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Consistent pseudo-mode informed topology optimization for structural stability applications
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DOI：10.1016/j.cma.2020.113276.png)
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Abstract
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This study presents a computational strategy to address the challenge associated with the emergence of spurious modes in topology optimization with global stability considerations. In a discrete setting these modes pertain to the very low stiffness regions of the design domain occupied by hair-like elements with vanishing cross-sections and often surface when the computational optimizer tries to make dramatic changes to the topology. We demonstrate the inability of the classical approach to discrete topology optimization in capturing and repositioning these modes, and provide an elegant alternative which rests on the idea of expanding the set of design variables to include an indicator set, that similar to element densities in continuum domain, allow for quick clustering of contributing and non-contributing elements. The interplay between the set of basic design variables and the indicator set is shown to have the ability to identify the dominant eigenpairs that get pushed away in the presence of spurious modes and to effectively reposition them back to their original place where accurate values for the objective, constraints and the associated eigen-sensitivities are needed. A set of 2D frame structural topology optimization problems are used to demonstrate the effectiveness of the proposed methodology as well as the impact of parameters that affect the size of the design space, such as minimum to maximum thickness ratio and constraint bounds, on the optimized topology. (C) 2020 Elsevier B.V. All rights reserved.
Keywords:
Topology optimization
Computational design
Stability constraints
Spurious modes
Eigenvalue maximization
Eigen-sensitivity
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