Abstract

Lattice structures exhibit unique properties including a large surface area and a highly distributed load-path. This makes them very effective in engineering applications where weight reduction, thermal dissipation, and energy absorption are critical. Furthermore, with the advent of additive manufacturing (AM), lattice structures are now easier to fabricate. However, due to inherent surface complexity, their geometric construction can pose significant challenges. A classic strategy for constructing lattice structures exploits analytic surface–surface intersection; this, however, lacks robustness and scalability. An alternate strategy is voxel mesh-based isosurface extraction. While this is robust and scalable, the surface quality is mesh-dependent, and the triangulation will require significant postdecimation. A third strategy relies on explicit geometric stitching where tessellated open cylinders are stitched together through a series of geometric operations. This was demonstrated to be efficient and scalable, requiring no postprocessing. However, it was limited to lattice structures with uniform beam radii. Furthermore, existing algorithms rely on explicit convex-hull construction which is known to be numerically unstable. In this paper, a combinatorial stitching strategy is proposed where tessellated open cylinders of arbitrary radii are stitched together using topological operations. The convex hull construction is handled through a simple and robust projection method, avoiding expensive exact-arithmetic calculations and improving the computational efficiency. This is demonstrated through several examples involving millions of triangles. On a typical eight-core desktop, the proposed algorithm can construct approximately up to a million cylinders per second.

