Skip to main content
SpringerLink
Log in
Book cover

Advances in Structural Optimization pp 47–70Cite as

Structural Design Sensitivity Analysis: Continuum and Discrete Approaches

  • Chapter

Part of the book series: Solid Mechanics and Its Applications ((SMIA,volume 25))

Abstract

A unified approach for structural design sensitivity analysis involving both shape and sizing variables is presented. Starting with a continuum formulation and a general response functional needing sensitivity analysis, the direct variation and adjoint approaches are derived. Discretization of the continuum expressions for the two approaches is presented and the numerical implementation aspects are discussed. The discretized forms of the continuum sensitivity expressions are compared with the ones obtained by starting with the discretized model ab initio. This comparison shows that the two approaches give similar discretized expressions for numerical calculations. Therefore, exactly same procedures can be used for computer implementation of both the approaches. The continuum approach, however, gives certain insights that would not be possible with only the discrete approach. The presented analyses and insights lead to a unified view point for numerical implementation of design sensitivity analysis which is quite straightforward with existing or new finite element analysis codes. The explicit design variations (partial derivatives with respect to the design variables) of the internal and external nodal forces are the major calculations needed to implement the design sensitivity analysis. An implementation scheme is suggested that is quite general and simple needing minimal programming.

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

  • Adelman, H.M. and Haftka, R.T. (1986), “Sensitivity Analysis of Discrete Structural Systems,” AIAA Journal 24, 823–832.

    Article  ADS  Google Scholar 

  • Arora, J.S. (1991), “Structural Shape Optimization: An Implementable Algorithm,” O. Ural and T-L. Wong (eds.), Electronic Computation, Proceedings of the Tenth Conference, American Society of Civil Engineers, New York, pp. 213–222.

    Google Scholar 

  • Arora, J.S. (1993), “An Exposition of Material Derivative Approach for Structural Shape Sensitivity Analysis,” Computer Methods in Applied Mechanics and Engineering 105, 41–62.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Arora, J.S. and Cardoso, J. B. (1986), “Design Sensitivity Analysis with Nonlinear Response,” Proceedings of the NASA Symposium on Sensitivity Analysis in Engineering, NASA Langley Research Center, September 25–26, NASA CP-2457.

    Google Scholar 

  • Arora, J.S. and Cardoso, J.B. (1989), “A Design Sensitivity Analysis Principle and Its Implementation into ADINA,” Computers and Structures 32, 691–705.

    Article  MATH  Google Scholar 

  • Arora, J.S. and Lee, T.H. (1993), “Shape Sensitivity Analysis of Nonlinear Nonconservative Problems”, in G. Rozvany (ed.),Optimization of Large Structural Systems, Proceedings of the NATO Advanced Study Institute, 23 September -4 October, 1991, Berchtesgaden, Germany, Kluwer Academic Publishers, NATO ASI Series, Series E: Applied Sciences -Vol. 231, Boston, MA, pp. 345–361.

    Google Scholar 

  • Arora, J.S., Lee, T.H. and Cardoso, J.B. (1992), “Structural Shape Sensitivity Analysis: Relationship between Material Derivative and Control Volume Approaches” AIAA Journal 30, 1638–1648.

    Article  ADS  MATH  Google Scholar 

  • Belegundu, A.D. and Rajan, S.D. (1988), “A Shape Optimization Approach Based on Natural Design Variables and Shape Functions,” Computer Methods in Applied Mechanics and Engineering 66, 87–106.

    Article  ADS  MATH  Google Scholar 

  • Belegundu, A.D., Rajan, S.D., Choi, B.K. and Budiman, J. (1987), “Shape Optimal Design Using Natural Shape Functions,” Technical Report PSU-ME-86/87–0029,Dept. of Mechanical Engineering, College of Engineering, The Pennsylvania State University, University Park, Pa 16802.

    Google Scholar 

  • Bennett, J.A. and Botkin, M.E. (eds.) (1986), The Optimum Shape: Automated Structural Design, Proceedings of International Symposium, G.M. Research Labs, Warren, MI, September 30-October 1, 1985, published by Plenum Press, New York.

    Google Scholar 

  • Cardoso, J.B. and Arora, J.S. (1988), “Variational Method for Design Sensitivity Analysis in Nonlinear Structural Mechanics,” AIAA Journal 26, 595–603.

    Article  MathSciNet  ADS  Google Scholar 

  • Cardoso, J.B. and Arora, J.S. (1992), “Design Sensitivity analysis of Nonlinear Dynamic Response of Structural and Mechanical Systems,” Structural Optimization. 4, 37–46.

