Computational design
Besides modeling, the field of computational inverse design can also benefit from the use of FEM models. Building up the \class{Fem} class, the objective is to find a topological structure of a continuum system based on a desired deformations or compliance. One widely adopted method is the Solid Isotropic Material with Penalization (SIMP) approach, which is a commonly used material interpolation technique in topology optimization \cite{Bendsoe2003}. In the SIMP method, each finite element
where
where
The optimization routine in the Sorotoki
framework is incorporated into the Fem
class and can be invoked by utilizing the command fem.optimize('type')
, where 'type'
represents the optimization problem at hand. For minimizing compliance, the cost function is self-adjoint \cite{Bendsoe2003}, hence objective function and constraints are linear operators. However, when dealing with compliant mechanisms, it is necessary to specify the selection vector fem.addOutput(id)
command. The value of id
represents the nodal indices of interest, which can be identified using the fem.Mesh.findNode
functionality.
Example: optimization of linear elastic beam
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Krister Svanberg. The method of moving asymptotes\ifmmode —\else —\fi a new method for structural optimization. International Journal for Numerical Methods in Engineering, 24(2):359–373, 1987. doi:10.1002/nme.1620240207. ↩
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Krister Svanberg. Mma and gcmma-two methods for nonlinear optimization. vol, 1:1–15, 2007. ↩
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Brandon Caasenbrood, Alexander Pogromsky, and Henk Nijmeijer. Dynamic modeling of hyper-elastic soft robots using spatial curves. IFAC Proceedings Volumes (IFAC-PapersOnline), 2020. ↩