411
Views
4
CrossRef citations to date
0
Altmetric
Articles

A three-dimensional topology optimization model for tooth-root morphology

, &
Pages 177-185 | Received 03 Jul 2017, Accepted 20 Jan 2018, Published online: 06 Feb 2018

References

  • Andrade-Campos A, Ramos A, Simoes J. 2012. A model of bone adaptation as a topology optimization process with contact. J Biomed Sci Eng. 5:229–244.10.4236/jbise.2012.55030
  • Andreassen E, Clausen A, Schevenels M, Lazarov BS, Sigmund O. 2001. Efficient topology optimization in MATLAB using 88 lines of code. Struct Multidisc Optim 43(1):1–16.
  • Baumgartner A, Harzheim L, Mattheck C. 1992. SKO (soft kill option): the biological way to find an optimum structure topology. Int J Fatigue. 14(6):387–393.10.1016/0142-1123(92)90226-3
  • Bendsøe M. 1989. Optimal shape design as a material distribution problem. Struct Optim. 1(4):193–202.10.1007/BF01650949
  • Bendsøe M, Sigmund O. 2003. Topology optimization: Theory, methods, and applications. Berlin: Springer.
  • Bruns TE, Tortorelli DA. 2001. Topology optimization of non-linear elastic structures and compliant mechanisms. Comput Methods Appl Mech Engrg. 190(26–27):3443–3459.10.1016/S0045-7825(00)00278-4
  • Brunski JB. 1999. In Vivo bone response to biomechanical loading at the bone/dental-implant interface. Adv Dent Res. 13:99–119.10.1177/08959374990130012301
  • Buschang PH, Julien K, Sachdeva R, Demirjian A. 1992. Childhood and pubertal growth changes of the human symphysis. Angle Orthod. 62(3):203–210.
  • Chang CL, Chen CS, Huang CH, Hsu ML. 2012. Finite element analysis of the dental implant using a topology optimization method. Med Eng Phys. 34(7):999–1008.10.1016/j.medengphy.2012.06.004
  • Cheng YC, Lin DH, Jiang CP, Lin YM. 2017. Dental implant customization using numerical optimization design and 3-dimensional printing fabrication of zirconia ceramic. Int J Numer Methods Biomed Eng. 33 (5). DOI:10.1002/cnm.2820
  • Choi AH, Conway RC, Ben-Nissan B. 2014. Finite-element modeling and analysis in nanomedicine and dentistry. Nanomed. 9(11):1681–1695.10.2217/nnm.14.75
  • Dìaz A, Sigmund O. 1995. Checkerboard patterns in layout optimization: structural optimization. Struct Optim. 19(1):40–45.
  • Farah JW, Craig RG, Meroueh KA. 1989. Finite element analysis of three- and four-unit bridges. J Oral Rehabil. 16(6):603–611.10.1111/jor.1989.16.issue-6
  • Guo X, Zhang W, Zhong W. 2014. Doing topology optimization explicitly and geometrically – a new moving morphable components based framework. J Appl Mech. 81(8):081009.10.1115/1.4027609
  • Guo X, Zhang W, Zhang J, Yuan J. 2016. Explicit structural topology optimization based on moving morphable components (MMC) with curved skeletons. Comp Meth Appl Mech Eng. 310:711–748.10.1016/j.cma.2016.07.018
  • Harzheim L. 2008. Strukturoptimierung: Grundlagen und Anwendungen [Structural optimization: basics and applications]. 1st ed. Frankfurt: Harri Deutsch. Deutsch.
  • Harzheim L, Graf G. 2006. A review of optimization of cast parts using topology optimization. Struct Multidiscipl Optim. 31(5):388–399.10.1007/s00158-005-0554-9
  • Hasegawa A, Shinya A, Nakasone Y, Lassila LVJ, Vallittu PK, Shinya A. 2010. Development of 3D CAD/FEM analysis system for natural teeth and jaw bone constructed from X-ray CT images. Intern J Biomater. 2010. DOI:10.1155/2010/659802
  • Koca OL, Eskitascioglu G, Usumez A. 2005. Three-dimensional finite-element analysis of functional stresses in different bone locations produced by implants placed in the maxillary posterior region of the sinus floor. J Prosthet Dent. 93(1):38–44.10.1016/j.prosdent.2004.10.001
