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A spatial kernel approach for topology optimization
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DOI：10.1016/j.cma.2019.112794.png)
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Abstract
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This paper introduces a spatial kernel approach for topology optimization. This kernel influences the material distribution in the final design. The resulting spatial variables not only have physical meaning - such as the mass of the part, a stiffness gradient, or a local strengthening; but the spatial variables can also tailor the structural performances - such as the occupant protection - of the resulting design. This means only a few spatial variables are needed to represent a design otherwise described using millions of topology design variables. This ability to restate the problem in terms of the spatial variables unlocks new design schemes. Here we use a few spatial variables to address (i) constrained topology design optimization, (ii) to compute the derivatives of the constraints using numerical finite differences, and (iii) to build metamodels to the topology design optimization results. A significant benefit is therefore that complex design problems can be considered: the mechanics can include highly nonlinear events, while the use of metamodels allows a diversity of design optimization studies. Examples, including a simplified side impact occupant protection problem, are used to demonstrate. (C) 2019 Elsevier B.V. All rights reserved.
Keywords:
Spatial kernel
Topology optimization
Projected subgradient method
Occupant protection
Multi-level design optimization
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