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Computational Mechanics
Published in: Computational Mechanics 4/2016

01-10-2016 | Original Paper

Stress analysis of 3D complex geometries using the scaled boundary polyhedral finite elements

Authors: Hossein Talebi, Albert Saputra, Chongmin Song

Published in: Computational Mechanics | Issue 4/2016

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Abstract

While dominating the numerical stress analysis of solids, the finite element method requires a mesh to conform to the surface of the geometry. Thus the mesh generation of three dimensional complex structures often require tedious human interventions. In this paper, we present a formulation for arbitrary polyhedral elements based on the scaled boundary finite element method, which reduces the difficulties in automatic mesh generation. We also propose a simple method to generate polyhedral meshes with local refinements. The mesh generation method is based on combining an octree mesh with surfaces defined using signed distance functions. Through several numerical examples, we verify the results, study the convergence behaviour and depict the many advantages and capabilities of the presented method. This contribution is intended to assist us to eventually frame a set of numerical methods and associated tools for the full automation of the engineering analysis where minimal human interaction is needed.
previous article A regularized model for impact in explicit dynamics applied to the split Hopkinson pressure bar

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Literature
1.
Bazyar MH, Song C (2006) Time-harmonic response of non-homogeneous elastic unbounded domains using the scaled boundary finite-element method. Earthq Eng Struct Dyn 35(3):357–383CrossRef
2.
Bazyar MH, Song C (2006) Transient analysis of wave propagation in non-homogeneous elastic unbounded domains by using the scaled boundary finite-element method. Earthq Eng Struct Dyn 35(14):1787–1806CrossRef
3.
4.
Belytschko T, Parimi C, Moës N, Sukumar N, Usui S (2003) Structured extended finite element methods for solids defined by implicit surfaces. Int J Numer Methods Eng 56(4):609–635MATHCrossRef
5.
Benson D, Bazilevs Y, Hsu MC, Hughes T (2010) Isogeometric shell analysis: the reissner-mindlin shell. Comput Methods Appl Mech Eng 199(5):276–289MathSciNetMATHCrossRef
6.
Biabanaki S, Khoei A (2012) A polygonal finite element method for modeling arbitrary interfaces in large deformation problems. Comput Mech 50(1):19–33MathSciNetMATHCrossRef
7.
Bishop JE (2009) Simulating the pervasive fracture of materials and structures using randomly close packed voronoi tessellations. Comput Mech 44(4):455–471MATHCrossRef
8.
Bishop JE, Martinez MJ, Newell P, et al (2012) A finite-element method for modeling fluid-pressure induced discrete-fracture propagation using random meshes. In: 46th US rock mechanics/geomechanics symposium. American Rock Mechanics Association
9.
Bouchard P, Bay F, Chastel Y (2003) Numerical modelling of crack propagation: automatic remeshing and comparison of different criteria. Comput Methodsn Appl Mech Eng 192(35):3887–3908MATHCrossRef
10.
Bouchard PO, Bay F, Chastel Y, Tovena I (2000) Crack propagation modelling using an advanced remeshing technique. Comput Methodsn Appl Mech Eng 189(3):723–742MATHCrossRef
11.
Bower AF (2009) Applied mechanics of solids. CRC Press, New York
12.
Chen HH, Huang TS (1988) A survey of construction and manipulation of octrees. Comput Vis Graph Image Process 43(3):409–431CrossRef
13.
Chessa J, Belytschko T (2003) An enriched finite element method and level sets for axisymmetric two-phase flow with surface tension. Int J Numer Meth Eng 58(13):2041–2064MathSciNetMATHCrossRef
14.
15.
Chidgzey SR, Deeks AJ (2005) Determination of coefficients of crack tip asymptotic fields using the scaled boundary finite element method. Eng Fract Mech 72(13):2019–2036CrossRef
16.
Chiong I, Ooi ET, Song C, Tin-Loi F (2014) Scaled boundary polygons with application to fracture analysis of functionally graded materials. Int J Numer Meth Eng 98(8):562–589MathSciNetCrossRef
17.
Contreras D, Hitschfeld-Kahler N (2014) Generation of polyhedral delaunay meshes. Proc Eng 82:291–300CrossRef
