摘要:
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。
Abstract:
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-laver 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 resells 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.
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