A Novel Discrete Adjoint-based Level Set Topology Optimization Method in B-spline Space

TL;DR

This paper introduces a new discrete adjoint-based approach for sensitivity analysis in level set topology optimization using B-spline space, simplifying the process and improving efficiency for engineering design problems.

Contribution

The work demonstrates that the velocity field in level set methods can be fully obtained via the discrete adjoint method, removing the need for traditional shape sensitivity analysis.

Findings

Effective optimization of stress and buckling problems

Elimination of shape sensitivity analysis in level set methods

Potential for simplified and efficient topology optimization

Abstract

This paper presents a novel computational scheme for sensitivity analysis of the velocity field in the level set method using the discrete adjoint method. The velocity field is represented in B-spline space, and the adjoint equations are constructed based on the discretized governing equations. The key contribution of this work is the demonstration that the velocity field in the level set method can be entirely obtained from the discrete adjoint method. This eliminates the need for shape sensitivity analysis, which is commonly used in standard level set methods. The results demonstrate the effectiveness of the approach in producing optimized results for stress and linearized buckling problems. Overall, the proposed method has the potential to simplify the way in which topology optimization problems using level set methods are solved, and has significant implications for the design of a broad range of engineering applications.