层合板大挠度分析的一种新方法

提出了一种用于求解薄板结构大挠度问题的缩减基方法。分析了复合材料层合板结构在简单铰支和可移夹紧两种不同边界条件下的静态响应。数值结果表明本文方法克服了摄动方法和Ｇａｌｅｒｋｉｎ方法的不足之处，拓展了正则摄动法的使用范围，提高了Ｇａｌｅｒｋｉｎ法的有效性。

A New Method for the Large Deflection Analysis of CompositeLaminate ThinPlate

Compositelaminate thin plate often has deflections of the order of plate thickness. This makes the application of either perturbation method or Galerkin method to computing deflections very tedious. We developed a new method that can be much less tedious. In our development of the new method, we made use of the reduced basis function first proposed by A.K.Noor in his finite element analysis. Different from Noor, we applied perturbation technique for generation of reduced basis functions as trial functions in Galerkin method. By applying perturbation technique, we converted the partial differential equations for compositelaminate as given by eq.(13) into their perturbation forms, which are eqs.(18a), (18b), etc. With eqs.(18a) and (18b), etc, we generated the reduced basis functions as given by eqs.(19a) and (19b). We took the numerical example given in Ref., whose computation was very tedious. Our results, shown in Fig.2, agree very well with those in Ref.. The solid curve in Fig.2 is for a simply supported laminate plate and the dotted curve is for clamped plate with movable edges. For deflection up to as large as twice the thickness ( w c/h =2.0), we only had to go to third order accuracy, which required eqs.(18c), omitted in the paper for the sake of saving space. Our computation work was very much less tedious than that required in Ref..