Skip to main content
SpringerLink
Log in
Book cover

Computer Aided Optimal Design: Structural and Mechanical Systems pp 605–631Cite as

Boundary Elements in Shape Optimal Design of Structural Components

  • Conference paper

Part of the book series: NATO ASI Series ((NATO ASI F,volume 27))

Abstract

The shape optimal design of shafts and two-dimensional elastic structural components is formulated using boundary elements. The design objective is to maximize torsional rigidity of the shaft or to minimize compliance of the structure, subject to an area constrain Also a model based on minimum area and stress constraints is developed, where the real and adjoint structures are identical, but with different loading conditions. All degrees of freedom of the models are at the boundary and there is no need for calculating displacements and stresses in the domain. Formulations based on constant, linear and quadratic boundary elements are developed. A method for calculating accurately the stresses at the boundary is presented, which improves considerably the design sensitivity information. It is developed a technique for an automatic mesh refinement of boundary element models. The corresponding nonlinear programming problems are solved by Pshenichny’s linearization method. The models are applied to shape optimal design of several shafts and elastic structural components. The advantages and disadvantages of the boundary element method over the finite element technique for shape optimal design of structures are discussed with reference to applications. A literature survey of the development of the boundary element method for shape optimal design is presented.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. O. Pironnneau, Optimal Shape Design for Elliptical Systems, Springer–Verlag, (1984).

    Google Scholar 

  2. E.J. Haug, K.K. Choi and V. Komkov, Design Sensitivity Analysis of Structural Systems, Academic Press, (1986).

    MATH  Google Scholar 

  3. O.C. Zienkiewicz and J.S. Campbell, Shape Optimization and Sequential Linear Programming, Optimum Structural Design (Ed. R.H. Gallagher and O.C. Zienziewicz), Wiley, 109–126 (1973).

    Google Scholar 

  4. C.A. Mota Soares, H.C. Rodrigues, L.M. Oliveira Faria and E.J. Haug, Optimization Of the Geometry of Shafts Using Boundary Elements. ASME Journal of Mechanisms, Transmissions and Automation in Design, 106, 199–203 (1984).

    Google Scholar 

  5. C.A. Mota Soares, H.C. Rodrigues, L.M. Oliveira Faria and E.J. Haug, Optimization of the Shape of Solid and Hollow Shafts Using Boundary Elements, Boundary Elements (Ed. C.A. Brebbia), Springer–Verlag, 883–889 (1983).

    Google Scholar 

  6. C.A. Mota Soares, H.C. Rodrigues, L.M. Oliveira Faria and E.J. Haug, Boundary Elements in Shape Optimal Design of Shafts, Optimization in Computer Aided Design (Ed. J.S. Gero), North–Holland, 155–175 (1985).

    Google Scholar 

  7. H.C. Rodrigues and C.A. Mota Soares, Shape Optimization of Shafts, Third National Congress of Theoretical and Applied Mechanics, Lisbon, (1983) (in Portuguese).

    Google Scholar 

  8. H.C. Rodrigues, Shape Optimization of Shafts Using Boundary Elements, M.Sc. Thesis, Technical University of Lisbon, (1984) (in Portuguese).

    Google Scholar 

  9. T. Burczynski and T. Adamczyk, Multiparameter Shape Optimization of a Bar in Torsion by the Boundary Element Method, Proc. 28rd Symposium on Modelling in Mechanics, The Polish Society of Theoretical and Applied Mechanics, Gliwice, (1984) (in Polish).

    Google Scholar 

  10. A. Zochowski and K. Mizukami, A Comparison of BEM and FEM in Minimum Weight Design, Boundary Elements (Ed. C.A. Brebbia), Springer–Verlag, 901–911 (1983).

    Google Scholar 

  11. C.A. Mota Soares, H.C. Rodrigues and K.K. Choi, Shape Optimal Design of Elastic Structural Components Using Boundary Elements, Tenth International Congress on the Applications of Mathematics in Engineering Science, Weimar, 5, 80–82 (1984).

