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Introduction

  • Ernest Hinton
  • Johann Sienz
  • Mustafa Özakça

Abstract

Chapter 1 provides an overview of the scope of this book. It begins with a simplified classification of shell structures to differentiate between the various idealizations of shell structures considered. Computer-aided curve and surface modelling tools used to represent the geometries of the shell structures are then briefly described. Next, the element technology required for the analysis of shell structures is presented. Later, the basic algorithm for structural shape optimization is outlined. In the penultimate section, the main computer programs contained in the book are summarized. Finally, the layout of the book is described.

Keywords

Design Variable Shell Structure Structural Optimization Problem Mathematical Programming Method Finite Strip 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Kirchhoff G. Ü ber das Gleichgewicht und die Bewegung einer elastischen Scheibe. J Reine Angew Mathe (Crelle’s J) 1850;40:51–88.MATHCrossRefGoogle Scholar
  2. [2]
    Kirchhoff G. Vorlesungen über mathematische Physik. Vols 1-4. Berlin: University of Berlin; 1876-1894.Google Scholar
  3. [3]
    Kirchhoff G. Über die Gleichungen des Gleichgewichts eines elastischen Körpers bei nicht unendlich kleinen Verschiebungen seiner Teile. Sitzungsberichte der Kgl. Akademie der Wissenschaften in Wien 1852;9:762–73.Google Scholar
  4. [4]
    Love AEH. A Treatise on the mathematical Theory of Elasticity. Vols 1-2, 4th ed. Cambridge: Cambridge University Press; 1892-1893. Reprinted by Dover Publ, ISBN 0486601749; 1944.MATHGoogle Scholar
  5. [5]
    Kruzelecki J, Zyczkowski M. Optimum structural Design of Shells-a Survey. SM Arch 1985;10:101–70.MATHGoogle Scholar
  6. [6]
    Mota Soares CM, Barbosa JI, Mota Soares CA, Pinto P. Optimal Design of axisymmetric Shell Structures. FEMCAD 1987; 68–78.Google Scholar
  7. [7]
    Marcelin JL, Trompette P. Optimal Shape Design of thin axisymmetric Shells. Eng Optim 1988;13:109–117.CrossRefGoogle Scholar
  8. [8]
    Hartmann D, Neumann M. Structural Optimization of a Box-girder Bridge by Means of the Finite Strip Method. In: Brebbia CA, Hernandez S, editors. Computer Aided Optimum Design of Structures. 1989. p 337–46.Google Scholar
  9. [9]
    Olhoff N. Optimal Design of vibrating circular Plates. Int J Solids Struct 1970;6:139–56.MATHCrossRefGoogle Scholar
  10. [10]
    Bletzinger KU, Reitinger R. Shape Optimization of Shells. In: Proceedings of International Symposium on Natural Structures-Principles, Strategies and Models in Architecture and Nature, 1991 Oct 1-4, Stuttgart, Germany. Stuttgart: Universität Stuttgart; 1991.Google Scholar
  11. [11]
    Plaut RH, Johnson LW, Parbery R. Optimum Forms of shallow Shells with circular Boundary, Parts 1-3. J Appl Mech 1984;51:526–39.MATHCrossRefGoogle Scholar
  12. [12]
    Hamada M. On the Optimum Shape of some axisymmetric Shells. In: Sawczuk A, Mroz Z, editors. Optimization in Structural Design. New York: Springer-Verlag, 1975.Google Scholar
  13. [13]
    Thambiratnam DP, Thevendran V. Optimum vibrating Shapes of Beams and circular Plate. J Sound Vib 1988;121:13–23.MATHCrossRefGoogle Scholar
  14. [14]
    Roozen-Kroon PJM. Structural Optimization of Bells [PhD thesis]. Eindhoven: Technische Universiteit Eindhoven; 1992.Google Scholar
  15. [15]
    Hinton E, Rao NVR. Structural Shape Optimization of Shells and folded Plates using two noded Finite Strips. Comput Struct 1993;46:1055–1071.MATHCrossRefGoogle Scholar
  16. [16]
    Hinton E, Rao NVR. Analysis and Shape Optimization of variable-thickness prismatic folded Plates and curved Shells, Parts 1-2. Thin Walled Struct 1993;17:81–111 and 161-83.CrossRefGoogle Scholar
  17. [17]
    Hinton E, Özakça M, Rao NVR. Free Vibration Analysis and Shape Optimization of variable-thickness prismatic folded Plates and curved Shells, Parts 1-2. J Sound Vib 1995;181:553–66 and 567-81.CrossRefGoogle Scholar
  18. [18]
    Hinton E, Özakça M, Rao NVR. Free Vibration Analysis and Shape Optimization of prismatic folded Plates and Shells with circular curved Planform. Int J Numer Methods Eng 1994;37:1713–39.CrossRefGoogle Scholar
  19. [19]
