An automatic approach to constrained quadrilateral mesh generation

Abstract

Purpose

Arbitrary constraints might be included into the problem domain in many engineering applications, which represent specific features such as multi-domain interfaces, cracks with small yield stresses, stiffeners attached on the plate for reinforcement and so on. To imprint these constraints into the final mesh, additional techniques need to be developed to treat these constraints properly.

Design/methodology/approach

This paper proposes an automatic approach to generate quadrilateral meshes for the geometric models with complex feature constraints. Firstly, the region is decomposed into sub-regions by the constraints, and then the quadrilateral mesh is generated in each sub-region that satisfies the constraints. A method that deals with constraint lines and points is presented. A distribution function is proposed to represent the distribution of mesh size over the region by using the Laplace equation. The density lines and points can be specified inside the region and reasonable mesh size distribution can be obtained by solving the Laplace equation.

Findings

An automatic method to define sub-regions is presented, and the user interaction can be avoided. An algorithm for constructing loops from constraint lines is proposed, which can deal with the randomly distributed constraint lines in a general way. A method is developed to deal with constraint points and quality elements can be generated around constraint points. A function defining the distribution of mesh size is put forward. The examples of constrained quadrilateral mesh generation in actual engineering analysis are presented to show the performance of the approach.

Originality/value

An automatic approach to constrained quadrilateral mesh generation is presented in this paper. It can generate required quality meshes for special applications with complex internal feature constraints.

Citation

Ma, X. and Sun, L. (2020), "An automatic approach to constrained quadrilateral mesh generation", Engineering Computations, Vol. 37 No. 3, pp. 929-951. https://doi.org/10.1108/EC-03-2019-0114