Superellipse

Superellipse

Distribution of stresses and strains in roads

Published in Bernardo Caicedo, Geotechnics of Roads, 2021

To discretize the uniform load, a rectangle of 0.3 m × 0.18 m, which circumscribes the superellipse, is divided into 48 × 48 rectangular areas. Therefore, the size of each rectangular area is Δx × Δy, where Δx = 0.3/48 = 0.00625 m and Δy = 0.18/48 = 0.00375 m.

Explicit multi-material topology optimization embedded with variable-size movable holes using moving morphable bars

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Journal Information

Published in Engineering Optimization, 2021

Xuan Wang, Kai Long, Zeng Meng, Bo Yu, Changzheng Cheng

For holes of regular shape (e.g. circle, ellipse, superellipse), the corresponding level-set function can be simply expressed in general form as follows: with Here, are local coordinates on the embedded hole. θ is the rotation angle of the embedded hole relative to the horizontal direction. and are the horizontal and vertical coordinates of a specified reference point on the embedded hole. For illustration purposes, Equation (8) gives the level-set function representing a rounded rectangular hole: where the parameters a and b denote semi-major and semi-minor lengths of a rounded rectangular hole, respectively.

Bimanual robot control for surface treatment tasks

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Published in International Journal of Systems Science, 2022

Alberto García, J. Ernesto Solanes, Luis Gracia, Pau Muñoz-Benavent, Vicent Girbés-Juan, Josep Tornero

As shown in Figure 3, the equation above describes a rectangle with smoothed corners, with for its short side and for its long side, by attaching a rectangle to two offseted halfs of an even-sided superellipse.

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Distribution of stresses and strains in roads

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