    Bendsøe MP, Kikuchi N. Generating optimal Topologies in structural Design using a Homogenization Method. Comput Methods Appl Mech Eng 1988;71:197–224.CrossRefGoogle Scholar
  20. [20]
    Bendsøe MP. Optimal Shape Design as a Material Distribution Problem. Struct Optim 1989;l:193–202.CrossRefGoogle Scholar
  21. [21]
    Issued by Indian Standards Institution: Indian Standard Criteria for the Design of reinforced Concrete Shells and folded Plates; Apr 1963. Report No.: IS 2210-1962, New Delhi: Indian Standards Institution.Google Scholar
  22. [22]
    Ramaswamy G.S. Design and Construction of Reinforced Concrete Shell Roofs. Malabar: Robert E Krieger Publishing Co.; 1984.Google Scholar
  23. [23]
    Cheung YK. Recent Advances in Finite Strip Method. In: Cheung YK, Lee JHW, Leung AYT, editors. Computational Mechanics. Rotterdam: Balkema; 1991.Google Scholar
  24. [24]
    Faux ID, Pratt MJ. Computational Geometry for Design and Manufacture. Chichester: Ellis Horwood; 1979.MATHGoogle Scholar
  25. [25]
    Qing SB, Yuan LD. Computational Geometry, Curve and Surface Modelling. London: Academic Press; 1989.Google Scholar
  26. [26]
    Zienkiewicz OC, Taylor RL. The Finite Element Method. Vols 1-2, 4th ed. New York: McGraw-Hill; 1991.Google Scholar
  27. [27]
    Gould PL. Finite Element Analysis of Shells of Revolution. New York: Pitman Publishing Co.; 1985.Google Scholar
  28. [28]
    Hinton E, Owen DRJ. Finite Element Software for Plates and Shells. Swansea: Pineridge Press; 1984.MATHGoogle Scholar
  29. [29]
    Cheung YK. Finite Strip Method in Structural Analysis. Sydney: Pergamon Press; 1976.Google Scholar
  30. [30]
    Zienkiewicz OC, Bauer J, Morgan K, Oñate, E. A simple and efficient Element for axisymmetric Shells. Int J Numer Methods Eng 1977;11:1545–58.MATHCrossRefGoogle Scholar
  31. [31]
    Day RA, Potts DM. Curved Mindlin Beam and axisymmetric Shell Elements — a new Approach. Int J Numer Methods Eng 1990;30:1263–74.MATHCrossRefGoogle Scholar
  32. [32]
    Shephard MS. Approaches to the automatic Generation and Control of Finite Element Meshes. Appl Mech Rev 1988;41:169–85.CrossRefGoogle Scholar
  33. [33]
    Zienkiewicz OC, Campbell JS. Shape Optimization and sequential linear Programming. In: Gallagher RH, Zienkiewicz OC, editors. Optimum Structural Design. Chichester: John Wiley; 1973. Chapter 7.Google Scholar
  34. [34]
    Haftka RT, Adelman HM. Recent Developments in structural Sensitivity Analysis. Struct Optim 1989;1:137–151.CrossRefGoogle Scholar
  35. [35]
    Dailey RL. Eigenvector Derivatives with repeated Eigenvalues. AIAA J 1988;27: 486–491.MathSciNetCrossRefGoogle Scholar
  36. [36]
    Fox RL, Kapoor MP. Rate of Change of Eigenvalues and Eigenvectors. AIAA J 1968;6:2426–29.MATHCrossRefGoogle Scholar
  37. [37]
    Wang BP. An improved approximate Method for computing Eigenvector Derivatives. In: Proceedings of the AIAA/ASME/ASCE/AHS 26th Structures, Structural Dynamics and Materials Conference; 1985. Orlando, USA.Google Scholar
  38. [38]
    Nelson RB. Simplified Calculation of Mode Eigenvector Derivatives. AIAA J 1976;14:1201–5.MathSciNetMATHCrossRefGoogle Scholar
  39. [39]
    Murthy DV, Haftka RT. Derivatives of Eigenvalues and Eigenvectors of a general complex Matrix. Int J Numer Methods Eng 1988;26:293–311.MathSciNetMATHCrossRefGoogle Scholar
  40. [40]
    Powell MJD. Algorithms for nonlinear Constraints that use Lagrangian Functions. Math Program 1978;14:224–48.MATHCrossRefGoogle Scholar
  41. [41]
    Svanberg K. The Method of moving Asymptotes-a new Method for structural Optimization. Int J Numer Methods Eng 1987;13:359–73.MathSciNetCrossRefGoogle Scholar
  42. [42]
    Powell MJD. VMCWD: A Fortran Subroutine for constrained Optimization [internal report]. Cambridge: Department of Applied Mathematics and Theoretical Physics, University of Cambridge; 1982. Report No.: DAMTP 1982/NA4.Google Scholar
  43. [43]

Copyright information

© Springer-Verlag London 2003

Authors and Affiliations

  • Ernest Hinton
    • 1
  • Johann Sienz
    • 2
  • Mustafa Özakça
    • 3
  1. 1.Department of Civil EngineeringUniversity of Wales SwanseaSwanseaUK
  2. 2.Department of Mechanical EngineeringUniversity of Wales SwanseaSwanseaUK
  3. 3.Department of Civil Engineering, Faculty of EngineeringUniversity of GaziantepGaziantepTurkey

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