The path-engulfment method for topology optimization of structures

To address the challenge of establishing and solving mathematical models for engineering structural optimization, a new topological optimization method that integrates load-transfer path theory with the engulfment algorithm is presented in this paper. The presented method applies the load-transfer path theory to identify the main load-bearing areas of the structure and utilizes the principle of concentrating more materials in relatively high-stress regions and fewer materials in relatively low-stress regions. An engulfment algorithm is introduced to optimize the material distribution. A comparative analysis between the presented and variable-density methods revealed that the path-engulfment method enhances the structural stiffness and strength while reducing its mass, confirming its precision and efficacy in structural optimization. The path-engulfment method was implemented on a truck crane frame, resulting in an optimized structure with increased stiffness and strength and reduced mass compared to the original design. Furthermore, this method eliminates the need for establishing and solving complex mathematical models while addressing issues related to checkerboards and gray-scale elements. A smooth boundary approach was introduced by leveraging the engulfment algorithm, enabling the direct application of the optimized structure for manufacturing purposes, particularly in engineering applications.