Contributions to automatic meshing in the AMORE scheme

Abstract

Traditional Finite Element (FE) analysis requires the discretisation of continuous bodies into connected meshes of triangles and quadrilaterals (in 2D; tetrahedrals [tet] and hexahedrals [hex] in 3D) elements. Besides the restrictions due to compatibility of adjacent elements, one primary concern regarding mesh generation is that of minimizing the distortion of elements and the number of distorted elements so as to reduce the discretisation error. This has generally steered research in 2D mesh generation techniques away from grid-based methods, which tends to generate significant numbers of distorted elements; additionally, such methods are generally not considered at all in 3D mesh generation. Furthermore, significant amounts of man-hours are used during the meshing phase of FE analyses to partition and prescribe element types, where the ability to mesh portions of the geometry with hex elements is preferred over using tet elements in the mesh. The recent advances in the theory of Overlapping Finite Elements (OFE) now allow for the use of distorted elements without compromising on the accuracy of the FE analysis. However, a trade-off arises because more degrees of freedom (DOFs) are required at triangular (and tetrahedral) nodes. We propose the reintroduction of optimised 2D grid-based mesh generation techniques to decrease the DOFs in a way that is generalizable to arbitrary 3D geometries, as part of a step towards a truly automated meshing paradigm, referred to as the Automatic Meshing with Overlapping and Regular Elements (AMORE), which requires minimal-to-no input from the engineer.