2. Shape optimization analysis

Shape optimization analysis

  • Graduate School of Informatics
  • Department of Complex Systems Science
  • Complex Systems Computing

Hideyuki Azegami [Professor]


Outline of Seeds

In the design of a product such as vehicle, many numerical analyses are conducted. We are studying the theory and numeric solution of the shape optimization problem to connect the results of numerical analyses to an optimal design. It has so far been proved that shape optimization analyses for practical problems of elastic bodies, flow fields, heat conduction fields, electromagnetic fields, and those coupling fields can be conducted.
Moreover, the method which we developed is used also in a commercial software of structure optimal design.

Novelty and originality of this research

Optimal design is classified into two categories according to how to choose a design variable. One is the method of choosing the size of CAD as a design variable. This optimization problem is called a parametric optimization problem. Another is the method of choosing the function defining shape variation as a design variable. This method is called a nonparametric optimization problem. The feature of this research is applying the functional analysis to the latter.

Application and research area for Industry collaboration

A commercial software incorporating our method is being used in the industry. For practical problems which are not solved by the software, we would like to solve them by joint research with companies.

Key Takeaway

The optimum shape which could not be found by depending on engineer's intuition will be found by our method.


optimum design, shape optimization, topology optimization, CAD(computer aided design), CAE(computer aided engineering), finite-element method


  • shape optimization method


  • WO2003/017147 Domain shape optimization method

Monographs, Papers and Articles

  • Azegami, H., Regularized Solution to Shape Optimization Problem (in Japanese), Transactions of the Japan Society for Industrial and Applied Mathematics, 23(2), 2014, pp. 83-138
  • Kouhei Shintani, Hideyuki Azegami: Construction method of the cost function for the minimax shape optimization problem, JSIAM Letters, 5, 2013.09, pp. 61-64.
  • Hideyuki Azegami, Liren Zhou, Kimihiro Umemura, Naoya Kondo: Shape optimization for a link mechanism, Structural and Multidisciplinary Optimization, 48(1), 2013.02, pp. 115-125.
  • Hideyuki Azegami, Shota Fukumoto, Taiki Aoyama: Shape optimization of continua using {NURBS} as basis functions, Structural and Multidisciplinary Optimization, 47(2), 2013.01, pp. 247-258.