    Google Scholar 

  12. C.A. Mota Soares, H.C. Rodrigues and K.K. Choi, Shape Optimal Structural Design Using Boundary Elements and Minimum Compliance Techniques, ASME Journal of Mechanisms, Transmissions and Automation in Design, 106, 518–523 (1984).

    Google Scholar 

  13. R.P. Leal,Boundary Elements in Bidimensional Elasticity, M.Sc. Thesis, Technical University of Lisbon, (1985) (in Portuguese).

    Google Scholar 

  14. C. Mota Soares and K.K. Choi. Boundary Elements in Shape Optimal Design of Structures, The Optimum Shape–Automated Structural Design (Editor J.A. Bennett and M.E. Botkin), Plenum Press, 199–236 (1986).

    Google Scholar 

  15. T. Burczynski and T. AdamczyK, The Application of the Boundary Element Method to Optimal Design of Shape of Structures, Proc. 4th Conference on Methods and Instrumentations of Computer Aided Design, Warsaw, (1983) (in Polish).

    Google Scholar 

  16. T. Burczynski and T. Adamczyk, The Boundary Element Formulation for Multiparameter Structure Shape Optimization, Applied Mathematical Modelling, 9, 195–200 (1985).

    Article  MathSciNet  MATH  Google Scholar 

  17. T. Burczynski and T. Adamczyck, The Boundary Element Method for Shape Design Synthesis of Elastic Structures, Seventh International Conference on Boundary Element Methods (Ed. C.A. Brebbia ), Springer– Verlag, (1985).

    Google Scholar 

  18. T. Burczynski and T. Adamczyck, Generation of Optimal Shape of Structures by Means of the Boundary Element Method, Zeszyty Naukowe Politechniki Slaskiej, Mechanika Z.82, Slaska, (1985) (in Polish).

    Google Scholar 

  19. T. Burczynski and T. Adamczyck, The Boundary Element Procedure for Dependence of Eigenvalues with Respect to Stochastic Shape of Elastic Systems, Proc. 25th Symposium in Mechanics, Gliwice, (1986).

    Google Scholar 

  20. D. Eizadian, Optimization of The Shape of Bidimensional Structures by the Boundary Integral Equation Method, Ph.D. Thesis, National Institute of Applied Science of Lyon, (1984) (in French).

    Google Scholar 

  21. D. Eizadian and M. Trompette, Shape of Bidimensional Structures by the Boundary Element Method, Conference on CAD/CAM, Robotics and Automation in Design, Tucson, Arizona, (1985).

    Google Scholar 

  22. J.H. Kane, Optimization of Continuum Structures Using a Boundary Moment Formulation, Ph.D. Thesis, University of Connecticut, (1986).

    Google Scholar 

  23. J.H. Kane, Shape Optimization Utilizing a Boundary Element Formulation, to appear.

    Google Scholar 

  24. T. Futagami, Boundary Element and Linear Programming Method in Optimizationof Partial Differential Systems, Boundary Element Methods (Ed. C.A. Brebbia), Springer– Verlag, 457–471 (1981).

    Google Scholar 

  25. T. Futagami, Boundary Element and Dynamic Programming Method in Optimization of Transient Partial Differential Systems, Boundary Elements Methods in Enginnering (Ed. C.A. Brebbia), Springer–Verlag, 58–71 (1982).

    Google Scholar 

  26. T. Futagami, Boundary Element Method–Finite Element Method Coupled with Linear Programming for Optimal Control of Distributed Parameter Systems, Boundary Elements (Ed. C.A. Brebbia), Springer–Verlag, 891–900 (1983).

    Google Scholar 

  27. M.R. Barone and D.A. Caulk, Optimal Arrangement of Holes in a Two– Dimensional Heat Conductor by a Special Boundary Integral Method, International Journal of Numerical Methods in Engineering, 18, 675–685 (1982).

    Article  MATH  Google Scholar 

  28. R.A. Meric, Boundary Integral Equation and Conjugate Gradient Methods for Optimal Boundary Heating of Solids, International Journal of Heat and Mass Transfer, 26, 261–264 (1983).