  • Li T, Hu K, Cheng L, Ding Y, Ding Y, Shao J, Kong L. 2010. Optimum selection of the dental implant diameter and length in the posterior mandible with poor bone quality – A 3D finite element analysis. Appl Math Model. 35(1):446–456.
  • Liu K, Tovar A. 2014. An efficient 3d topology optimization code written in matlab. Struct Multidiscipl Optim. 50(6):1175–1196.
  • Martinez Choy SE, Lenz J, Schweizerhof K, Schmittmer M, Schindler HJ. 2017. Realistic kinetic loading of the jaw system during single chewing cycles: a finite element study. J Oral Rehab. 44(5):375–384.10.1111/joor.2017.44.issue-5
  • Mattheck C. 1990. Design and growth rules for biological structures and their application to engineering. Fatigue Fract Eng Mater Struct. 13(5):535–550.10.1111/ffe.1990.13.issue-5
  • Meijer HJ, Kuiper JH, Starmans FJ, Bosman F. 1992. Stress distribution around dental implants: Influence of superstructure, length of implants, and height of mandible. J Prosthet Dent. 68(1):96–102.10.1016/0022-3913(92)90293-J
  • Murakami N, Wakabayashi N. 2014. Finite element contact analysis as a critical technique in dental biomechanics: A review. J Prosthodont Res. 58(2):92–101.10.1016/j.jpor.2014.03.001
  • Nutu E. 2015. Interpretation of parameters in strain energy density bone adaptation equation when applied to topology optimization of inert structures. Mechanika. 21(6):443–449.
  • Pucker T, Grabe J. 2011. Structural optimization in geotechnical engineering: basics and application. Acta Geotechnic. 6:41–49.10.1007/s11440-011-0134-7
  • Querin OM, Steven GP, Xie YM. 1998. Evolutionary structural optimization (ESO) using a bi-directional algorithm. Eng Comput. 15:1031–1048.10.1108/02644409810244129
  • Rozvany GIN. 2009. A critical review of established methods of structural topology optimization. Struct Multidisc Optim. 37:217–237.10.1007/s00158-007-0217-0
  • Seitz K, Grabe J. 2016. Three-dimensional topology optimization for geotechnical foundations in granular soil. Comput Geotech. 80:41–48.10.1016/j.compgeo.2016.06.012
  • Shi L, Li H, Fok AS, Ucer C, Devlin H, Horner K. 2007. Shape optimization of dental implants. Int J Oral Maxillofac Implants. 22(6):911–920.
  • Sigmund O. 1997. On the design of compliant mechanisms using topology optimization. Mech Struct Mach. 25(4):493–524.10.1080/08905459708945415
  • Sigmund O. 2001. A 99 line topology optimization code written in Matlab. Struct Multidisc Optim. 21(2):120–127.10.1007/s001580050176
  • Sigmund O, Petersson J. 1998. Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Struct Optim. 16(1):68–75.10.1007/BF01214002
  • Van Staden RC, Guan H, Loo YC. 2006. Application of the finite element method in dental implant research. Comput Methods Biomech Biomed Eng. 9(4):257–270.10.1080/10255840600837074
  • Wolff  J.  1892. Das Gesetz der Transformation von Knochen [The law of bone remodelling]. Berlin: Springer. Deutsch.
  • Yoon Y, Sun X, Huang J, Hou G, Rechowicz K, McKenzie F. 2013. Designing natural-tooth-shaped dental implants based on soft-kill option optimization. Computer-Aided Des Appl. 10(1):59–72.10.3722/cadaps.2013.59-72
  • Zhang W, Yang W, Zhou J, Li D, Guo X. 2017. Structural Topology Optimization Through Explicit Boundary Evolution. J Appl Mech. 84(1):11011.
  • Zhang W, Chen J, Zhu X, Zhou J, Xue D, Lei X, Guo X. 2017. Explicit three dimensional topology optimization via moving Morphable void (MMV) approach. Comp Meth Appl Mech Eng. 322:590–614.10.1016/j.cma.2017.05.002
  • Zhou M, Rozvany G. 1991. The COC algorithm, Part II: Topological, geometrical and generalized shape optimization. Comp Methods Appl Mech Eng. 89(1–3):309–336.10.1016/0045-7825(91)90046-9

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.