Innovative structural topology optimization method via spatial points control technology

This paper presents Spatial Points Control Technology (SPCT) as a novel method for structural topology optimization. SPCT constructs a field function to map the structure by controlling the positions and number of spatial points, which significantly reduces the number of design variables compared with traditional topology optimization, improves the computational efficiency, and yields clear structural boundaries. Benefiting from the flexible configuration of control points, SPCT allows the integration of prior knowledge to arrange the initial layout, enabling localized optimization and a more targeted and efficient design process. The sensitivity of the SPCT-based topology optimization model with respect to the variations of control points is derived, a complete gradient-based topology optimization framework is established, and a non-gradient solving strategy is further provided for complex nonlinear topology optimization problems. The effectiveness, efficiency, and versatility of the proposed method are verified through a series of numerical examples, including minimum compliance problems, optimizations with predefined initial configurations, and problems solved by non-gradient optimization algorithms.