双模量复合材料层板的大挠度分析

本文用动力松弛法(DRM)分析了双模量复合材料层板的大挠度弯曲问题。文中介绍了求解该问题的主要公式和步骤;对轻度双模量材料及高度双模量材料的两层正交铺层矩形板在正弦载荷和均匀载荷作用下的挠度和内力进行了数值计算,并把其结果与小挠度结果及单模量结果做了比较,讨论了大挠度分析的必要性及模量性质对大挠度分析的影响。 

LARGE DEFLECTION ANALYSIS OF LAMINATED PLATES OF BIMODULAR COMPOSITE

In engineering practice,the following questions are often raised about laminated constructions made of fiber reinforced bimodular composites:(1)Under what circumstances do we need to make nonlinear analysisp?(2)How much do bimodular properties affect the displacernents,force and moment resultanEs in,large deflection analysis?How is the effect different from that in linear analysisy However,the problem becomes very complex if the effects of physically bi-linear and geometrically nonlinear behaviors are all taken into account and the exact solutions are difficult to obtain.Hence selecting an effewive and simple approximate method is necessary.In this paper Dynamic-Relaxation Method(DRM) is adopted to investigate the large deflection beading of rectangular plates laminated of bimorlular composite materials.The basic,formulae of iterations and the main steps of solving this subject are outlined.The numerical results are given for simply supported,two-layer cross-ply square plates made of mildly bimodular material(Boron/Epoxy (B/E)) and highly bimodnlar material(Aramid/Rubber(A/R)) under sinusoidally distributed and uniformly distributed transverse loads.The results obtained are 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 or the compressive moduli of the bimodular materials.The necessity of large deflection analysis and the effects of bimodnlar properties on the large deflection analysis are discussed.The main conclusions of this paper are as following:(1) The DRM proves an effective numerical method for solving the problem taking into account the effects of physically bilinear and geometrically nonlinear behavior.(2)The relative error between linear theory solution and nonlinear theory solution of normalized center deflection w increases with increasing of the load.When w=1.0 It is about 75% for the A/R laminate,and about 40% for the B/E laminate.Therefore,it is necessary to consider nonlinear effect when the load gets greater.(3) When w=1.0 the relative error between tensile moduli solutions and bimodular solutions of the B/E laminate is below 500 for w,whereas it is below 1500 for force and moment resultants.The relative error,in general,decreases with increasing of the load.This implies that the tensile moduli become predominant for large deflections.(4) For the A/R laminate,even though the relative error between tensile moduli solutions and bimodular solutions of w decreases somewhat with increasing load parameter,the effect of bimodularity on deflection,force and moment resultants is very significant.Therefore,it is necessary to consider the influence of bimodular properties in large deflction analysis for highly bimodular materials.