Level set topology optimization of metamaterial-based heat manipulators using isogeometric analysis

TL;DR

This paper presents a level set topology optimization method using NURBS for designing metamaterial-based heat manipulators, demonstrating efficiency, robustness, and manufacturability improvements through numerical examples.

Contribution

It introduces a novel NURBS-based level set topology optimization framework for heat manipulators, integrating advanced mathematical programming and regularization techniques.

Findings

Method efficiently handles complex geometries and objectives.

Numerical examples validate robustness and versatility.

Regularization improves manufacturability of designs.

Abstract

We exploit level set topology optimization to find the optimal material distribution for metamaterial-based heat manipulators. The level set function, geometry, and solution field are parameterized using the non-uniform rational B-spline (NURBS) basis functions in order to take advantage of easy control of smoothness and continuity. In addition, NURBS approximations can produce conic geometries exactly and provide higher efficiency for higher-order elements. The values of the level set function at the control points (called expansion coefficients) are utilized as design variables. For optimization, we use an advanced mathematical programming technique, Sequential Quadratic Programming (SQP). Taking into account a large number of design variables and the small number of constraints associated with our optimization problem, the adjoint method is utilized to calculate the required sensitivities with respect to the design variables. The efficiency and robustness of the proposed method are demonstrated by solving three numerical examples. We have also shown that the current method can handle different geometries and types of objective functions. In addition, regularization techniques such as Tikhonov regularization and volume regularization have been explored to reduce unnecessary complexity and increase the manufacturability of optimized topologies.