A Concept of Equivalent Load Scheme for Easy Prediction of Structural Topology When Load Position Changes Randomly

The contemporary optimal design methodologies must be aligned with actual operating conditions of the structures, like, for example, load uncertainty—a situation which often occurs in engineering problems. This paper focuses on the topology optimization of structures under loads uncertainty, a situation which often occurs in engineering problems. It is worth underlining that random load changes can significantly affect generated topologies, therefore predicting them is an important design task. In this paper, a numerical approach suited to cope with this task is proposed. It is based on the idea that while minimizing structure compliance, random load changes can be mimicked by the deterministic problem of multiple load cases. This very useful approach, however, requires hundreds of load cases to consider. To reduce the number of load cases to a few, a new concept, the Equivalent Load Scheme—ELS, is proposed. This idea, being very simple, does not require specialized software to predict the structural topology of minimal compliance for uncertain point of load application. The implementation of this idea has been tested on numerical examples, including an engineering one. The results confirmed that the presented ELS concept can be regarded as a useful alternative to the existing techniques, significantly simplifying the design process. Taking into account the effectiveness, ease of implementation, and versatility, the proposed idea stands for an original contribution to structural topology optimization, suited for the case of loads exposed to random changes, in particular, when the position of the load changes randomly.