Generating optimal topologies in structural design using a homogenization method
Computer Methods in Applied Mechanics and Engineering
Semi-Lagrangian methods for level set equations
Journal of Computational Physics
Principles of CAD/CAM/CAE Systems
Principles of CAD/CAM/CAE Systems
A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model
International Journal of Computer Vision
Structural optimization using sensitivity analysis and a level-set method
Journal of Computational Physics
Shape sensitivity of constructively represented geometric models
Computer Aided Geometric Design
A study on X-FEM in continuum structural optimization using a level set model
Computer-Aided Design
A semi-Lagrangian level set method for structural optimization
Structural and Multidisciplinary Optimization
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Engineering features are regular and simple shape units containing specific engineering significance. It is useful to combine feature design with structural optimization. This paper presents a generic method to design engineering features for level set based structural optimization. A Constructive Solid Geometry based Level Sets (CSGLS) description is proposed to represent a structure based on two types of basic entities: a level set model containing either a feature shape or a freeform boundary. By treating both entities implicitly and homogeneously, the optimal design of engineering features and freeform boundary are unified under the level set framework. For feature models, constrained affine transformations coupled with an accurate particle level set updating scheme are utilized to preserve feature characteristics, where the design velocity approximates continuous shape variation via a least squares fitting. Meanwhile, freeform models undergo a standard shape and topology optimization using a semi-Lagrangian level set scheme. With this method, various feature requirements can be translated into a CSGLS model, and the constrained motion provides flexible mechanisms to design features at different stages of the model tree. As a result, a truly optimal structure with engineering features can be created in a convenient way. Several numerical examples are provided to demonstrate the applicability and potential of this method.