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Initial Attempts on CAD/CAE Integration

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Precursors of Isogeometric Analysis

Part of the book series: Solid Mechanics and Its Applications ((SMIA,volume 256))

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Abstract

This chapter discusses the meaning of the conventional “integrated CAD/CAE systems ,” which is contradicted from the “CAD/ CAE integration ” (under the umbrella of isogeometric analysis) adopted throughout this book. The history of several important CAD interpolations since 1964 is outlined. Five precursors of the NURBS -based isogeometric analysis are discussed. The general boundary value problem is posed. In order to solve it, three computational methods, i.e., the finite element method , the Boundary Element Method, and the collocation method are presented in brief. The implementation of Coons and Gordon interpolation formulas in mesh generation is discussed. Moreover, the utilization of the closely related transfinite elements in engineering analysis in conjunction with the aforementioned three major computational methods is discussed.

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References

  1. Argyris JH (1955) Energy theorems and structural analysis: a generalized discourse with applications on energy principles of structural analysis including the effects of temperature and non-linear stress strain relations. Aircr Eng 26(1):347–356

    Google Scholar 

  2. Auricchio F, Beirão da Veiga L, Hughes TJR, Reali A, Sangalli G (2010) Isogeometric collocation methods. Math Models Methods Appl Sci 20(11):2075–2107

    Article  MathSciNet  MATH  Google Scholar 

  3. Bajaj C, Chen J, Xu G (1995) Modeling with cubic A-patches. ACM Trans Graph 14:103–133

    Article  Google Scholar 

  4. Barnhill RE, Birkhoff G, Gordon WJ (1973) Smooth interpolation on triangles. J Approx Theory 8:114–128

    Article  MathSciNet  MATH  Google Scholar 

  5. Barnhill RE, Mansfield L (1974) Error bounds for smooth interpolation on triangles. J Approx Theory 11:306–318

    Article  MathSciNet  MATH  Google Scholar 

  6. Barnhill RE (1985) A survey of patch methods. NASA Report. Available at: https://ntrs.nasa.gov/search.jsp?R=19850020255

  7. Barnhill RE, Gregory JA (1975) Compatible smooth interpolation on triangles. J Approx Theory 15:214–225

    Article  MathSciNet  MATH  Google Scholar 

  8. Bathe KJ (1996) Finite element procedures. Prentice-Hall, Upper Saddle River, New Jersey

    MATH  Google Scholar 

  9. Beer G, Watson JO (2002) Introduction to finite and boundary element methods for engineers. Wiley, Chichester, Chapter 11, pp 357–377

    Google Scholar 

  10. Bercovier M, Shilat E (1993) Enhancement of Gordon-Coons interpolations by ‘bubble functions’. Comput Aided Des 10:253–265

    Article  MathSciNet  MATH  Google Scholar 

  11. Βezier P (1966) Définition numérique des courbes et surfaces I. Automatisme 11:625–632

    Google Scholar 

  12. Βezier P (1967) Définition numérique des courbes et surfaces II. Automatisme 12:17–21

    Google Scholar 

  13. Βezier P (1968) Procédé de définition numérique des courbes et surfaces non mathématiques. Automatisme 13(5):189–196

    Google Scholar 

  14. Βezier P (1968b) How Renault uses numerical control for car body design and tooling. SAE Paper 680010

    Google Scholar 

  15. Bezier PE (1971) Example of an existing system in motor industry: the UNISURF system. Proc R Soc Lond Ser A 321:207–218

    Google Scholar 

  16. Bezier P (1971) Numerical control and foundries. FOND-FR 26(299):77

    Google Scholar 

  17. Bezier P (1972) Numerical control: mathematics and applications. Wiley (translated by A. R. Forrest)

    Google Scholar 

  18. Bezier P (1973) UNISURF system: principles, program, language. In: Harvany J (ed)Proceedings of 1973 PROLAMAT conference, Budapest, North Holland Publ. Co., Amsterdam