    Article  Google Scholar 

  29. R.A. Meric, Boundary Element Methods for Static Optimal Heating of Solids, ASME Journal of Heat Transfer, 106, 876–880 (1984).

    Article  Google Scholar 

  30. R.A. Meric, Boundary Element Methods for Optimization of Distributed Parameter Systems, International Journal of Numerical Methods in Engineering, 20, 1291–1306 (1984).

    Article  MATH  Google Scholar 

  31. R.A. Meric, Boundary Elements in Shape Design Sensitivity Analysis of Thermoelastic Solids, Computer Aided Optimal Design: Structural and Mechanical Systems (Ed. C.A. Mota Soares ), Springer–Verlag, (1987).

    Google Scholar 

  32. R.A. Meric, Shape Design Sensitivity Analysis for Nonlinear Anisotropic Heat Conducting Solids and Shape Optimization by BEM, International Journal of Numerical Methods in Engineering, to appear.

    Google Scholar 

  33. B.M. Kwak and J.H. Choi, Shape Design Sensitivity Analysis Using Boundary Integral Equation for Potential Problems,Computer Aided Optimal Design: Structural and Mechanical Systems, (Ed. C.A. Mota Soares ), Springer–Verlag, (1987).

    Google Scholar 

  34. J.H. Choi and B.M. Kwak, Boundary Integral Equation Method for Shape Design Sensitivity Analysis, Journal of Structural Mechanics, to appear.

    Google Scholar 

  35. P.K. Banerjee and R. Butterfield, Boundary Element Methods in Engineering Science, Mcgraw–Hill, (1981).

    MATH  Google Scholar 

  36. G. Fairweather, F.J. Rizzo, D.J. Shippy and Y.S. Wu, On the Numerical Solution of Two– Dimensional Potential Problems by an Improved Boundary Integral Equation Method, Journal of Computational Physics, 31, 96–112 (1979).

    Article  MathSciNet  MATH  Google Scholar 

  37. CA. Brebbia, J. Teiles and L. Wrobel, Boundary Element Techniques: Theory and Applications in Engineering, Springer–Verlag, (1984).

    MATH  Google Scholar 

  38. B.N. Pshenichny and J.M. Danilin, Numerical Methods in Extremal Problems, MIR, (1978).

    Google Scholar 

  39. I.M. Gelfand and S.W. Fomin, Calculus of Variations, Prentice– Hall, (1961).

    Google Scholar 

  40. N.W. Banichuk, Problems and Methods of Optimal Structural Design, Plenum Press, (1983).

    Google Scholar 

  41. F. Hartmann, Elastostatics, Progress in Boundary Element Methods Volume I (Ed. C.A. Brebbia), Wiley, 84–167 (1981).

    Google Scholar 

  42. E. Rank, A-Posteriori Error Estimates and Adaptive Refinement for Some Boundary Integral Element Methods,Proceeddings of the International Conference on Accuracy Estimates and Adaptive Refinement in Finite Element Computations, Lisboa, (1984).

    Google Scholar 

  43. E. Rank, Adaptivity and Accuracy Estimation for Finite Element and Boundary Integral Element Methods, Accuracy Estimates and Adaptivity for Finite Element, (Ed. J. Babuska, O.C. Zienckiencz, J.P. Gago and E. Arantes e Oliveira ), Wiley, (1986).

    Google Scholar 

  44. G.C. Hsiao, P. Kopp and W.C. Wendland, A Galerkin Colocation Method for Some Integral Equations of the First Kind, Computing, 25, 88–130 (1980).

    Article  Google Scholar 

  45. J. Rencis and R.L. Mullen, A Self Adaptive Mesh Refinement Technique for Boundary Element Solution of the Laplace Equation, 21st Annual Meeting of the Society of Engineering Science, Blacksburg, Virginia, (1984).

    Google Scholar 

  46. J.J. Rencis and R.L. Muellen, A Self–Adaptive Mesh Refinement Technique for Boundary Element Solution of the Laplace Equation, Computer Methods in Applied Mechanics and Engineering, (1986).

