Integrating moving morphable components and plastic layout optimization: a two-stage approach for enhanced structural topology optimization

Abstract

The concept of Moving Morphable Components (MMC) represents a novel and effective technique within structural topology optimization, requiring fewer design variables and providing an explicit boundary definition. However, the optimal topology heavily depends on the initial shape and position of the components. Plastic layout optimization, on the other hand, quickly determines globally optimal layouts via linear programming but lacks detailed information about member connections, which are crucial for applications like additive manufacturing. This study introduces an innovative two-stage methodology that synergizes the strengths of MMC and plastic layout optimization, while addressing their individual limitations. The method builds on the concept that the topology optimization formulation for minimizing compliance under a single load case is mathematically equivalent to a minimum-weight plastic layout optimization formulation. In the first stage, the global optimal layout is obtained using plastic layout optimization, which serves as an advantageous starting point for the MMC approach in the second stage. This integration significantly reduces computational time, lowers compliance, and mitigates the risk of converging to local optima. The proposed methodology is adaptable to complex three-dimensional domains and provides a robust framework for efficient and precise structural topology optimization. Several examples demonstrate the efficacy, accuracy, and rapid convergence of this approach, validating its potential for advancing optimization techniques in engineering.