    Google Scholar 

  19. Bezier P (1974) Mathematical and practical possibilities of UNISURF. In: Barnhill R, Riesenfeld R (eds) Computer aided geometric design. Academic Press, Cambridge

    Google Scholar 

  20. Βezier P (1977) Essay de définition numérique des courbes et des surfaces expérimentales. Ph.D. thesis, University of Paris VI

    Google Scholar 

  21. Βezier P (1978) General distortion of an ensemble of biparametric surfaces. Comput Aided Des 10(2):116–120

    Article  Google Scholar 

  22. Bezier PE (1981) A view of CAD-CAM. Comput Aided Des 13(4):207–209

    Article  Google Scholar 

  23. Bezier PE, Sioussiou S (1983) Semi-automatic system for defining free-form curves and surfaces. Comput Aided Des 15(2):65–72

    Article  Google Scholar 

  24. Bezier PE (1983) UNISURF, from styling to tool-shop. Comput Ind 4(2):115–126

    Article  Google Scholar 

  25. Bezier PE (1984) CADCAM—past, requirements, trends. Comput Aided Des 16(2):102

    Article  Google Scholar 

  26. Bezier P (1986) The mathematical basis of the UNISURF CAD system. Butterworths, London

    Google Scholar 

  27. Bezier P (1989) 1st steps of CAD. Comput Aided Des 21(5):259–261

    Article  Google Scholar 

  28. Bezier P (1990) Style, mathematics and NC. Comput Aided Des 22(9):524–526

    Article  Google Scholar 

  29. Bezier P (1998) A view of the CAD/CAM development period. IEEE Ann Hist Comput 20(2):37–40

    Google Scholar 

  30. Boyse JW, Rosen JM (1981) GMSOLID—a system for interactive design and analysis of solids. SAE Trans, 90, Section 1: 810010-810234, pp 847–857

    Google Scholar 

  31. Brebbia CA (1982) Finite element systems: a handbook, 2nd edn. Springer, Berlin

    Book  MATH  Google Scholar 

  32. Brebbia CA, Dominguez J (1992) Boundary elements: an introductory course. Computational Mechanics Publications, McGraw-Hill Book Company, Southampton

    MATH  Google Scholar 

  33. Casale MS (1989) Integration of geometric analysis and structural analysis using trimmed patches. Ph.D. thesis, University of California, Irvine

    Google Scholar 

  34. Casale MS, Bobrow JE (1989) The analysis of solids without mesh generation using trimmed patch boundary elements. Eng Comput 5:249–257

    Article  Google Scholar 

  35. Casale MS, Bobrow JE, Underwood R (1992) Trimmed-patch boundary elements: bridging the gap between solid modeling and engineering analysis. Comput Aided Des 24:193–199

    Article  MATH  Google Scholar 

  36. Cavendish JC, Gordon WJ, Hall CA (1976) Ritz-Galerkin approximations in blending function spaces. Numer Math 26:155–178

    Article  MathSciNet  MATH  Google Scholar 

  37. Cavendish JC, Gordon WJ, Hall CA (1977) Substructured macro elements based on locally blending interpolation. Int J Numer Meth Eng 11:1405–1421

    Article  MATH  Google Scholar 

  38. Cavendish JC, Hall CA (1984) A new class of transitional blended finite elements for the analysis of solid structures. Int J Numer Meth Eng 28:241–253

    Article  MATH  Google Scholar 

  39. Charlesworth WW, Cox JJ, Anderson DC (1994) The domain decomposition method applied to Poisson’s equation in two dimensions. Int J Solids Struct 37(18):3093–3115

    MATH  Google Scholar 

  40. Clark BW, Anderson DC (2003) The penalty boundary method for combining meshes and solid models in finite element analysis. Eng Comput 20(4):344–365

    Article  MATH  Google Scholar 

  41. Clark BW, Anderson DC (2003) The penalty boundary method. Finite Elem Anal Des 39:387–401

    Article  Google Scholar 

  42. Collatz L (1960) The numerical treatment of differential equations, 3rd edn. Springer-Verlag, Berlin

    Book  MATH  Google Scholar 

  43. Cook WA (1974) Body oriented (natural) co-ordinates for generating three-dimensional meshes. Int J Numer Meth Eng 8:27–43

