Quad-Layer: Layered Quadrilateral Meshing of Narrow Two-Dimensional Domain by Bubble Packing and Chordal Axis Transformation

Author(s):  
Soji Yamakawa ◽  
Kenji Shimada

Abstract This paper presents a new computational method for quadrilateral meshing of a thin, or narrow, two-dimensional domain. An output mesh of our method is well-shaped and either single-layered, multi-layered, or partially multi-layered. Element sizes can be uniform or graded. A high quality, layered quadrilateral mesh is often required for finite element analyses of a narrow two-dimensional domain with a large deformation such as the analysis of rubber deformation or sheet metal forming. Our method consists of two steps: (1) extraction of the skeleton of a given domain by the discrete chordal axis transformation, and (2) discretization of the chordal axis into a set of line segments and conversion of each of the line segments to a single quadrilateral element or multiple layers of quadrilateral elements. In both steps we use a physically-based computational method called bubble packing to discretize a curve into a set of line segments of specified sizes. Experiments show that the accuracy of a large-deformation FEM analysis can be significantly improved by using a well-shaped quadrilateral mesh created by the proposed method.

2002 ◽  
Vol 124 (3) ◽  
pp. 564-573 ◽  
Author(s):  
Soji Yamakawa ◽  
Kenji Shimada

This paper presents a computational method for quadrilateral meshing of a thin, or narrow, two-dimensional domain for finite element analysis. The proposed method creates a well-shaped single-layered, multi-layered, or partially multi-layered quadrilateral mesh. Element sizes can be uniform or graded. A high quality, layered quadrilateral mesh is often required for finite element analysis of a narrow two-dimensional domain with a large deformation such as in the analysis of rubber deformation or sheet metal forming. Fully automated quadrilateral meshing is performed in two stages: (1) extraction of the skeleton of a given domain by discrete chordal axis transformation, and (2) discretization of the chordal axis into a set of line segments and conversion of each of the line segments to a single quadrilateral element or multiple layers of quadrilateral elements. In each step a physically-based computational method called bubble packing is applied to discretize a curve into a set of line segments of specified sizes. Experiments show that the accuracy of a large-deformation FEM analysis can be significantly improved by using a well-shaped quadrilateral mesh created by the proposed method.


2020 ◽  
Author(s):  
Bipul Hawlader ◽  
◽  
Chen Wang ◽  
Ripon Karmaker ◽  
Didier Perret ◽  
...  

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Xu Zhang ◽  
Hoang Nguyen ◽  
Jeffrey T. Paci ◽  
Subramanian K. R. S. Sankaranarayanan ◽  
Jose L. Mendoza-Cortes ◽  
...  

AbstractThis investigation presents a generally applicable framework for parameterizing interatomic potentials to accurately capture large deformation pathways. It incorporates a multi-objective genetic algorithm, training and screening property sets, and correlation and principal component analyses. The framework enables iterative definition of properties in the training and screening sets, guided by correlation relationships between properties, aiming to achieve optimal parametrizations for properties of interest. Specifically, the performance of increasingly complex potentials, Buckingham, Stillinger-Weber, Tersoff, and modified reactive empirical bond-order potentials are compared. Using MoSe2 as a case study, we demonstrate good reproducibility of training/screening properties and superior transferability. For MoSe2, the best performance is achieved using the Tersoff potential, which is ascribed to its apparent higher flexibility embedded in its functional form. These results should facilitate the selection and parametrization of interatomic potentials for exploring mechanical and phononic properties of a large library of two-dimensional and bulk materials.


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