Automated Design of Trusses for Optimum Geometry

Three-dimensional indeterminate elastic trusses subjected to multiple loading conditions are optimally designed for least weight. The member areas and joint coordinates are treated as design variables for problems where a reasonable initial geometry is specified. Members are designed to stress and Euler buckling limits and linking constraints between area variables. The fully stressed design is assumed optimal. Coordinate variables may be linked to maintain geometric symmetry. The design problem is, in effect, divided into two separate, but dependent, design spaces—one for member sizes and one for coordinates. While changing coordinate variables, the member areas are treated as dependent variables. Design of larger structures by sequential design of substructures is illustrated. Examples are presented with computer run times (UNIVAC 1108, FORTRAN V) ranging from 28 sec for a 25-bar space truss to 2 min for a 47-bar planar tower. Design of the tower by substructure required 1 min. Significant weight reductions are reported when geometric changes are included in the optimization process.