    Article  MATH  Google Scholar 

  44. Coons SA (1964) Surfaces for computer aided design of space form, Project MAC, MIT (1964), revised for MAC-TR-41 (1967), Springfield, VA 22161, USA. Available as AD 663 504 from the National Technical Information Service (CFSTI), Sills Building, 5285 Port Royal Road. Now, online available at: http://publications.csail.mit.edu/lcs/pubs/pdf/MIT-LCS-TR-041.pdf

  45. Coons S (1968) Rational bibubic surface patches. Technical report, MIT, Project MAC

    Google Scholar 

  46. Cottrell JA, Hughes TJR, Bazilevs Y (2009) Isogeometric analysis: towards integration of CAD and FEA. Wiley, Chichester

    Book  MATH  Google Scholar 

  47. Cox MG (1972) The numerical evaluation of B-splines. J Inst Math Its Appl 10:134–149

    Article  MathSciNet  MATH  Google Scholar 

  48. De Boor C (1972) On calculating with B-splines. J Approx Theory 6:50–62

    Article  MathSciNet  MATH  Google Scholar 

  49. De Casteljau P (1959) Courbes à poles. National Industrial Property Institute (INPI, France)

    Google Scholar 

  50. De Casteljau PF (1999) De Casteljau’s autobiography: my life at Citroën. Comput Aided Geom Des 16:583–586

    Google Scholar 

  51. Dimitriou V (2004) Adaptive finite elements and related meshes, Ph.D. Dissertation (advisor: Prof. Andreas E. Kanarachos), National Technical University of Athens, School of Mechanical Engineering, Athens, August, 2004

    Google Scholar 

  52. El-Zafrany A, Cookson RA (1986) Derivation of Lagrangian and Hermitian shape functions for triangular elements. Int J Numer Meth Eng 23(2):275–285

    Article  MathSciNet  MATH  Google Scholar 

  53. El-Zafrany A, Cookson RA (1986) Derivation of Lagrangian and Hermitian shape functions for quadrilateral elements. Int J Numer Meth Eng 23(10):1939–1958

    Article  MATH  Google Scholar 

  54. Farin G (1990) Curves and surfaces for computer aided geometric design: a practical guide. Academic Press, Boston

    MATH  Google Scholar 

  55. Farin G, Hoschek J, Kim MS (2002) Handbook of computer aided geometric design. Elsevier, North-Holland

    MATH  Google Scholar 

  56. Forrest AR (1968) Curves and surfaces for computer-aided design, Ph.D. dissertation, Cambridge University, Cambridge, UK

    Google Scholar 

  57. Gordon WJ (1969) Spline-blended surface interpolation through curve networks. Indiana Univ Math J 18, 10, pp 931–952. Online available at: http://www.iumj.indiana.edu/IUMJ/FULLTEXT/1969/18/18068

  58. Gordon WJ (1971) Blending functions methods of bivariate and multivariate interpolation and approximation. SIAM J Numer Anal 8:158–177

    Article  MathSciNet  MATH  Google Scholar 

  59. Gordon WJ (1983) An operator calculus for surface and volume modeling. IEEE Comput Graph Appl 3:18–22

    Article  Google Scholar 

  60. Gordon WJ, Hall CA (1973) Construction of curvilinear co-ordinate systems and application to mesh generation. Int J Numer Meth Eng 7:461–477

    Article  MathSciNet  MATH  Google Scholar 

  61. Gordon WJ, Hall CA (1973) Transfinite element methods: Blending-function interpolation over arbitrary curved element domains. Numer Math 21:109–112

    Article  MathSciNet  MATH  Google Scholar 

  62. Gordon WJ, Thiel LC (1982) Transfinite mappings and their application to grid generation. In: Thompson JP (ed) Numerical grid generation. Applied mathematics and computation, vol 11–12. Elsevier, pp. 171–233

