In order to analyze the approximate applicability of general simple-supported symmetric laminated plates, according to the Ritz method and the minimum potential energy principle, the closed form solution of the laminated plates was obtained after the algebraic manipulations and matrix transformation, which was convenient for MATLAB programming.Values about the orthotropic laminate and the 10％ rule laminate, obtained through the orthotropic laminated plate approximation ( OA ) , the finite element method ( FEM ) , the orthotropic long-plate laminate approximation ( OLA) , were compared with the value of exact solution, under different aspect ratio AR and ply angleθ. The result shows that maximum displacement w0 of FEM is within 5％errors compared with exact solution.As the aspect ratio AR increases, the error tends to be stable and consistent.Under the low bending stiffness D16 , OLA w0 at the critical AR is 294.4％errors compared with exact solution about the orthotropic laminate, while w0 is consistent at the large AR ratio.For the 10％rule laminates, as AR is getting greater than 3, FEM w0 and OA w0 are consistent with the exact solution, and as AR getting less than 3, the w0 from the prior approximate methods meets the engineering requirements, however, error is large when under the large bending-twist coupling stiffness D16 , D26 , at AR =1 and 2 withθ=90°, the OA w0 are 10.98％and 8.67％errors compared with the exact solution w0 .The research has certain directive significance on the design of composite structure.%为了研究一般简支对称层合板近似求法适用性问题,依据Ritz法、最小势能原理经代数转化获得便于MATLAB编程的力学解析解;不同长宽比AR与铺层角度θ下,正交与10％原则设计层合板通过有限元法(FEM)、正交长层合板近似(OLA)、正交层合板近似(OA)得到值和解析解对比.结果表明:FEM法与解析解中面最大位移值w0误差在5％以内,随AR增大,两者误差趋于稳定并一致;正交板在低弯曲刚度D11下,OLA法在临界AR处w0误差达294.4％,而大AR下,OLA与解析解结果一致;10％原则板在AR大于3时,FEM和OA法得到w0与解析解一致,AR小于3时,两近似法符合工程需求,但大弯扭耦合D16,D26下,在AR=1,2,θ=90°时,误差为10.98％,8.67％,相较于解析解有较大误差.研究结果为复合材料结构设计阶段提供了一定的参考.
展开▼
