Iranian Journal of Manufacturing Engineering

Iranian Journal of Manufacturing Engineering

Topology optimization of continuous structures using a combination of Galerkin mesh-free methods and bidirectional evolutionary topology optimization

Document Type : Original Article

Authors
Alireza Lavaei
Ali Rahmani Firoozjaee
Department of Civil Engineering, Babol Noshirvani University of Technology, Babol, Iran
10.22034/ijme.2025.531262.2107
Abstract
This paper presents an advanced approach to optimize the topology of structures by combining the bidirectional evolutionary structural optimization method with the mesh-free Galerkin method. The main goal of this hybrid approach is to significantly reduce the computational time while maintaining high accuracy in the optimization process. Traditional mesh-based methods, especially in problems involving complex geometries, often require accurate mesh generation and repeated mesh reconstruction during the optimization process, which can significantly increase the computational cost and complexity. Therefore, by combining a mesh-free method such as the mesh-free Galerkin method, the proposed approach eliminates the need for mesh generation and, when combined with the efficiency of the bidirectional evolutionary topology optimization algorithm, leads to a faster and simpler optimization process. The numerical results presented in this study show that this hybrid method is up to 2.5 times faster than conventional finite element-based approaches, while still ensuring reliable mechanical performance and structural integrity. Furthermore, due to the flexibility of the Galerkin mesh-free method in handling complex geometries and variable boundary conditions, the proposed technique is particularly effective for real-world engineering applications. It is particularly suitable for industries such as aerospace, automotive, and mechanical engineering where the demand for lightweight, robust, and complex structural designs is high. Overall, the integration of the Galerkin mesh-free method and bidirectional evolutionary optimization provides a robust and efficient solution to the limitations of traditional topology optimization techniques.

Numerical results presented in this study show that this combined method is up to 2.5 times faster than conventional approaches based on the finite element method (FEM), while still ensuring reliable mechanical performance and structural integrity. Furthermore, due to the flexibility of the EFG method in handling complex geometries and variable boundary conditions, the proposed technique is particularly effective for real-world engineering applications. This method is particularly suitable for industries such as aerospace, automotive, and mechanical engineering where the demand for lightweight, strong, and complex structural designs is high. Overall, the integration of BESO and EFG provides a robust and efficient solution to the limitations of traditional topology optimization techniques.
Keywords
Topology Optimization
Galerkin Network-Free Method
Bidirectional Evolutionary Topology
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