    Google Scholar 

  63. Gregory JA (1983) N-sided surface patches. In: Gregory JA (ed) Math Surf. Clarendon Press, Oxford, pp 217–232

    Google Scholar 

  64. Haber RB, Shephard MS, Abel JF, Gallagher RH, Greensberg DP (1981) A general three-dimensional graphical finite element preprocessor utilizing discrete transfinite mappings. Int J Numer Meth Eng 17:1015–1044

    Article  MATH  Google Scholar 

  65. Haber RB, Abel JF (1982) Discrete transfinite mappings for the description and meshing of three-dimensional surfaces using interactive computer graphics. Int J Numer Meth Eng 18:41–66

    Article  MATH  Google Scholar 

  66. Hartmann S, Benson D, Nagy A (2016) Isogeometric analysis with LS-DYNA. J Phys Conf Ser 734:032125. https://doi.org/10.1088/1742-6596/734/3/032125

    Article  Google Scholar 

  67. Higuchi F, Gofuku S, Maekawa T, Mukundan H, Patrikalakis NM (2007) Approximation of involute curves for CAD-system processing. Eng Comput 23(3):207–214

    Article  Google Scholar 

  68. Höllig K (2002) Finite element approximation with splines. In: Farin G, Hoschek J, Kim MS (eds) Handbook of computer aided geometric design, North-Holland, Amsterdam, Chapter 11, pp 283–307

    Chapter  Google Scholar 

  69. Höllig K (2003) Finite element methods with B-splines. SIAM, Philadelphia

    Book  MATH  Google Scholar 

  70. Hughes TJR (2000), The finite element method: Linear static and dynamic finite element analysis. Dover Publications, Mineola, NY

    Google Scholar 

  71. Hughes TJR, Cottrell JA, Bazilevs Y (2005) Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comput Methods Appl Mech Eng 194:4135–4195

    Article  MathSciNet  MATH  Google Scholar 

  72. Inoue K, Kikuchi Y, Masuyama T (2005) A NURBS finite element method for product shape design. J Eng Des 16(2):157–174

    Article  Google Scholar 

  73. Kagan P, Fischer A (2000) Integrated mechanical based CAE systems using B-spline based finite elements. Comput Aided Des 32(8–9):539–552

    Article  MATH  Google Scholar 

  74. Kanarachos A, Röper O (1979) Rechnerunterstützte Netzgenerierung mit Hilfe der Coonsschen Abbildung. VDI-Z 121:297–303

    Google Scholar 

  75. Kanarachos A, Provatidis Ch (1987) Performance of mass matrices for the BEM dynamic analysis of wave propagation problems. Comput Methods Appl Mech Eng 63:155–165

    Article  MATH  Google Scholar 

  76. Kanarachos AE, Spentzas CN (1988) Comparison of four finite element solutions of self-adjoint and non-self-adjoint problems governed by differential equations with predominant lower order derivatives. Eng Comput 5:71–74

    Article  Google Scholar 

  77. Kanarachos A, Deriziotis D (1989) On the solution of Laplace and wave propagation problems using ‘C-elements’. Finite Elem Anal Des 5:97–109

    Article  MATH  Google Scholar 

  78. Kanarachos A, Provatidis C, Deriziotis D, Foteas N (1999),A new approach of the FEM analysis of two-dimensional elastic structures using global (Coons’s) interpolation functions. In: Wunderlich J (ed) CD proceedings first european conference on computational mechanics, München-Germany, August–September, 1999

    Google Scholar 

  79. Lanczos C (1938) Trigonometric interpolation of empirical and analytical functions. Stud Appl Math 17(1–4):123–199

    MATH  Google Scholar 

  80. Lee K (1999) Principles of CAD/CAM/CAE systems. Addison-Wesley, Reading, MA

    Google Scholar 

  81. Liu B, Xing Y, Wang Z, Lu X, Sun H (2017) Non-uniform rational Lagrange functions and its applications to isogeometric analysis of in-plane and flexural vibration of thin plates. Comput Methods Appl Mech Eng 321:173–208

