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
On some techniques for approximating boundary conditions in the finite element method
Modelling 94 Proceedings of the 1994 international symposium on Mathematical modelling and computational methods
Structural boundary design via level set and immersed interface methods
Journal of Computational Physics
Computational techniques for materials, composites and composite structures
SIAM Journal on Optimization
Structural optimization using sensitivity analysis and a level-set method
Journal of Computational Physics
Shape and topology optimization of compliant mechanisms using a parameterization level set method
Journal of Computational Physics
A study on X-FEM in continuum structural optimization using a level set model
Computer-Aided Design
On projection methods, convergence and robust formulations in topology optimization
Structural and Multidisciplinary Optimization
A level set solution to the stress-based structural shape and topology optimization
Computers and Structures
Sensitivity filtering from a continuum mechanics perspective
Structural and Multidisciplinary Optimization
Level-set methods for structural topology optimization: a review
Structural and Multidisciplinary Optimization
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This paper studies level set topology optimization of structures predicting the structural response by the eXtended Finite Element Method (XFEM). In contrast to Ersatz material approaches, the XFEM represents the geometry in the mechanical model by crisp boundaries. The traditional XFEM approach augments the approximation of the state variable fields with a fixed set of enrichment functions. For complex material layouts with small geometric features, this strategy may result in interpolation errors and non-physical coupling between disconnected material domains. These defects can lead to numerical instabilities in the optimized material layout, similar to checker-board patterns found in density methods. In this paper, a generalized Heaviside enrichment strategy is presented that adapts the set of enrichment functions to the material layout and consistently interpolates the state variable fields, bypassing the limitations of the traditional approach. This XFEM formulation is embedded into a level set topology optimization framework and studied with "material-void" and "material-material" design problems, optimizing the compliance via a mathematical programming method. The numerical results suggest that the generalized formulation of the XFEM resolves numerical instabilities, but regularization techniques are still required to control the optimized geometry. It is observed that constraining the perimeter effectively eliminates the emergence of small geometric features. In contrast, smoothing the level set field does not provide a reliable geometry control but mainly improves the convergence rate of the optimization process.