Abstract
We present a free-form optimization method for designing the optimal shape of a shell structure with curvature constraint. Compliance is minimized under the volume and the state equation constraints. In addition, a target mean curvature of the surface is considered as the equality constraint in order to control the free-form of the shell. It is assumed that a shell is arbitrarily varied in the out-of-plane direction to the surface to create the optimal free-form. A parameter-free, or a node-based shape optimization problem is formulated in a distributed-parameter system based on the variational method. The distribution of the discrete mean curvature is calculated by the area strain obtained from the material derivative formula. The shape gradient function for this problem is theoretically derived using the Lagrange multiplier method and the adjoint variable method, and is applied to the H1 gradient method for shells. With the proposed method, the optimal free-form of a shell structure with curvature constraint can be efficiently determined. The validity and effectiveness of the method is verified through the numerical examples and the influence of the curvature constraint is demonstrated.
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Acknowledgements
This work was supported by a grant-in-aid from the Research Center for Smart Vehicles at Toyota Technological Institute.
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Shimoda, M., Ikeya, K. (2019). Free-Form Optimization of A Shell Structure with Curvature Constraint. In: Andrés-Pérez, E., González, L., Periaux, J., Gauger, N., Quagliarella, D., Giannakoglou, K. (eds) Evolutionary and Deterministic Methods for Design Optimization and Control With Applications to Industrial and Societal Problems. Computational Methods in Applied Sciences, vol 49. Springer, Cham. https://doi.org/10.1007/978-3-319-89890-2_25
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DOI: https://doi.org/10.1007/978-3-319-89890-2_25
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