    Article  MathSciNet  Google Scholar 

  82. Loop CT, DeRose TD (1989) A multisided generalization of Bezier surfaces. ACM Trans Graph 8:204–234

    Article  MATH  Google Scholar 

  83. Martin W, Cohen E (2001) Representation and extraction of volumetric attributes using trivariate splines: a mathematical framework. In: Proceedings of the solid modelling symposium (http://www.cs.utah.edu)

  84. Natekar D, Zhang X, Subbarayan G (2004) Constructive solid analysis: a hierarchical, geometry-based meshless analysis procedure for integrated design and analysis. Comput Aided Des 36(5):473–486

    Article  Google Scholar 

  85. Park S, Lee K (1997) High-performance trivariate NURBS representation for analyzing and visualizing fluid flow data. Comput Graph 21:473–482

    Article  Google Scholar 

  86. Provatidis C (1987) On the application of the boundary element method in the analysis of field and dynamic problems, Doctoral Dissertation, National Technical University of Athens, Mechanical Engineering Department, Greece, November 1987 (in Greek)

    Google Scholar 

  87. Provatidis CG, Kanarachos AE (1995) Further research on the performance of consistent mass matrices using BEM for symmetric/nonsymmetric formulations. Comput Mech 16:197–207

    Article  MathSciNet  MATH  Google Scholar 

  88. Provatidis C, Kanarachos A (2001) Performance of a macro-FEM approach using global interpolation (Coons’) functions in axisymmetric potential problems. Comput Struct 79(19):1769–1779

    Article  Google Scholar 

  89. Provatidis C (2001b) A global approximation technique in noise-control. In: Tsahalis DT (ed) Proceedings 4th European conference on noise control (EuroNoise-2001, 14–17 January 2001, Patras, Greece), vol I, pp 23–31

    Google Scholar 

  90. Provatidis C (2001c) Acoustic analysis of two-dimensional mufflers using large finite elements derived from Coons’ interpolation. In: Drakatos PA (ed) CD proceedings of ASME—Greek Section, September 17–20, 2001, Patras, Greece (Paper ANG1/P099, pages 1–6)

    Google Scholar 

  91. Provatidis C (2001d) Stress analysis of 3D solid structures using large boundary elements derived from 2D-Coons’ interpolation. In: Drakatos PA (ed) CD proceedings of ASME—Greek Section, September 17–20, 2001, Patras, Greece (Paper ANG1/P129, pages 1–6)

    Google Scholar 

  92. Provatidis C (2002) Coons-patch macroelements in potential Robin problems. Forsch Ingenieurwes 67(1):19–26

    Article  Google Scholar 

  93. Provatidis C (2002b) A comparative study between Coons-patch macroelements and boundary elements in two-dimensional potential problems. In: Tsahalis DT (ed) Proceedings 4th GRACM congress on computational mechanics, 27–29 June, 2002, Patras, Greece, pp 43–50

    Google Scholar 

  94. Provatidis C (2002c) Analysis of three-dimensional sound radiation problems using trimmed patch boundary elements. In: Tsahalis DT (ed) Proceedings 4th GRACM Congress on Computational Mechanics, 27–29 June, 2002, Patras, Greece, pp. 402-409

    Google Scholar 

  95. Provatidis CG (2002d) CAD-FEA integration using Coons interpolation. Technical Report MD&CS 01–2002, National Technical University of Athens, Mechanical Engineering Department; also submitted to “Engineering with Computers” (EWC03-019, Sept 12, 2003)

    Google Scholar 

  96. Provatidis C (2003) Analysis of axisymmetric structures using Coons’ interpolation. Finite Elem Anal Des 39:535–558

    Article  Google Scholar 

  97. Provatidis C (2003b) Frequency analysis and transient response of two-dimensional structures using Coons-patch macroelements. In: Brennan MJ, Ferman MA, Petersson BAT, Rizzi SA, Wentz K (eds) Proceedings of the VIII international conference on recent advances in structural dynamics, 14–16 July 2003, Southampton, UK (paper No. 24)