18.
19.
Deeks A, Wolf J (2002) A virtual work derivation of the scaled boundary finite-element method for elastostatics. Comput Mech 28(6):489–504MathSciNetMATHCrossRef
20.
Dohrmann C, Heinstein M, Jung J, Key S, Witkowski W (2000) Node-based uniform strain elements for three-node triangular and four-node tetrahedral meshes. Int J Numer Meth Eng 47(9):1549–1568MATHCrossRef
21.
Dréau K, Chevaugeon N, Moës N (2010) Studied x-fem enrichment to handle material interfaces with higher order finite element. Comput Methods Appl Mech Eng 199(29):1922–1936MathSciNetMATHCrossRef
22.
Gain AL, Talischi C, Paulino GH (2014) On the virtual element method for three-dimensional linear elasticity problems on arbitrary polyhedral meshes. Comput Methods Appl Mech Eng 282:132–160MathSciNetCrossRef
23.
Gee M, Dohrmann C, Key S, Wall W (2009) A uniform nodal strain tetrahedron with isochoric stabilization. Int J Numer Meth Eng 78(4):429–443MathSciNetMATHCrossRef
24.
Gomez H, Hughes TJ, Nogueira X, Calo VM (2010) Isogeometric analysis of the isothermal navier-stokes-korteweg equations. Comput Methods Appl Mech Eng 199(25):1828–1840MathSciNetMATHCrossRef
25.
Gracie R, Ventura G, Belytschko T (2007) A new fast finite element method for dislocations based on interior discontinuities. Int J Numer Meth Eng 69(2):423–441MATHCrossRef
26.
Hettich T, Ramm E (2006) Interface material failure modeled by the extended finite-element method and level sets. Comput Methods Appl Mech Eng 195(37):4753–4767MathSciNetMATHCrossRef
27.
Hughes TJ, Cottrell JA, Bazilevs Y (2005) Isogeometric analysis: Cad, finite elements, nurbs, exact geometry and mesh refinement. Comput Methods Appl Mech Eng 194(39):4135–4195MathSciNetMATHCrossRef
28.
Hughes TT, Bazilevs Y, Cottrell J (2009) Isogeometric analysis: toward integration of CAD and FEA. Wiley, New York
29.
30.
Kagan P, Fischer A (2000) Integrated mechanically based cae system using b-spline finite elements. Comput Aid Des 32(8):539–552
31.
Legrain G, Allais R, Cartraud P (2011) On the use of the extended finite element method with quadtree/octree meshes. Int J Numer Meth Eng 86(6):717–743MathSciNetMATHCrossRef
32.
Legrain G, Cartraud P, Perreard I, Moës N (2011) An x-fem and level set computational approach for image-based modelling: application to homogenization. Int J Numer Meth Eng 86(7):915–934
33.
Martin S, Kaufmann P, Botsch M, Wicke M, Gross M (2008) Polyhedral finite elements using harmonic basis functions. Comput Graph Forum 27:1521–1529CrossRef
34.
Moës N, Cloirec M, Cartraud P, Remacle JF (2003) A computational approach to handle complex microstructure geometries. Comput Methods Appl Mech Eng 192(28):3163–3177MATHCrossRef
35.
Moes N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Meth Eng 46(1):133–150MATHCrossRef
36.
Mousavi S, Xiao H, Sukumar N (2010) Generalized gaussian quadrature rules on arbitrary polygons. Int J Numer Meth Eng 82(1):99–113MathSciNetMATH
37.
Natarajan S, Wang J, Song C, Birk C (2015) Isogeometric analysis enhanced by the scaled boundary finite element method. Comput Methods Appl Mech Eng 283:733–762MathSciNetCrossRef
38.
Oaks W, Paoletti S (2000) Polyhedral mesh generation. In: IMR, pp 57–67
39.
Ooi ET, Natarajan S, Song C, Ooi EH (2015) Dynamic fracture simulations using the scaled boundary finite element method on hybrid polygon–quadtree meshes. Int J Impact Eng 90:154–164CrossRef
40.
Ooi ET, Song C, Tin-Loi F, Yang Z (2012) Polygon scaled boundary finite elements for crack propagation modelling. Int J Numer Methods Eng 91(3):319–342MathSciNetMATHCrossRef
41.
42.
Rashid M, Selimotic M (2006) A three-dimensional finite element method with arbitrary polyhedral elements. Int J Numer Methods Eng 67(2):226–252MathSciNetMATHCrossRef
43.
Saputra AA, Birk C, Song C (2015) Computation of three-dimensional fracture parameters at interface cracks and notches by the scaled boundary finite element method. Eng Fract Mech 148:213–242CrossRef
44.
Schillinger D, Ruess M (2014) The finite cell method: A review in the context of higher-order structural analysis of cad and image-based geometric models. Arch Comput Methods Eng. doi:10.​1007/​s11831-014-9115-y
45.
