimen size and type is shown. On the basis of these investigations, a suitable specimen for the evaluation of meaningful fracture toughness is suggested.