    Google Scholar 

  98. Provatidis C (2003c) Free vibrations of two-dimensional structures using Coons-patch macroelements, FEM and BEM. In: Atluri SN, Beskos DE, Polyzos D (eds) Proceedings from ICCES 2003, advances in computational & experimental engineering & sciences, 24–29 July 2003, Corfu, Greece, Chapter 5, Paper No. 249

    Google Scholar 

  99. Provatidis C, Zafiropoulos N (2003d) Free-vibration analysis of three-dimensional solids using Coons-patch Boundary Superelements. In: Aifantis E (ed) Proceedings 5th European solids mechanics conference, Thessaloniki, 17–22 August 2003

    Google Scholar 

  100. Provatidis C, Zafiropoulos N (2003e) Determination of eigenfrequencies in three-dimensional acoustic cavities using Coons-patch Boundary Superelements. In: Aifantis E (ed) Proceedings 5th European solids mechanics conference, Thessaloniki, 17–22 August 2003

    Google Scholar 

  101. Provatidis CG (2004) Coons-patch macroelements in two-dimensional eigenvalue and scalar wave propagation problems. Comput Struct 82(4–5):383–395

    Article  MathSciNet  Google Scholar 

  102. Provatidis CG (2004) On DR/BEM for eigenvalue analysis of 2-D acoustics. Comput Mech 35:41–53

    Article  MATH  Google Scholar 

  103. Provatidis CG (2004) Solution of two-dimensional Poisson problems in quadrilateral domains using transfinite Coons interpolation. Commun Numer Methods Eng 20(7):521–533

    Article  MathSciNet  MATH  Google Scholar 

  104. Provatidis CG (2005) Performance of large Gordon-Coons finite elements in 2-D potential problems. In: Proceedings GRACM 05, Limassol, Cyprus, 29 June–1 July, 2005

    Google Scholar 

  105. Provatidis CG, Vossou CG, Theodorou EG (2006) On the CAD/CAE integration using Coons interpolation. In: Proceedings 2nd international conference “from scientific computing to computational engineering”, Athens, Greece, 5–8 July, 2006

    Google Scholar 

  106. Provatidis CG (2007) Final report for the project: PROTAGORAS (DIDYMO: Investigation on CAD/CAE integration), EDEIL Contract No. 65/1388-June 2004, February, 2007

    Google Scholar 

  107. Provatidis C, Kanarachos A (2000) On the use of Coons’ interpolation in CAD/CAE systems. In: Mastorakis N (ed) Systems and control: theory and applications. World Scientific and Engineering Society Press, pp 343–348. Online available on: http://www.wseas.us/e-library/conferences/athens2000/Papers2000/547.pdf

  108. Provatidis CG (2005) Three-dimensional Coons macroelements in Laplace and acoustic problems. Comput Struct 83:1572–1583

    Article  MathSciNet  Google Scholar 

  109. Provatidis CG (2005) Analysis of box-like structures using 3-D Coons’ interpolation. Commun Numer Methods Eng 21:443–456

    Article  MATH  Google Scholar 

  110. Provatidis CG (2005c) Performance of several RBFs in DR/BEM eigenvalue analysis of 2-D structures. GRACM 05, Limassol, Cyprus, 29 June–1 July 2005

    Google Scholar 

  111. Provatidis CG (2006) Coons-patch macroelements in two-dimensional parabolic problems. Appl Math Model 30:319–351

    Article  MATH  Google Scholar 

  112. Provatidis CG (2006) Free vibration analysis of two-dimensional structures using Coons-patch macroelements. Finite Elem Anal Des 42(6):18–531

    Article  MATH  Google Scholar 

  113. Provatidis CG (2006) Transient elastodynamic analysis of two-dimensional structures using Coons-patch macroelements. Int J Solids Struct 43(22–23):6688–6706

    Article  MATH  Google Scholar 

  114. Provatidis CG (2006) Three-dimensional Coons macroelements: application to eigenvalue and scalar wave propagation problems. Int J Numer Meth Eng 65:111–134

