3 years ago
Heaviside projection–based aggregation in stress‐constrained topology optimization
The paper introduces an approach to stress‐constrained topology optimization through
Heaviside projection–based constraint aggregation. The aggregation is calculated by
integrating Heaviside projected local stresses over the design domain, and then, it
is normalized over the total material volume. Effectively, the normalized integral
measures the volume fraction of the material that has violated the stress constraint.
Hence, with the Heaviside aggregated constraint, we can remove the stress failed material
from the final design by constraining the integral to a threshold value near zero.
An adaptive strategy is developed to select the threshold value for ensuring that
the optimized design is conservative. By adding a stress penalty factor to the integrand,
the Heaviside aggregated constraint can further penalize high stresses and becomes
more stable and less sensitive to the selection of the threshold value. Our two‐dimensional
and three‐dimensional numerical experiments demonstrate that the single Heaviside
aggregated stress constraint can efficiently control the local stress level. Compared
with the traditional approaches based on the Kreisselmeier‐Steinhauser and p‐norm
aggregations, the Heaviside aggregation–based single constraint can substantially
reduce computational cost on sensitivity analysis. These advantages make it possible
to apply the proposed approach to large‐scale stress‐constrained problems.
Publisher URL: https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.5828
DOI: 10.1002/nme.5828
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