In this paper, a numerical calculation method in order to perform effectively shape analysis and optimization of structure is proposed. The procedure is based on an iterative calculation process known as the Cross method for indeterminate rigid-framed structural analysis or the relaxation method for pin-jointed frameworks. First of all, a given area in analysis is divided into partial regions and an elemental coefficient matrix is derived with the conventional finite element technique. Instead of solving the finite element equation of the overall structural system, the finite element equation in some neighborhood at the nodal point is only required. The procedure consists of a calculation for converting mechanical behavior on one node in the neighborhood into the influential forces on the adjacent node and repeats this manipulation in all the area. To make sure of availability and efficiency, this method is applied to forward analyses, both optimizations and a shape analysis of truss structure. All results are good in any case. The proposed method can be applied to any model of which a finite element method can be applicable.