    Article  MATH  Google Scholar 

  115. Provatidis CG (2007) Performance of a Lagrange based global finite element collocation method for eigenvalue structural analysis. In: Proceedings 8th HSTAM international congress on mechanics, Patras, 12–14 July, 2007

    Google Scholar 

  116. Provatidis CG (2008) Free vibration analysis of elastic rods using global collocation. Arch Appl Mech 78(4):241–250

    Article  MATH  Google Scholar 

  117. Provatidis CG (2008) Time- and frequency-domain analysis using lumped mass global collocation. Arch Appl Mech 78(11):909–920

    Article  MATH  Google Scholar 

  118. Provatidis CG (2008) Global collocation method for 2-D rectangular domains. J Mech Mater Struct 3(1):185–194

    Article  Google Scholar 

  119. Provatidis CG (2009) Integration-free Coons macroelements for the solution of 2-D Poisson problems. Int J Numer Meth Eng 77:536–557

    Article  MathSciNet  MATH  Google Scholar 

  120. Provatidis CG (2009) Eigenanalysis of two-dimensional acoustic cavities using transfinite interpolation. J Algorithms Comput Technol 3(4):477–502

    Article  MathSciNet  Google Scholar 

  121. Provatidis CG (2009c) Higher order Galerkin/Ritz approximations in 1-D eigenval problems. In: Tsahalis D (ed) Proceedings 3rd international conference on experiments/process/system modeling/simulation & optimization (3rd IC-EpsMsO), Athens, 8–11 July, 2009

    Google Scholar 

  122. Provatidis CG, Isidorou S (2009) Comparison of advanced collocation methods for the solution of ordinary differential equations. In: Tsahalis D (ed) Proceedings 3rd international conference on experiments/process/system modeling/simulation & optimization (3rd IC-EpsMsO), Athens, 8–11 July, 2009

    Google Scholar 

  123. Provatidis CG, Ioannou KS (2010) Static analysis of two-dimensional elastic structures using global collocation. Arch Appl Mech 80(4):389–400

    Article  MATH  Google Scholar 

  124. Provatidis CG (2011) Equivalent finite element formulations for the calculation of eigenvalues using higher-order polynomials. Appl Math 1(1):13–23

    Article  MathSciNet  Google Scholar 

  125. Provatidis CG (2011b) Global versus local interpolation in the FEM free vibration analysis of prismatic bars. In: Proceedings 7th GRACM international congress in mechanics, Athens, 30 June–2 July, 2011

    Google Scholar 

  126. Provatidis CG (2011c) Some issues on CAD/CAE integration: global interpolation using isoparametric and isogeometric techniques. In: Proceedings 7th GRACM international congress in mechanics, Athens, 30 June-2 July, 2011

    Google Scholar 

  127. Provatidis CG, Isidorou SK (2011) B-splines collocation eigenvalue analysis of 1-D problems. In: Proceedings 7th GRACM international congress in mechanics, Athens, 30 June–2 July, 2011

    Google Scholar 

  128. Provatidis CG (2012) Two-dimensional elastostatic analysis using Coons-Gordon interpolation. Meccanica 47(4):951–967

    Article  MathSciNet  MATH  Google Scholar 

  129. Provatidis C (2013) A review on attempts towards CAD/CAE integration using macroelements. Comput Res 1(3):61–84

    Google Scholar 

  130. Provatidis CG (2014) Bezier versus Lagrange polynomials-based finite element analysis of 2-D potential problems. Adv Eng Softw 73:22–34

    Article  Google Scholar 

  131. Provatidis CG (2018) Engineering analysis with CAD-based macroelements. Arch Appl Mech 88:121–140

    Article  Google Scholar 

  132. Rabut C (2002) On Pierre Bezier’s life and motivations. Comput Aided Des 34(7):493–510

    Article  MATH  Google Scholar 

  133. Renken FP, Subbarayan G (2000) NURBS-based solution to inverse boundary problems in droplet shape prediction. Comput Methods Appl Mech Eng 190(11):1391–1406