References

References
1.
Gibson
,
L. J.
, and
Ashby
,
M. F.
,
1999
,
Cellular Solids: Structure and Properties
,
Cambridge University Press
,
Cambridge
.
2.
Beyer
,
C.
, and
Figueroa
,
D.
,
2016
, “
Design and Analysis of Lattice Structures for Additive Manufacturing
,”
ASME J. Manuf. Sci. Eng.
,
138
(
12
), p.
121014
. 10.1115/1.4033957
3.
Tao
,
W.
, and
Leu
,
M. C.
,
2016
, “
Design of Lattice Structure for Additive Manufacturing
,”
International Symposium on Flexible Automation (ISFA)
,
Columbus, OH
,
Aug. 1–3
, IEEE, pp.
325
332
.
4.
Aremu
,
A.
,
Maskery
,
I.
,
Tuck
,
C.
,
Ashcroft
,
I.
,
Wildman
,
R.
, and
Hague
,
R.
,
2014
, “
A Comparative Finite Element Study of Cubic Unit Cells for Selective Laser Melting
,”
The Twenty-Fifth Annual International Solid Freeform Fabrication (SFF) Symposium—An Additive Manufacturing Conference
,
University of Texas in Austin
,
Aug.
, pp.
4
6
.
5.
Yan
,
C.
,
Hao
,
L.
,
Hussein
,
A.
, and
Raymont
,
D.
,
2012
, “
Evaluations of Cellular Lattice Structures Manufactured Using Selective Laser Melting
,”
Int. J. Mach. Tools Manuf.
,
62
(
Nov.
), pp.
32
38
. 10.1016/j.ijmachtools.2012.06.002
6.
Wang
,
H.
,
Chen
,
Y.
, and
Rosen
,
D. W.
,
2005
, “
A Hybrid Geometric Modeling Method for Large Scale Conformal Cellular Structures
,”
ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
,
Long Beach, CA
,
Sept. 24–28
, American Society of Mechanical Engineers, pp.
421
427
.
7.
Bourell
,
D. L.
,
Rosen
,
D. W.
, and
Leu
,
M. C.
,
2014
, “
The Roadmap for Additive Manufacturing and Its Impact
,”
3D Print. Addit. Manuf.
,
1
(
1
), pp.
6
9
. 10.1089/3dp.2013.0002
8.
Shewchuk
,
J. R.
,
1997
, “
Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric Predicates
,”
Discrete Comput. Geom.
,
18
(
3
), pp.
305
363
. 10.1007/PL00009321
9.
Biermann
,
H.
,
Kristjansson
,
D.
, and
Zorin
,
D.
,
2001
, “
Approximate Boolean Operations on Free-Form Solids
,”
Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques
,
New York
,
Jan.
, ACM, pp.
185
194
.
10.
Aremu
,
A.
,
Brennan-Craddock
,
J.
,
Panesar
,
A.
,
Ashcroft
,
I.
,
Hague
,
R.
,
Wildman
,
R.
, and
Tuck
,
C.
,
2017
, “
A Voxel-Based Method of Constructing and Skinning Conformal and Functionally Graded Lattice Structures Suitable for Additive Manufacturing
,”
Addit. Manuf.
,
13
(
Jan.
), pp.
1
13
. 10.1016/j.addma.2016.10.006
11.
Panesar
,
A.
,
Abdi
,
M.
,
Hickman
,
D.
, and
Ashcroft
,
I.
,
2018
, “
Strategies for Functionally Graded Lattice Structures Derived Using Topology Optimisation for Additive Manufacturing
,”
Addit. Manuf.
,
19
(
Jan.
), pp.
81
94
. 10.1016/j.addma.2017.11.008
12.
Meyer
,
F.
,
1992
, “
Mathematical Morphology: From Two Dimensions to Three Dimensions
,”
J. Microsc.
,
165
(
1
), pp.
5
28
. 10.1111/jmi.1992.165.issue-1
13.
Chougrani
,
L.
,
Pernot
,
J.-P.
,
Veron
,
P.
, and
Abed
,
S.
,
2017
, “
Lattice Structure Lightweight Triangulation for Additive Manufacturing
,”
Comput. Aided Des.
,
90
(
Sept.
), pp.
95
104
. 10.1016/j.cad.2017.05.016
14.
Srinivasan
,
V.
,
Mandal
,
E.
, and
Akleman
,
E.
,
2005
, “
Solidifying Wireframes
,”
Proceedings of the 2004 Bridges Conference on Mathematical Connections in Art, Music, and Science
,
Alberta, CA
.
15.
De Berg
,
M.
,
Van Kreveld
,
M.
,
Overmars
,
M.
, and
Schwarzkopf
,
O.
,
1997
,
Computational Geometry
,
Springer
,
New York
, pp.
1
17
.
16.
Robbins
,
J.
,
Owen
,
S.
,
Clark
,
B.
, and
Voth
,
T.
,
2016
, “
An Efficient and Scalable Approach for Generating Topologically Optimized Cellular Structures for Additive Manufacturing
,”
Addit. Manuf.
,
12(B)
(
July
), pp.
296
304
. 10.1016/j.addma.2016.06.013
17.
Preparata
,
F. P.
, and
Shamos
,
M. I.
,
2012
,
Computational Geometry: An Introduction
,
Springer Science & Business Media
,
New York
.
18.
Si
,
H.
,
2015
, “
Tetgen, a Delaunay-Based Quality Tetrahedral Mesh Generator
,”
ACM Trans. Math. Softw.
,
41
(
2
), pp.
11:1
11:36
. 10.1145/2732672
19.
He
,
L.
, and
Gilbert
,
M.
,
2015
, “
Rationalization of Trusses Generated Via Layout Optimization
,”
Struct. Multidiscipl. Optim.
,
52
(
4
), pp.
677
694
. 10.1007/s00158-015-1260-x
20.
Smith
,
C. J.
,
Gilbert
,
M.
,
Todd
,
I.
, and
Derguti
,
F.
,
2016
, “
Application of Layout Optimization to the Design of Additively Manufactured Metallic Components
,”
Struct. Multidiscipl. Optim.
,
54
(
5
), pp.
1297
1313
. 10.1007/s00158-016-1426-1
21.
Gupta
,
A.
,
Allen
,
G.
, and
Rossignac
,
J.
,
2018
, “
Quador: Quadric-of-Revolution Beams for Lattices
,”
Comput. Aided Des.
,
102
(
Sept.
), pp.
160
170
. 10.1016/j.cad.2018.04.015
22.
Xiong
,
G.
,
Musuvathy
,
S.
, and
Fang
,
T.
,
2013
, “
Automated Structured All-Quadrilateral and Hexahedral Meshing of Tubular Surfaces
,”
Proceedings of the 21st International Meshing Roundtable
,
San Jose, CA
,
Oct. 7–10
, Springer, pp.
103
120
.
23.
Suresh
,
K.
,
2013
, “
Efficient Generation of Large-Scale Pareto-Optimal Topologies
,”
Struct. Multidiscipl. Optim.
,
47
(
1
), pp.
49
61
. 10.1007/s00158-012-0807-3
24.
Suresh
,
K.
,
2010
, “
A 199-Line Matlab Code for Pareto-Optimal Tracing in Topology Optimization
,”
Struct. Multidiscipl. Optim.
,
42
(
5
), pp.
665
679
. 10.1007/s00158-010-0534-6
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