    Article  Google Scholar 

  • Choi, K.K. and Seong, H.G. (1986), “A Domain Method for Shape Design Sensitivity Analysis of Built-up Structures,” Computer Methods in Applied Mechanics and Engineering, 57, 1–15.

    Article  ADS  MATH  Google Scholar 

  • Choi, K.K. and Santos, J.L.T. (1987), “Design Sensitivity Analysis of Nonlinear Structural Systems. Part I: General Theory,” International Journal for Numerical Methods in Engineering, 24, 2039–2055.

    Article  ADS  MATH  Google Scholar 

  • Choi, K.K. and Twu, S-L. (1989), “Equivalence of Continuum and Discrete Methods of Shape Design Sensitivity Analysis,” AIAA Journal, 27, 1418–1424.

    Article  MathSciNet  ADS  Google Scholar 

  • Dems, K. and Haftka, R.T. (1989), “Two Approaches to Sensitivity Analysis for Shape Variation of Structures,” Mechanics of Structures and Machines, 16, 501–522.

    Article  MathSciNet  Google Scholar 

  • Dems, K. and Mróz, Z. (1984), “Variational Approach by Means of Adjoint Systems to Structural Optimization and Sensitivity Analysis -II. Structure Shape Variation,” International Journal of Solids and Structures, 20, 527–552.

    Article  MathSciNet  MATH  Google Scholar 

  • Haber, R.B. (1987), “A New Variational Approach to Structural Shape Design Sensitivity Analysis,” in Computer-Aided Optimal Design, C.A. Mota Soares (ed.), Series F: Computer and System Sciences, Vol. 27, Springer-Verlag, New York, pp. 573–587.

    Google Scholar 

  • Haftka, R.T. and Adelman, H.M. (1989), “Recent Developments in Structural Sensitivity Analysis,” Structural Optimization, 1, 137–152.

    Article  Google Scholar 

  • Haririan, M., Cardoso, J.B. and Arora, J.S. (1987), “Use of ADINA for Design Optimizatioa of Nonlinear Structures,” Computers and Structures, 26, 123–134.

    Article  MATH  Google Scholar 

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

    MATH  Google Scholar 

  • Holtz, D.L. and Arora, J.S. (1994), “A Study of Large Scale Nonlinear Optimal Control,” Proceedings of the 5th ALAA/NASA/USAF/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Panama City, Florida, pp. 1459–1458.

    Google Scholar 

  • Hou, J.W., Chen, J.L. and Sheen, J.S. (1986), “Computational Method for Optimization of Structural Shapes,” AIAA Journal, 24, 1005–1012.

    Article  ADS  Google Scholar 

  • Hsieh, C.C. and Arora, J.S. (1984), “Design Sensitivity Analysis and Optimization of Dynamic Response,” Computer Methods in Applied Mechanics and Engineering, 43, 195–219.

    Article  ADS  MATH  Google Scholar 

  • Kamat, M. (ed.) (1993), Structural Optimization: Status & Review, AIAA Series in Astronautics and Aeronautics, Vol. 150, American Institute of Aeronautics and Astronautics, Washington, D.C.

    Google Scholar 

  • Lee, T.H. and Arora, J.S. (1995), “A Computational Method for Design Sensitivity Analysis of Elastoplastic Structures,” Computer Methods in Applied Mechanics and Engineering, to appear.

    Google Scholar 

  • Lee, T.H., Arora, J.S. and Kumar,V. (1993), “Shape Design Sensitivity Analysis of Viscoplastic Structures,” Computer Methods in Applied Mechanics and Engineering, 108, 237–259.

    Article  ADS  MATH  Google Scholar 

  • Mota Soares, C.A. (ed.) (1987), Computer-Aided Optimal Design, Proceedings of a NATO Advanced Study Institute, Series F: Computer and System Sciences, Vol. 27, Springer-Verlag, New York.

    Google Scholar 

  • Mukherjee, S. and Chandra, A. (1989), “A Boundary Element Formulation for Design Sensitivity Analysis in Materially Nonlinear Problems,” Acta Mechanica, 78, 243–253.

    Article  MathSciNet  MATH  Google Scholar 

  • Ohsaki, M. and Arora, J.S. (1994), “Design Sensitivity Analysis of Elasto-Plastic Structures,” Internationaljournal for Numerical Methods in Engineering, 37, 737–762.