    Article  MATH  Google Scholar 

  134. Röper O (1978) Ein Geometrieprozessor für die rechnerunterstützte Auslegung von Maschinenbauteilen mit Hilfe der Methode der Finite Elemente, Dissertation, Ruhr-Universität Bochum, Mai 1978

    Google Scholar 

  135. Schillinger D, Ruthala PK, Nguyen LH (2016) Lagrange extraction and projection for NURBS basis functions: a direct link between isogeometric and standard nodal finite element formulations. Int J Numer Meth Eng 108(6):515–534

    Article  MathSciNet  Google Scholar 

  136. Schoenberg IJ (1946) Contributions to the problem of approximation of equidistant data by analytic functions. Q Appl Math 4:45–99

    Article  Google Scholar 

  137. Schramm U, Pilkey WD (1993) The coupling of geometric descriptions and finite element using NURBS—a study in shape optimization. Finite Elem Anal Des 15:11–34

    Article  MATH  Google Scholar 

  138. Schramm U, Pilkey WW (1994) Higher order boundary elements for shape optimization using rational B-splines. Eng Anal Boundary Elem 14(3):255–266

    Article  Google Scholar 

  139. Szabó B, Babuška I (1991) Finite element analysis. Wiley, New York

    MATH  Google Scholar 

  140. Turner MJ, Clough RW, Martin HC, Topp LT (1956) Stiffness and deflection analysis of complex structures. Journal of the Aeronautical Sciences 23 (9):805–823

    Google Scholar 

  141. Van Blerk JJ, Botha JF (1993) Numerical solution of partial differential equations on curved domains by collocation. Numer Methods Partial Differ Equat 9:357–371

    Article  MathSciNet  MATH  Google Scholar 

  142. Versprille KJ (1975) Computer-aided design applications of the rational B-spline approximation form, Ph.D. Dissertation, Syracuse University, USA, 1975, http://surface.syr.edu/eecs_etd/262 (advisor: Prof. S. A. Coons)

  143. Wu SC, Abel JF (1979) Representation and discretization of arbitrary surfaces for finite element shell analysis. Int J Numer Meth Eng 14:813–836

    Article  MATH  Google Scholar 

  144. Yildir YB, Wexler A (1983) MANDAP—a FEM/BEM preparation package. IEEE Trans Magn 19:2562–2565

    Article  Google Scholar 

  145. Zhaobei Z, Zhiqiang X (1987) Coons’ surface method for formulation of finite element of plates and shells. Comput Struct 27(1):79–88

    Article  MATH  Google Scholar 

  146. Zhang YJ (2017) Integrating CAD with Abaqus: a practical isogeometric analysis software platform for industrial applications. In: IACM 19th international conference on finite elements in flow problems—FEF 2017, 5–7 April 2017, Rome, Italy (paper: a79.pdf)

    Google Scholar 

  147. Zienkiewicz OC (1977) The finite element method, 3rd edn. McGraw-Hill, London

    MATH  Google Scholar 

  148. Zienkiewicz OC, Taylor RL (1988) The finite element method, 4rd edn, vol 1: Basic formulation and linear problems, and vol 2: Solid and fluid mechanics, dynamics and non-linearity. McGraw-Hill, London

    Google Scholar 

  149. Zienkiewicz OC, Taylor RL (2000) The finite element method, 5rd edn, 3 volume set. Butterworth-Heinemann, Elsevier, Kidlington, Oxford

    Google Scholar 

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  1. School of Mechanical Engineering, National Technical University of Athens, Athens, Greece

    Christopher G. Provatidis

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Provatidis, C.G. (2019). Initial Attempts on CAD/CAE Integration. In: Precursors of Isogeometric Analysis. Solid Mechanics and Its Applications, vol 256. Springer, Cham. https://doi.org/10.1007/978-3-030-03889-2_1

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  • DOI: https://doi.org/10.1007/978-3-030-03889-2_1

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