Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
On the Topological Derivative in Shape Optimization
SIAM Journal on Control and Optimization
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Structural optimization using sensitivity analysis and a level-set method
Journal of Computational Physics
An element-based displacement preconditioner for linear elasticity problems
Computers and Structures
Incorporating topological derivatives into shape derivatives based level set methods
Journal of Computational Physics
Feature sensitivity: A generalization of topological sensitivity
Finite Elements in Analysis and Design
A 199-line Matlab code for Pareto-optimal tracing in topology optimization
Structural and Multidisciplinary Optimization
A level set solution to the stress-based structural shape and topology optimization
Computers and Structures
Stress-based topology optimization using an isoparametric level set method
Finite Elements in Analysis and Design
Solving stress constrained problems in topology and material optimization
Structural and Multidisciplinary Optimization
Efficient generation of large-scale pareto-optimal topologies
Structural and Multidisciplinary Optimization
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The objective of this paper is to introduce and demonstrate an algorithm for stress-constrained topology optimization. The algorithm relies on tracking a level-set defined via the topological derivative. The primary advantages of the proposed method are: (1) the stresses are well-defined at all points within the evolving topology, (2) the finite-element stiffness matrices are well-conditioned, making the analysis robust and efficient, (3) the level-set is tracked through a simple iterative process, and (4) the stress constraint is precisely satisfied at termination. The proposed algorithm is illustrated through numerical experiments in 2D and 3D.