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Shape Optimization by Generalized J-Integral in Poisson’s Equation with a Mixed Boundary Condition

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Mathematical Analysis of Continuum Mechanics and Industrial Applications II (CoMFoS 2016)

Part of the book series: Mathematics for Industry ((MFI,volume 30))

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Abstract

Generalized J-integral is the tool for shape sensitivity analysis of singular points in boundary value problem for partial differential equations. We can solve shape optimization problems of singular points by using Generalized J-integral and \(H^{1}\)-gradient method (Azegami’s method). Here, the mathematical method is proposed to examine shape optimization in detail by dividing the sensitivity on sets of singular points, and apply the method to Poisson’s equation defined on a polygonal domain with mixed boundary condition. The boundary divides into the parts that Dirichlet boundary condition, Neumann boundary condition, and the joint of them are given. It is examined about each role of the parts of boundary in shape optimization process on a numerical example of finite element analysis.

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Acknowledgements

I am deeply grateful to Prof. H. Azegami and M. Kinumra. This work was supported by JSPS KAKENHI Grant Number 16K05285.

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Authors and Affiliations

  1. Hiroshima Kokusai Gakuin University, Hiroshima, Japan

    Kohji Ohtsuka

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  1. Kohji Ohtsuka
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Correspondence to Kohji Ohtsuka .

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Editors and Affiliations

  1. Kanazawa University, Kanazawa, Ishikawa, Japan

    Patrick van Meurs

  2. Kanazawa University, Kanazawa, Ishikawa, Japan

    Masato Kimura

  3. Kanazawa University, Kanazawa, Ishikawa, Japan

    Hirofumi Notsu

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Ohtsuka, K. (2018). Shape Optimization by Generalized J-Integral in Poisson’s Equation with a Mixed Boundary Condition. In: van Meurs, P., Kimura, M., Notsu, H. (eds) Mathematical Analysis of Continuum Mechanics and Industrial Applications II. CoMFoS 2016. Mathematics for Industry, vol 30. Springer, Singapore. https://doi.org/10.1007/978-981-10-6283-4_7

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  • DOI: https://doi.org/10.1007/978-981-10-6283-4_7

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-6282-7

  • Online ISBN: 978-981-10-6283-4

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