Geometry and Topology Optimization of Statically Determinate Beams under Fixed and Most Unfavorably Distributed Load

The paper concerns topology and geometry optimization of statically determinate beams with an arbitrary number of pin supports. The beams are simultaneously exposed to uniform dead load and arbitrarily distributed live load and optimized for the absolute maximum bending moment. First, all the beams with fixed topology are subjected to geometrical optimization by genetic algorithm. Strict mathematical formulas for calculation of optimal geometrical parameters are found for all topologies and any ratio of dead to live load. Then beams with the same minimal values of the objective function and different topologies are classified into groups called topological classes. The detailed characteristics of these classes are described.