    Google Scholar 

  47. J.J. Rencise R. L. Muellen, Solutation of Elasticity Problems by a Self–Adaptive Mesh Refinement Technique for Boundary Element Computation, International Journal for Numerical Methods in Engineering, 23, 1509–1527 (1986).

    Article  Google Scholar 

  48. E.Alarcon, L. Avia and A. Revester, On the Possibility of Adaptive Boundary Element, International Conference on Accuracy Estimates and Adaptive Refinements in Finite Element Computations, Lisbon, 25– 34 (1984).

    Google Scholar 

  49. E. Alarcon, A. Revester e J. Molina, Hierarchical Boundary Elements, Computer and Structures, 20, 151–156 (1985).

    Article  MATH  Google Scholar 

  50. E. Alarcon and A. Revester, p–Adaptive Boundary Elements, International Journal for Numerical Methods in Engineering, 23, 801– 829, (1986).

    Google Scholar 

  51. A. Gonzalez and E. Alarcon. Adaptive Refinements in Boundary Elements, Proceedings of the First World Congress on Computational Mechanics, Austin, Texas, 22–26 September, (1986).

    Google Scholar 

  52. A. Peano, A. Pasini, R. Riccioni and L. Sardella, Adaptive Approximation in Finite Element Structural Analysis, Computer and Structures, 10, 333–342 (1979).

    Article  MATH  Google Scholar 

  53. J.C. Lachat, A Further Developement of the Boundary Integral Technique for Elastostatics, Ph.D. Thesis, Univ. of Southampton, (1973).

    Google Scholar 

  54. K.K. Choi, E.J. Haug, J.W. Hou and V.M. Sohoni, Pshenichny’s Linearizations Method for Mechanical Systems Optimization, ASME Journal of Mechanisms, Transmissions and Automation in Design, 105, 97–104 (1983).

    Article  Google Scholar 

  55. J.W. Hou, E.J. Haug and R.L. Benedict, Shape Optimization of Elastic Bars in Torsion, Sensitivity of Functionals with Applications to Engineering Problems (Ed. V. Komkov), Springer–Verlag, 31–55 (1984).

    Google Scholar 

  56. E.J. Haug, K.K. Choi, J.W. Hou and Y.M. Yoo, A Variational Method for Shape Optimal Design of Elastic Structures,New Directions in Optimum Structural Design (Ed. E. Atrek, R.H. Gallagher, K.M. Ragsdell and O.C. Zienziewicz), Wiley, 105–137 (1984).

    Google Scholar 

  57. R.J. Yang, K.K. Choi and E.J. Haug, Numerical Considerations in Structural Component Shape Optimization, ASME Journal of Mechanisms, Transmissions and Automation in Design, to appear.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Instituto Superior Técnico, Centro de Mecânica e Materials da Universidade, Técnica de Lisboa (CEMUL), Av. Rovisco Pais, 1096, Lisboa Codex, Portugal

    C. A. Mota Soares & R. P. Leal

  2. Center for Computer Aided Design, College of Engineering, The University of Iowa, Iowa City, IA, 52242, USA

    K. K. Choi

Authors
  1. C. A. Mota Soares
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. P. Leal
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. K. K. Choi
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Instituto Superior Técnico, Centro de Mecânica e Materiais da Universidade Técnica de Lisboa — CEMUL, Avenida Rovisco Pais, 1096, Lisboa Codex, Portugal

    Carlos A. Mota Soares

Rights and permissions

Reprints and permissions

Copyright information

© 1987 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Mota Soares, C.A., Leal, R.P., Choi, K.K. (1987). Boundary Elements in Shape Optimal Design of Structural Components. In: Mota Soares, C.A. (eds) Computer Aided Optimal Design: Structural and Mechanical Systems. NATO ASI Series, vol 27. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83051-8_18

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-83051-8_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-83053-2

  • Online ISBN: 978-3-642-83051-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation