Optimization Method for Thin-walled Structures with Directional Stiffeners Based on Single-variable Characteristic Functions

Continuum topology optimization is a powerful structural optimization method, but its application often leads to thin-walled structures with complex and irregular stiffening patterns, making the manufacturing process challenging. To address this issue, a novel optimization method for thin-walled structures with directional stiffeners is proposed. By introducing the single-variable characteristic function into the Discrete Material Optimization (DMO) model, a diagonal elements scheme is developed. This approach significantly reduces the number of design variables and enables the rapid optimal design of thin-walled structures with directional stiffeners. Firstly, a set of single-variable are introduced to describe the stiffeners in a given direction. The original variables are transformed into a set of density functions using the single-variable characteristic function. These density functions are incorporated into the DMO model to construct a new interpolation model. The update of design variables is driven by the genetic algorithm. An adaptive smoothing strategy is employed to adjust the projection slope and penalty parameters, which improves optimization efficiency. A numerical example verifies that the proposed method not only successfully achieves optimized results but also ensures good manufacturability.