Topology optimization with continuously varying load magnitude and direction for compliance minimization

Traditional topology optimization methods only consider a limited number of loads in the optimization procedure, neglecting load variations common in real-world scenarios. To incorporate real load scenarios, robust topology optimization considers uncertainties in load directions while minimizing compliance, generating structures capable of withstanding variations in the load. This paper incorporates the angles of the load directions as parameters into the optimization formulation to design structures that perform well under a range of load directions. Additionally, the formulation is extended to incorporate local volume constraints to balance the solution distribution throughout a domain, achieving more complex designs with proper material distribution as the angle of the loads and the number of sub-regions increases while maintaining consistency in the worst-case scenario. Two and three-dimensional examples demonstrate that topology-optimized designs are susceptible to loads that vary in direction and magnitude, and by considering realistic loading conditions, this formulation yields robust, reliable designs, markedly enhancing their suitability for actual engineering applications.