On the Topological Derivative in Shape Optimization
SIAM Journal on Control and Optimization
Structural optimization using sensitivity analysis and a level-set method
Journal of Computational Physics
Algorithm 887: CHOLMOD, Supernodal Sparse Cholesky Factorization and Update/Downdate
ACM Transactions on Mathematical Software (TOMS)
A level set solution to the stress-based structural shape and topology optimization
Computers and Structures
Topology-adaptive interface tracking using the deformable simplicial complex
ACM Transactions on Graphics (TOG)
Parameter free shape and thickness optimisation considering stress response
Structural and Multidisciplinary Optimization
Guide to Computational Geometry Processing: Foundations, Algorithms, and Methods
Guide to Computational Geometry Processing: Foundations, Algorithms, and Methods
Multiphase flow of immiscible fluids on unstructured moving meshes
EUROSCA'12 Proceedings of the 11th ACM SIGGRAPH / Eurographics conference on Computer Animation
Delaunay Mesh Generation
A mesh evolution algorithm based on the level set method for geometry and topology optimization
Structural and Multidisciplinary Optimization
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We introduce the Deformable Simplicial Complex method to topology optimization as a way to represent the interface explicitly yet being able to handle topology changes. Topology changes are handled by a series of mesh operations, which also ensures a well-formed mesh. The same mesh is therefore used for both finite element calculations and shape representation. In addition, the approach unifies shape and topology optimization in a complementary optimization strategy. The shape is optimized on the basis of the gradient-based optimization algorithm MMA whereas holes are introduced using topological derivatives. The presented method is tested on two standard minimum compliance problems which demonstrates that it is both simple to apply, robust and efficient.