2024-03-28T21:06:57Z
https://nagoya.repo.nii.ac.jp/oai
oai:nagoya.repo.nii.ac.jp:02001354
2023-01-16T05:11:58Z
312:313:314
Shape optimization of running shoes with desired deformation properties
Nonogawa, Mai
Takeuchi, Kenzen
Azegami, Hideyuki
Running shoes
Hyper-elastic material
Shape optimization
Boundary value problem
H^1 gradient method
The present paper describes a shape optimization procedure for designing running shoes, focusing on two mechanical properties, namely, the shock absorption and the stability keeping the right posture. These properties are evaluated from two deformations of a sole at characteristic timings during running motion. We define approximate planes for the deformations of sole’s upper boundary by least squares method. Using the planes, we choose the tilt angle in the shoe width direction at the mid stance phase of running motion as an objective function representing the stability, and the sunk amount at the contact phase of running motion as a constraint function representing the shock absorption. We assume that the sole is a bonded structure of soft and hard hyper-elastic materials, and the bonding and side boundaries are variable. In this study, we apply the formulation of nonparametric shape optimization to the sole considering finite deformation and contact condition of the bottom of the sole with the ground. Shape derivatives of the cost (objective and constraint) functions are obtained using the adjoint method. The H^1 gradient method using these shape derivatives is applied as an iterative algorithm. To solve this optimization problem, we developed a computer program combined with some commercial softwares. The validity of the optimization method is confirmed by numerical examples.
journal article
Springer
2020-09
application/pdf
Structural and Multidisciplinary Optimization
3
62
1535
1546
1615-147X
https://nagoya.repo.nii.ac.jp/record/2001354/files/main.pdf
eng
https://doi.org/10.1007/s00158-020-02560-0