    Article  ADS  MATH  Google Scholar 

  • Phelan, D.G. and Haber, R.B. (1989), “Sensitivity Analysis of Linear Elastic Systems Using Domain Parameterization and Mixed Mutual Energy Principle,” Computer Methods in Applied Mechanics and Engineering, 11, 31–59.

    Article  MathSciNet  ADS  Google Scholar 

  • Poldneff, M. J. and Arora, J. S. (1993), “Design Sensitivity Analysis of Coupled Thermoviscoelastic Systems,” Intern. Journal of Solids and Structures, 30, 607–635.

    Article  MATH  Google Scholar 

  • Poldneff, M.J., Rai, I.S. and Arora, J.S. (1993), “Design Variations of Nonlinear Elastic Structures Subjected to Follower Forces,” Computer Methods in Applied Mechanics and Engineering, 110, 211–219.

    Article  ADS  MATH  Google Scholar 

  • Rozvany, G.I.N., (ed.) (1993), Optimization of Large Structural Systems, Proceedings of the NATO Advanced Study Institute, 23 September -4 October, 1991, Berchtesgaden, Germany, Kluwer Academic Publishers, NATO ASI Series, Series E: Applied Sciences -Vol. 231, Boston, MA.

    Google Scholar 

  • Ryu, Y.S., Haririan, M., Wu, C.C. and Arora, J.S. (1985), “Structural Design Sensitivity Analysis of Nonlinear Response,” Computers and Structures, 21, 245–255.

    Article  MATH  Google Scholar 

  • Tortorelli, D.A., Lu, S.C.Y. and Haber, R. (1990), “Design Sensitivity Analysis for Elastodynamic Systems,” Mechanics of Structures and Machines, 18, 77–106.

    Article  MathSciNet  Google Scholar 

  • Tortorelli, D.A., Haber, R. and Lu, S.C.Y. (1991), “Adjoint Sensitivity Analysis for Nonlinear Dynamic Thermoelastic Systems,” AIAA Journal, 29, 253–263.

    Article  ADS  Google Scholar 

  • Tsay, J.J. and Arora, J.S. (1990), “Nonlinear Structural Design Sensitivity Analysis with Path Dependent Response. Part 1: General Theory,” Computer Methods in Applied Mechanics and Engineering, 81, 183–208.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Tsay, J.J., Cardoso, J.B. and Arora, J.S. (1990), “Nonlinear Structural Design Sensitivity Analysis with Path Dependent Response. Part 2: Analytical Examples,” Computer Methods in Applied Mechanics and Engineering, 81, 209–228.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Tseng, C-H. and Arora, J.S. (1989), “Optimum Design of Systems for Dynamics and Controls Using Sequential Quadratic Programming,” AIAA Journal, 27, 1793–1800.

    Article  ADS  Google Scholar 

  • Vidal, CA., Lee, H.S. and Haber, R.B. (1991), “A Consistent Tangent Operator for Design Sensitivity Analysis of History-Dependent Response,” Computer Systems in Engineering, 2, 509–523.

    Article  ADS  Google Scholar 

  • Wu, C.C. and Arora, J.S. (1987), “Design Sensitivity Analysis of Nonlinear Response Using Incremental Procedure,” AIAA Journal, 25, 1118–1125.

    Article  ADS  MATH  Google Scholar 

  • Yang, R.J. and Choi, K.K. (1985), “Accuracy of Finite Element Based Shape Design Sensitivity Analysis,” J. of Structural Mechanics, 13, 223–229.

    Article  Google Scholar 

  • Zhang, Q., Mukherjee, S. and Chandra, A. (1992), “Shape Design Sensitivity Analysis for Geometrically and Materially Nonlinear Problems by the Boundary Element Method,” International Journal of Solids and Structures, 29, 2503–2525.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Optimal Design Laboratory, College of Engineering, The University of Iowa, Iowa City, Iowa, 52242, USA

    Jasbir S. Arora

Authors
  1. Jasbir S. Arora
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Mechanical Engineering Program, COPPE/Federal University of Rio de Janeiro, Rio de Janeiro, Brazil

    José Herskovits

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Arora, J.S. (1995). Structural Design Sensitivity Analysis: Continuum and Discrete Approaches. In: Herskovits, J. (eds) Advances in Structural Optimization. Solid Mechanics and Its Applications, vol 25. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0453-1_2

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-0453-1_2

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4203-1

  • Online ISBN: 978-94-011-0453-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation