Generating optimal topologies in structural design using a homogenization method
Computer Methods in Applied Mechanics and Engineering
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
A simple level set method for solving Stefan problems
Journal of Computational Physics
A PDE-based fast local level set method
Journal of Computational Physics
Structural boundary design via level set and immersed interface methods
Journal of Computational Physics
Journal of Computational Physics
Design of Compliant Mechanisms: Applications to MEMS
Analog Integrated Circuits and Signal Processing
Structural optimization using sensitivity analysis and a level-set method
Journal of Computational Physics
International Journal of Computer Vision
A new level-set based approach to shape and topology optimization under geometric uncertainty
Structural and Multidisciplinary Optimization
Structural and Multidisciplinary Optimization
Intelligent optimal design of spatial structures
Computers and Structures
Level-set methods for structural topology optimization: a review
Structural and Multidisciplinary Optimization
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A variational approach to shape feature control in topology optimization is presented in this paper. The method is based on a new class of surface energies known as higher-order energies as opposed to the conventional energies for problem regularization, which are linear. In employing a quadratic energy functional in the objective of the topology optimization, non-trivial interactions between different points on the structural boundary are introduced, thus favoring a family of shapes with strip-like (or beam) features. In addition, the quadratic energy functional can be seamlessly integrated into the level set framework that represents the geometry of the structure implicitly. The shape gradient of the quadratic energy functional is fully derived in the paper, and it is incorporated in the level set approach for topology optimization. The approach is demonstrated with benchmark examples of structure optimization and compliant mechanism design. The results presented show that this method is capable of generating strip-like (or beam) designs with specified feature width, which have highly desirable characteristics and practical benefits and uniquely distinguish the proposed method.