具有Homologous变形约束立体桁架的形态分析

Structural Shape Analysis with the Constraint Conditions of Homologous Deformation

本文研究了具有Homologous位移约束的结构形状分析问题。文中第一部分把结点分成三类:表示Homologous变形点(自由度=h),形状可变点(自由度=f)和边界点。然后对于任意的桁架结构给出Homologous参数,n=h+f和m=1+f,引入具有n×m的系数矩阵的基础方程。在第二部分,利用广义逆矩阵导出基础方程的解存在条件。然后建立包含未知结点坐标的非线性方程组,并由Newton-Raphson法进行数值分析,以找出最终形状。最后一部分举了一个三维桁架的例子,以说明该方法的有效性,实用性。

This paper deals with a structural shape analysis with the constraint conditions of homologous deformation. The homologous deformation is defined as 'the deformation of a structure shall be called homologous if a given geometric relation holds, for a given number of structural points, before, during and after the deformation'.In the first part of the paper, all nodal points are divided into three categories: nodal points representing the homologous deformation (degress of freedom = h), the shape change (degress of freedom = f ) and the fixed boundary, respectively. Then, the basic equations with the n×m coefficient matrix are introduced for any truss structures, giving a homologous parameter, where n= h + f and m= 1 + f, in the second part, the existence condition of solution for the derived basic equations is given by the use of the generalized inverse. This condition is a set of nonlinear equations with unknowns of nodal coordinates, and is numerically analyzed by Newton-Raphson method in order to find out the final shape. In the final part, an illustrative example is nummefically analyzed in order to examine the validity of the present method.