Shape Optimization Problems Considering Material Non-linearity and Geometrical Non-linearity

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  • 208 材料非線形性と幾何学的非線形性を考慮した形状最適化問題

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This paper presents a numerical solution to boundary shape optimization problems of continua with respect to minimization problem of external work under a volume constraint taking into account material non-linearity and minimization problem of the time integration of squared error on the responded velocity and the prescribed velocity under a volume constraint taking into account geometrical non-linerity. Shape variation is described by using a one-parameter family of mappings defined in a domain where a continuum lies initially. The shape sensitivities are derived using the Lagrange multiplier method and the formula of the material derivative. A procedure to solve this problem using the traction method is presented, which one of the authors has proposed as an approach to solving domain optimization problems. The varidity of proposed method is verified by applying basic numerical examples.

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