Solution of Shape Optimization Problem and Its Application to Product Design

  • Hideyuki AzegamiEmail author
Conference paper
Part of the Mathematics for Industry book series (MFI, volume 26)


In this paper, we define shape optimization problems as problems of finding the shapes of domains in which boundary value problems of partial differential equations are defined. A domain mapping from an initial domain to a new domain is chosen as the design variable. Functionals of the design variable and the solution to the boundary value problem are used as cost functions. In this paper, the formulation of the shape optimization problem and a numerical method of solving the problem are presented. In addition, our subsequent works applying this method to product design are introduced: (1) shape optimization of a link mechanism, (2) shape optimization for suppressing brake squeal, (3) a method of designing beads in a shell structure, (4) shape optimization of a flow field to improve hydrodynamic stability, and (5) shape optimization of an electrostatic capacitive sensor.


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© Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  1. 1.Graduate School of Information ScienceNagoya UniversityChikusa-kuJapan

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