Incorporating topological derivatives into level set methods
Journal of Computational Physics
Structural optimization using sensitivity analysis and a level-set method
Journal of Computational Physics
Velocity Extension for the Level-set Method and Multiple Eigenvalues in Shape Optimization
SIAM Journal on Control and Optimization
An extended level set method for shape and topology optimization
Journal of Computational Physics
Overview on Innovation of Topology Optimization in Vehicle CAE
ICECT '09 Proceedings of the 2009 International Conference on Electronic Computer Technology
A level set method for structural shape and topology optimization using radial basis functions
Computers and Structures
Application of Topology Optimization to Commercial Vehicle Cab Design
ICMTMA '09 Proceedings of the 2009 International Conference on Measuring Technology and Mechatronics Automation - Volume 02
Finite Elements in Analysis and Design
An isoparametric approach to level set topology optimization using a body-fitted finite-element mesh
Computers and Structures
Stress-constrained topology optimization: a topological level-set approach
Structural and Multidisciplinary Optimization
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This paper presents a novel framework for evaluating the shape sensitivities of the von Mises stress function using an isoparametric finite-element formulation. The use of the isoparametric formulation allows us to apply the level set method to structures that are confined to irregularly shaped domains and therefore must be modeled using body-fitted, nonuniform finite element meshes. The shape sensitivities of the von Mises stress function are evaluated on this nonuniform mesh and mapped isoparametrically to a uniform Cartesian grid on which the Hamilton-Jacobi equation is solved. The paper also introduces a new approach to the enforcement of volume constraints based on the augmented Lagrangian formulation. The method is demonstrated on a series of two-dimensional problems including an isoparametric variation of the classic L-bracket problem. We show that the isoparametric level set method produces converged, feasible designs whose performance is comparable to SIMP results in terms of their final objective value.