27.11.2017  Original Article  Ausgabe 3/2018 Open Access
An enhanced approach to automatic decomposition of thinwalled components for hexahedraldominant meshing
 Zeitschrift:
 Engineering with Computers > Ausgabe 3/2018
1 Introduction
2 Related work
3 Longslender region identification
3.1 Overview
3.2 Identify candidate edges and faces

Dictionary 1: stores the two bounded candidate faces of each candidate edge, i.e., {edge: face 1, face 2};

Dictionary 2: stores the bounding candidate edges of each candidate face, i.e., {face: edge 1, edge 2, edge 3, ...};

Dictionary 3: stores the adjacent candidate faces of each candidate face, i.e., {face: face 1, face 2, face 3,...}. Two adjacent candidate faces share at least one candidate edge.
3.3 Identify TLoops and GLoops

Let \(P_{0}^{\prime }\) be the midpoint of the shortest candidate edge;

Start with \(P_{0}^{\prime }\) and walk along the closed curves on the slicing section. The ith end point and curve on the path will be stored as \(P_{i}^{\prime }\) and \(C_{i}^{\prime }\) respectively, as shown in Fig. 9b;

The candidate edge that \(P_{i}^{\prime }\) lies on is stored as E _{ i } and the candidate face that \(C_{i}^{\prime }\) lies on is stored as F _{ i }, as shown in Fig. 9d.
3.4 Group the end points of the edges of a GLoop
3.5 Identify and assess edges at the end of the wall faces

Type1: is an existing face in the model;

Type2: results from an offset cutting face;

Type3: results from a cutting face bounded by one or more existing edges at the end of the wall faces.
3.5.1 The net number of positive and negative singularities on a surface
3.5.2 Edge assessment and classification

Type3 edge: it cannot be used for constructing the cap face and no offset is required. This is the case when n _{1} > 1, e.g., Fig. 15g, h. The bounding edges of the cap face on this wall face will be determined later.
3.5.3 End point traversal
3.6 Define the cap face
3.6.1 Cutting face for the type2 cap face
3.6.2 Cutting face for the type3 cap face
3.7 Volume decomposition and longslender region identification

No cutting faces required: no decomposition is required as the entire region is a longslender region. The two cap faces will be the source and target faces in a swept mesh.

One cutting face required: this means that one cap face for the longslender region exists in the original model. After decomposition, the region bounded by the cap face is identified as a longslender region. The existing cap face and the cap face resulting from the cutting face on the other end will be the source and target faces. For example, the left longslender region in Fig. 4f has one cap face which exists and only one cutting face is generated.

Two cutting faces required: this means that no cap faces exist in the original model (the right longslender region in Fig. 4f). The region that contains the midpoint of the shortest edge in a GLoop will be identified as the longslender region. The two cap faces resulting from the cutting faces will be the source and target faces.
4 Results
Models  Time (s)  Number of longslender regions  Volume of longslender regions (%)  Volume of thinsheet and longslender region (%) 

a  1  4  17  100 
b  6  11  9  90 
c  1  2  1  100 
d  1  2  2  98 
e  59  72  8  99 
f  480  93  7  99 
4.1 DOF reduction

Tet mesh: the model is meshed with 10node tet elements of a size of 4 mm, Fig. 27c;

Isotropic hex for thinsheets: the thinsheets are meshed with isotropic 8node hex elements of 4 mm and the remainder is tet meshed, Fig. 27d;

Anisotropic hex for thinsheets: the thinsheets are meshed with anisotropic 8node hex element with an aspect ratio (lateral dimensions to thickness) varying up to 5 and the reminder is tet meshed, Fig. 27e;

Anisotropic hex for thinsheets and longslender regions: both the thinsheet and longslender regions are meshed with anisotropic 8node hex element with an aspect ratio varying up to 5 and with tet elements in the residual regions, Fig. 27f.
Analysis models  Tet for the whole model  Isotropic hex for thinsheets  Anisotropic hex for thinsheets  Anisotropic hex for thinsheets and longslender region 

DOF  2,191,611  572,706  388,803  129,897 
% Tet  100  26.1  17.7  5.9 
Analysis models  Tet for the whole model  Isotropic hex for thinsheets  Anisotropic hex for thinsheets  Anisotropic hex for thinsheet and longslender region 

Time/min  45  7  3  1.4 
% Tet  100  15.6  6.7  3.2 
5 Discussion
6 Conclusions

New sizing metrics are used to identify the longslender region, which has greatly simplified the process compared to existing techniques;

Procedures have been developed to assess if an offset is required at the ends of the longslender region which terminate with complex geometry. The cutting faces are generated directly at the end of the longslender region if no offset is required;

Significant DOF saving can be achieved by applying anisotropic hex elements to the identified longslender region.