On Predicting Optimal Structural Topologies in the Presence of Random Loads.

Topology optimization has been present in modern engineering for several decades, becoming an important tool for solving design problems. Today, it is difficult to imagine progress in engineering design without the search for new approaches to the generation of optimal structural topologies and the development of efficient topological optimization algorithms. The generation of topologies for structures under random loads is one of many research problems where topology optimization is present. It is important to predict the topologies of structures in the case of load uncertainty, since random load changes can significantly affect resulting topologies. This paper proposes an easy-to-implement numerical approach that allows the prediction of the resulting topologies of structures. The basic idea is to transform a random loads case into the deterministic problem of multiple loads. The concept of equivalent load scheme (ELS) is introduced. Instead of generating hundreds of loads applied at random, the selection of a few representative load cases allows the reduction of the numerical effort of the computations. The numerical implementation of proposed concepts is based on the cellular automaton mimicking colliding bodies, which has been recently introduced as an efficient structural topology generator. The examples of topology optimization under randomly applied loads, performed for both plane and spatial structures, have been selected to illustrate the proposed concepts. Confirmed by results of numerical simulations, the efficiency, versatility and ease of implementation of the proposed concept can make an original contribution to research in topological optimization under loads applied in a random manner.