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Static and dynamic problem formulations for design optimization
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DOI：10.1007/s00158-014-1083-1.png)
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Abstract
En 中文
This paper concerns an issue that may arise in design optimization of dynamical systems that possess multiple equilibrium points. If one considers only such points, it is possible to pose optimization problems in which the state problem is treated as a static problem. This is attractive as it reduces the computational cost compared to approaches which account for the entire state trajectory. However, if the system has multiple equilibria, it could happen that the equilibrium point attained when the system was optimized has only a small region of attraction. This means that in order to attain the desired state, the system must be initialized in its close vicinity, something which may be difficult in practise. In the paper we demonstrate this issue by considering design optimization of Neuro-Mechanical Shape Memory Devices (NMSMDs), a type of mechatronic systems that take on prescribed shapes when subjected to certain input stimuli introduced by the authors in an earlier paper. The conclusion is that although the static problem formulation considered has some attractive features, the existence of multiple equilibria for the governing equations of NMSMDs seems to necessitate the use of dynamic problem formulations.
Keywords:
Optimal design
Nested and simultaneous formulations
Static and dynamic problems
Neuro-mechanical shape memory devices
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