Bounds for decoupled design and analysis discretizations in topology optimization
Deepak K. Gupta (TU Delft - Computational Design and Mechanics)
G.J. van der Veen (TU Delft - Computational Design and Mechanics)
A.M. Aragon (TU Delft - Computational Design and Mechanics)
Matthijs Langelaar (TU Delft - Computational Design and Mechanics)
Fred Van Keulen (TU Delft - Computational Design and Mechanics)
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Abstract
Topology optimization formulations using multiple design variables per finite element have been proposed to improve the design resolution. This paper discusses the relation between the number of design variables per element and the order of the elements used for analysis. We derive that beyond a maximum number of design variables, certain sets of material distributions cannot be discriminated based on the corresponding analysis results. This makes the design description inefficient and the solution of the optimization problem non-unique. To prevent this, we establish bounds for the maximum number of design variables that can be used to describe the material distribution for any given finite element scheme without introducing non-uniqueness.
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