Abstract
This paper presents a new method to determine optimum topologies for truss structre by using affinet transformation. Our basic idea is to obtain optimum topology in complex design domain from optimum topology obtained in simple design domain by using affine transformation. We define simple design domain and optimum design problem. We calculate optimum topology in the simple design domain. For determination of optimum topology we use Genetic Algorithms. We call this optimum topology as basic optimum topology. Then we apply affine transformation to basic optimum topology, and can obtain some optimum topologies. To compare with those topologies, we calculate optimum topologies directly in the same design domain after coordinate transformation. We show that strain energy between orthogonal and nonorthogonal coordinate system is conserved under a certain condition by affine transformation, and our proposed method are simple and faster to get the optimum topology.
