Topics on variational principles in engineering

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Abstract

First International Symposium on Flutter and its Application (May 15-17, 2016. Mielparque-tokyo), Minato-ku, Tokyo, Japan

More or less, the objectives of the engineering are to find optimal solution for the design of the products. Classically the variational methods have been used to find the optimal design in the engineering fields. So many numerical solutions are based upon the variational methods or its similar approaches even if the variational principle does not exist. Variational principles in the fluid dynamics has not been established yet, while those in elasticity and plasticity and optimal control theory have been highly confirmed and applied to actual problems. In this presentation, the methods of calculus variations are reviewed in the fields of structure and elasticity, optimal control theory and fluid dynamics. Firstly the fields of elasticity and optimal control theory are briefly reviewed. The details of them are not discussed here. Focusing on the fluid dynamics, a process of deriving the Hamilton’s principle is shown toward the applications for fluid-structure interaction problems like flutter or other interdisciplinary problems in engineering. The principle of virtual work is applied to the governing equations with boundary conditions. The conservation laws of mass and energy as well as the geometrical boundary conditions are treated as subsidiary conditions. In the present approach, a new concept of substantial variations of the state variables is introduced in order to describe the transportation terms and subsidiary conditions in a simple manner. It is a classical approach but might be useful for the development of computer aided design tools for aeroelasticity system and its optimal design.

形態: カラー図版あり

Physical characteristics: Original contains color illustrations

資料番号: AA1630046041

レポート番号: JAXA-SP-16-008E

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