A study of the postbuckling path of cylindrically curved panels of laminated composite materials during loading and unloading

In this paper, Dynamic Relaxation Method is applied to study the postbuckling path of cylindrically curved panels of laminated composite materials during loading and unloading. The phenomenon that loading paths do not coincide with unloading paths has been found. Numerical results are given for cylindrically curved cross-ply panels subjected to uniform uniaxial compression under two types of boundary conditions. The influence of the number of layers, the panels curvature and the initial imperfection on the postbuckling paths is discussed.Project supported by the National Natural Science Foundation of China. The main contents of this paper were presented at the Proceedings of the Seventh International Conference on Composite Materials (November 1989, Guangzhou, China).The authors thank Prof. Zhou Li for his guidance.     

EFFECTS OF TRANSVERSE SHEAR ON THE NONLINEAR BENDING OF RECTANGULAR PLATES LAMINATED OF BIMODULAR COMPOSITE MATERIALS

This paper investigates the application of Dynamic-Relaxation (DR) method to theproblems of nonlinear bending of rectangular plates laminated of bimodular compositematerials.The classical lamination theory and a shear deformation theory of layeredcomposite plates, taking account of large rotations (in the von Karman sense), areemployed separately to analyze the subject.It has been.found here that the estimation of the fictitious densities which control theconvergence and numerical stability of nonlinear DR solution consndring transverse sheareffect still needs to be.further investigated.In this paper,a procedure to calculate fictitiousdensities has been presented;hence the numerical stability of this topic has been ensured.In this paper the main steps of solving the nonlinear bending of bimodular compositelaminates by means of DR method are outlined.The numerical results are given for simplysupported,two-layer cross-ply rectangular platea made of mildly bimodular material(Boron-Epoxy (B-E)) and higltly     

横向剪切对双模量复合材料叠层矩形板非线性弯曲的影响

本文探讨了动力松弛(DR)法在双模量复合材料叠层矩形板非线性弯曲问题中的应用。在分析中分别采用叠层板大挠度经典理论和计及大转动(在Von Karman意义上)的复合材料叠层板剪切变形理论。我们发现,对于考虑横向剪切变形的非线性弯曲问题,如何计算虚拟密度以控制数值计算的稳定性,仍然需要进一步研究。本文提出了一种虚拟密度的计算方法,从而保证了本课题数值计算的稳定性。文中介绍了用DR法求解双模量复合材料叠层板非线性弯曲的主要步骤,给出了由轻度双模量材料(Born-Epxy(B-E))和高度双模量材料(Aramid-Rubber(A-R)和Polyester-Rubber(P-R))的两层正交叠层简支矩形板在正弦分布载荷及均布载荷作用下的非线性弯曲特性的数值结果。将所得结果和小挠度分析结果及普通复合材料的结果作了比较,并分析了横向剪切变形对无量纲中心挠度的影响。     

动力松弛法解双模量复合材料叠层板的弯曲问题

本文用动力松弛法(DR法)分析了双模量复合材料叠层板的线性弯曲问题。文中介绍了用DR法求解该问题的主要步骤及保证数值计算稳定性的重要参数——虚拟密度的计算方法,给出了三种双模量复合材料正交叠层简支矩形板在正弦载荷及均布载荷作用下的中性面位置、挠度和内力等的数值结果。与现有的精确解比较以及计算实践表明,该法简便、准确,易于程序化,是一种比较有效的数值分析方法,值得研究并推广应用。     

A STUDY OF THE POSTBUCKLING PATH OF CYLINDRICALLY CURVED PANELS OF LAMINATED COMPOSITE MATERIALS DURING LOADING AND UNLOADING

In this paper,Dynamic Relaxation Method is applied to study the postbuckling path ofcylindrically curved panels of laminated composite materials during loading and unloading.The phenomenon that loading paths do not coincide with unloading paths has been found.Numerical results are given for cylindrically curved cross-ply panels subjected to uniformuniaxial compression under two types of boundary conditions.The influence of the numberof layers,the panels curvature and the initial imperfection on the postbuckling pathsis discussed.     

用多参数非均匀等效体研究圆柱正交异性复合材料的剪切有效模量

有效模量是复合材料力学细观解过渡到宏观解的桥梁。宏观非均匀复合材料的有效模量是一个尚未认真研究过的课题。本文提出用多参数非均匀等效体的新方法,来研究圆柱正交异性宏观非均匀复合材料的剪切有效模量,克服了最近Dhoopar B.L.和SinhaP.K提出的方法的一些不足之处。     

复合材料非均匀圆柱正交异性圆板弯曲

本文研究了圆柱正交异性复合材料圆板的弯曲,求得了折算刚度按半径线性变化的非均匀圆柱正交异性圆板在均布载荷作用下的通解;同时给出了周边固定和简支、以及具有线性过渡区(核)的圆板的精确解和算例,结果表明,当核径比λ=δ/R小于10％时,非均匀性对最大挠度的影响不超过0.289％。     

复合材料单层的横向拉伸原地强度和0°/90°/O°叠层板张开型裂纹经典解的研究

本文:(1)用傅立叶变换和Copson的对偶积分方程法,求得了0°/90°/0°叠层板90°层内张开型裂纹问题的经典解;(2)应用所得解,对石墨/环氧叠层板中90°层的断裂特性和横向拉伸原地强度进行了定量研究。 结果表明,这类叠层板的应力强度因子不同于90°的单向层,它随0°层的厚度b、模量E_L或G_(LT)的增加而减小,也随90°层的厚度减小而减小,这就导致了叠层效应,并提高了90°层的横向原地强度。这里的理论计算与D.L.Flaggs的试验结果一致。     

Effects of transverse shear on the nonlinear bending of rectangular plates laminated of bimodular composite materials

This paper investigates the application of Dynamic-Relaxation (DR) method to the problems of nonlinear bending of rectangular plates laminated of bimodular composite materials. The classical lamination theory and a shear deformation theory of layered composite plates, taking account of large rotations (in the von Karman sense) are employed separately to analyze the subject. It has been found here that the estimation of the fictitious densities which control the convergence and numerical stability of nonlinear DR solution considering transverse shear effect still needs to be further investigated. In this paper, a procedure to calculate fictitious densities has been presented; hence the numerical stability of this topic has been ensured. In this paper the main steps of solving the nonlinear bending of bimodular composite laminates by means of DR method are outlined. The numerical results are given for simply supported, two-layer cross-ply rectangular plates made of mildly bimodular material (Boron-Epoxy (B-E)) and highly bimodular materials (Aramid-Rubber (A-R) and Polyester-Rubber (P-R)) under sinusoidally distributed and uniformly distributed transverse loads. The results obtained have been compared with linear results and those obtained for laminates fabricated from conventional composite materials, the elastic moduli of which are identical with the tensile moduli of the bimodular materials. In addition, the effect of transverse shear deformation on the nondimensionalized center deflection has been studied.The main contents of this paper were presented at the International Symposium of Composite Materials and Structures (June 1986, Beijing).The authors thank Prof. Zhou Li for his guidance.