弹性薄板分析的条形传递函数方法

提出一种用于矩形弹性薄板变形分析的条形传递函数方法．一个矩形区域首先沿某一个方向被剖分成若干个条形子域，分割这些子域的直线称为结线，在结线上定义位移函数，它是结线坐标的一维函数，结线的两个端点称为结点．为适应复杂边界条件，在边界结线上定义若干结点，该结线的位移函数用结点位移参数插值表示．每个条形子域的变形用结线位移函数和适当的插值函数（形函数）表示．结线位移函数和结点位移参数满足的平衡微分方程及代数方程由变分原理给出

STRIP DISTRIBUTED TRANSFER FUNCTION METHOD FOR ANALYSIS OF ELASTIC THIN PLATES 1)

A refined strip distributed transfer function method is presented for the analysis of elastic thin plates. In the analysis, a rectangular plate (substructure) is divided into strips by lines named nodal lines. The displacement functions defined on the nodal lines are one dimensional functions of the nodal line coordinate. Both ends of the nodal line are called nodes. To cope with complex boundary conditions, nodes are also defined on the boundary nodal lines, and the displacement of each strip is interpolated in nodal line displacements. The equilibrium differential equation of the nodal line functions and the boundary conditions of the nodal displacements are derived by variational principle. The equilibrium differential equations are cast into state space form and the exact solution is given in boundary node displacements. Substituting the solution into the boundary conditions, the algebra equations for nodal displacements are obtained. Solving this equation gives nodal displacements. Therefore, nodal line displacements, strain and stress can be found easily. Numerical examples are presented and compared with the exact analytic solution, FEM and SDTFM solutions. It can be concluded that this new method has the advantages of high precision, unified solution procedure and easy computer coding. The model can be used with FEM for complex geometry configuration.