Shephard MS, Georges MK (1991) Automatic three-dimensional mesh generation by the finite octree technique. Int J Numer Methods Eng 32(4):709–749MATHCrossRef
46.
Silani M, Talebi H, Ziaei-Rad S, Kerfriden P, Bordas SP, Rabczuk T (2014) Stochastic modelling of clay/epoxy nanocomposites. Compos Struct 118:241–249CrossRef
47.
Song C, Wolf J (1998) The scaled boundary finite-element method: analytical solution in frequency domain. Comput Methods Appl Mech Eng 164(1):249–264MathSciNetMATHCrossRef
48.
Song C, Wolf JP (1997) The scaled boundary finite-element method alias consistent infinitesimal finite-element cell method for elastodynamics. Comput Methods Appl Mech Eng 147(3):329–355MathSciNetMATHCrossRef
49.
Song C, Wolf JP (2002) Semi-analytical representation of stress singularities as occurring in cracks in anisotropic multi-materials with the scaled boundary finite-element method. Comput Struct 80(2):183–197CrossRef
50.
51.
Sukumar N, Chopp DL, Moës N, Belytschko T (2001) Modeling holes and inclusions by level sets in the extended finite-element method. Comput Methods Appl Mech Eng 190(46):6183–6200MathSciNetMATHCrossRef
52.
Sukumar N, Malsch E (2006) Recent advances in the construction of polygonal finite element interpolants. Arch Comput Methods Eng 13(1):129–163MathSciNetMATHCrossRef
53.
54.
Szeliski R (1993) Rapid octree construction from image sequences. CVGIP 58(1):23–32CrossRef
55.
56.
Talebi H, Silani M, Bordas SP, Kerfriden P, Rabczuk T (2014) A computational library for multiscale modeling of material failure. Comput Mech 53(5):1047–1071MathSciNetMATHCrossRef
57.
Talebi H, Zi G, Silani M, Samaniego E, Rabczuk T (2012) A simple circular cell method for multilevel finite element analysis. J Appl Math. doi:10.​1155/​2012/​526846
58.
Talischi C, Paulino GH, Pereira A, Menezes IF (2012) Polymesher: a general-purpose mesh generator for polygonal elements written in matlab. Struct Multidiscipl Optim 45(3):309–328
59.
Talischi C, Pereira A, Paulino GH, Menezes IF, Carvalho MS (2014) Polygonal finite elements for incompressible fluid flow. Int J Numer Meth Fluids 74(2):134–151MathSciNetCrossRef
60.
Temizer I, Wriggers P, Hughes T (2011) Contact treatment in isogeometric analysis with nurbs. Comput Methods Appl Mech Eng 200(9):1100–1112MathSciNetMATHCrossRef
61.
Tu T, O’Hallaron DR, Ghattas O (2005) Scalable parallel octree meshing for terascale applications. In: 2005 IEEE Proceedings of the ACM/IEEE SC 2005 conference on supercomputing, p 4
62.
da Veiga Beirão L, Brezzi F, Cangiani A, Manzini G, Marini L, Russo A (2013) Basic principles of virtual element methods. Math Models Methods Appl Sci 23(01):199–214MathSciNetMATHCrossRef
63.
64.
da Veiga Beirão L, Lovadina C, Mora D (2015) A virtual element method for elastic and inelastic problems on polytope meshes. Comput Methods Appl Mech Eng 295:327–346MathSciNetCrossRef
65.
Wachspress EL (1975) A rational finite element basis. Academic Press, LondonMATH
66.
Wolf JP (2003) The scaled boundary finite element method. Wiley, New York
67.
Wolf JP, Song C (2000) The scaled boundary finite-element method-a primer: derivations. Comput Struct 78(1):191–210CrossRef
68.
Yang Z, Deeks A (2007) Fully-automatic modelling of cohesive crack growth using a finite element-scaled boundary finite element coupled method. Eng Fract Mech 74(16):2547–2573MATHCrossRef
69.
Yaseri A, Bazyar M, Hataf N (2014) 3d coupled scaled boundary finite-element/finite-element analysis of ground vibrations induced by underground train movement. Comput Geotech 60:1–8CrossRef
70.
Yerry MA, Shephard MS (1984) Automatic three-dimensional mesh generation by the modified-octree technique. Int J Numer Meth Eng 20(11):1965–1990MATHCrossRef
71.
Zienkiewicz OC, Taylor RL (1977) The finite element method, vol 3. McGraw-hill, LondonMATH
Metadata
Title
Stress analysis of 3D complex geometries using the scaled boundary polyhedral finite elements
Authors
Hossein Talebi
Albert Saputra
Chongmin Song
Publication date
01-10-2016
Publisher
Springer Berlin Heidelberg
Published in
Computational Mechanics / Issue 4/2016
Print ISSN: 0178-7675
Electronic ISSN: 1432-0924
DOI
https://doi.org/10.1007/s00466-016-1312-0

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