# A novel three-dimensional mesh deformation method based on sphere relaxation

## Abstract

In our previous work (2013) [19], we developed a disk relaxation based mesh deformation method for two-dimensional mesh deformation. In this paper, the idea of the disk relaxation is extended to the sphere relaxation for three-dimensional meshes with large deformations. We develop a node based pre-displacement procedure to apply initial movements on nodes according to their layer indices. Afterwards, the nodes are moved locally by the improved sphere relaxation algorithm to transfer boundary deformations and increase the mesh quality. A three-dimensional mesh smoothing method is also adopted to prevent the occurrence of the negative volume of elements, and further improve the mesh quality. Numerical applications in three-dimension including the wing rotation, bending beam and morphing aircraft are carried out. The results demonstrate that the sphere relaxation based approach generates the deformed mesh with high quality, especially regarding complex boundaries and large deformations.

- Authors:

- Department of Mechanics & Engineering Science, College of Engineering, Peking University, Beijing, 100871 (China)
- (China)

- Publication Date:

- OSTI Identifier:
- 22465662

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Computational Physics

- Additional Journal Information:
- Journal Volume: 298; Other Information: Copyright (c) 2015 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9991

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; BENDING; LAYERS; MESH GENERATION; RELAXATION; ROTATION; SPHERES; THREE-DIMENSIONAL CALCULATIONS; TWO-DIMENSIONAL CALCULATIONS

### Citation Formats

```
Zhou, Xuan, Institute of Applied Physics and Computational Mathematics, Beijing, 100094, and Li, Shuixiang, E-mail: lsx@pku.edu.cn.
```*A novel three-dimensional mesh deformation method based on sphere relaxation*. United States: N. p., 2015.
Web. doi:10.1016/J.JCP.2015.05.046.

```
Zhou, Xuan, Institute of Applied Physics and Computational Mathematics, Beijing, 100094, & Li, Shuixiang, E-mail: lsx@pku.edu.cn.
```*A novel three-dimensional mesh deformation method based on sphere relaxation*. United States. doi:10.1016/J.JCP.2015.05.046.

```
Zhou, Xuan, Institute of Applied Physics and Computational Mathematics, Beijing, 100094, and Li, Shuixiang, E-mail: lsx@pku.edu.cn. Thu .
"A novel three-dimensional mesh deformation method based on sphere relaxation". United States. doi:10.1016/J.JCP.2015.05.046.
```

```
@article{osti_22465662,
```

title = {A novel three-dimensional mesh deformation method based on sphere relaxation},

author = {Zhou, Xuan and Institute of Applied Physics and Computational Mathematics, Beijing, 100094 and Li, Shuixiang, E-mail: lsx@pku.edu.cn},

abstractNote = {In our previous work (2013) [19], we developed a disk relaxation based mesh deformation method for two-dimensional mesh deformation. In this paper, the idea of the disk relaxation is extended to the sphere relaxation for three-dimensional meshes with large deformations. We develop a node based pre-displacement procedure to apply initial movements on nodes according to their layer indices. Afterwards, the nodes are moved locally by the improved sphere relaxation algorithm to transfer boundary deformations and increase the mesh quality. A three-dimensional mesh smoothing method is also adopted to prevent the occurrence of the negative volume of elements, and further improve the mesh quality. Numerical applications in three-dimension including the wing rotation, bending beam and morphing aircraft are carried out. The results demonstrate that the sphere relaxation based approach generates the deformed mesh with high quality, especially regarding complex boundaries and large deformations.},

doi = {10.1016/J.JCP.2015.05.046},

journal = {Journal of Computational Physics},

issn = {0021-9991},

number = ,

volume = 298,

place = {United States},

year = {2015},

month = {10}

}