纤维增强及匀质层层叠板动力分析的解析与半解析方法

本文引入复合板条振型函数系列,提出二种层叠板解法。一种纯解析法适用于各种边界条件的矩形层叠板的动力计算;另一种半解析半数值方法适用于任意形状、任意边界的层叠板动力计算,比现有数值计算方法节省大量内存与时间。文中还给出了一系列常用层叠板计算公式。

ANALYTICAL AND SEMI-ANALYTICAL METHODS FOR DYNAMIC COMPUTATIONS OF LAMINATED PLATES MADE OF FIBRE-REINFORCED OR HOMOGENEOUS LAYERS

Two methods of solution for laminated plates made of fibre-reinforced or homogeneous layers are presented by introducing mode shape functions series of composite strip.One of them is an analytical method,for which the deflection and angle of rotation mode shapes are expressed as where Xi（x）,Yj（y）andσi（x）,σj（y）are the deflection and angle of rotation mode shapes of the i-th or j-th order of the composite strip,corresponding to the boundary condition in the x and y directions of rectangular plate respectively.This method is suitable for dynamic calculations of rectangular laminated plates with various boundary conditions（about 500 types）.Another is a semi-analytical and semi-numerical method,which employs simple polynomials only in transverse direction and analytical functions in the longitudinal and thickness directions.An analytical solution of the dynamic equation for composite strip is chosen in practical construction of displacement functions.It contains two coefficients ID,Ip which represent the effects of material and constructional characteristics in the thickness direction.The solution of these functions is substituted for numerical calculation in longitudinal and thickness directions,hence the computational effort and memory requirements are reduced considerably.In addition,this type of analytical function in itself is an exact solution of one-dimensional problem of corresponding structure,therefore the present method is applicable to dynamic calculations of laminated plates with arbitrary shape and boundary conditions.A series of computing formulae are also given for ordinary laminated plates in this paper.