Multi-load cases topological optimization by weighted sum method based on load case severity degree and ideality

Mechanical structures always bear multiple loads under working conditions. Topology optimization in multi-load cases is always treated as a multi-objective optimization problem, which is solved by the weighted sum method. However, different weight factor allocation strategies have led to discrepant optimization results, and when ill loading case problems appear, some unreasonable results are obtained by those alternatives. Moreover, many multi-objective optimization problems have certain optimization objective, and an evaluation formula to measure Pareto solution in the multi-objective optimization problem area is lacking. Regarding these two problems, a new method for calculating the weight factor is proposed based on the definition of load case severity degree. Additionally, an amplified load increment is derived and suggested in the minimum compliance with a volume constraint problem. Ideality is formulized from Pareto front to the ideal solution to evaluate the different optimization results. Benchmark topology optimization examples are solved and discussed. The results show that the load case severity degree is less affected by the different weighted sum functions and can avoid ill loading case phenomena, and the ideality of optimization result obtained by the load case severity degree is the best.