Abstract
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 (degrees of freedom = k), the shape change (degrees 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 numerically analyzed in order to examine the validity of the present method.
