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Acta Mechanica Solida Sinica

, Volume 19, Issue 3, pp 264–274 | Cite as

Design optimization for truss structures under elasto-plastic loading condition

  • Tao Liu
  • Ziehen Deng
Article

Abstract

In this paper, a method for the design optimization of elasto-plastic truss structures is proposed based on parametric variational principles (PVPs). The optimization aims to find the minimum weight/volume solution under the constraints of allowable node displacements. The design optimization is a formulation of mathematical programming with equilibrium constraints (MPECs). To overcome the numerical difficulties of the complementary constraints in optimization, an iteration process, comprising a quadratic programming (QP) and an updating process, is employed as the optimization method. Furthermore, the elasto-plastic buckling of truss members is considered as a constraint in design optimization. A combinational optimization strategy is proposed for the displacement constraints and the buckling constraint, which comprises the method mentioned above and an optimal criterion. Three numerical examples are presented to show the validity of the methods proposed.

Key words

parametric variational principles elasto-plasticity truss structure optimization elasto-plasticity buckling 

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References

  1. [1]
    António, C.A.C., Barbosa, J.T. and Dinis, L.S., Optimal design of beam reinforced composite structures under elasto-plastic loading conditions, Struct. Multidisc. Optim., Vol.19, 2000, 50–63.CrossRefGoogle Scholar
  2. [2]
    Moita, J.S., Barbosa, J.I., Soares, C.M.M. and Soares, C.A.M., Sensitivity analysis and optimal design of geometrically non-linear laminated plates and shells, Computers and Structures, Vol.76, 2000, 407–420.CrossRefGoogle Scholar
  3. [3]
    Zienkiewicz, O.C. and Taylor, R.L., The Finite Element Method, London: McGraw-Hill, 1994.zbMATHGoogle Scholar
  4. [4]
    Clarke, M.J. and Hancock, G.J., A study of incremental-iterative strategies for nonlinear analysis, Int. J. Numer. Meth. Eng., Vol.29, 1990, 1365–1391.CrossRefGoogle Scholar
  5. [5]
    Chan, S.L. and Chui, P.P.T., Non-linear Static and Cyclic Analysis of Steel Frames with Semi-rigid Connections, Amsterdam, Lausanne: Elsevier, 2000.Google Scholar
  6. [6]
    Toklu, Y.C., On the solution of a minimum weight elastoplastic problem involving displacement and complementarity constraints, Computers methods in applied mechanics and engineering, Vol.174, 1999, 107–120.Google Scholar
  7. [7]
    Zhong, W.X. and Zhang, R.L., Parametric variational principles and their quadratic programming solutions in plasticity, Computers and Structures, Vol.30, 1988, 837–846.MathSciNetCrossRefGoogle Scholar
  8. [8]
    Zhong, W.X. and Sun, S.M., A finite element method for elasto-plastic structures and contact problems by parametric quadratic programming, Int. J. Numer. Meth. Eng., Vol.26, 1988, 2723–2738.CrossRefGoogle Scholar
  9. [9]
    Zhong, W.X., Zhang, H.W. and Wu, C.W., Parametric Variational Principles and Their Engineering Application, Beijing: Science Press, 1997 (in Chinese).Google Scholar
  10. [10]
    Zhong, W.X. and Zhang, H.W., Mixed Energy method for solution of quadratic programming problems and elastic-plastic analysis of truss structures, Acta Mechanica Solida Sinica, Vol.23, No.2, 2002, 125–132 (in Chinese).Google Scholar
  11. [11]
    Zhang, H.W, Zhong, W.X. and Gu, Y.X., A combined parametric quadratic programming and iteration method for 3D elastic-plastic frictional contact problem analysis, Comput. Meth. Appl. Mech., Vol.155, 1998, 307–324.CrossRefGoogle Scholar
  12. [12]
    Zhang, H.W., Zhang, X. and Chen, J.S., A new algorithm for numerical solution of dynamic elastic-plastic hardening and softening problems, Computers and Structures, Vol.81, 2003, 1739–1749.MathSciNetCrossRefGoogle Scholar
  13. [13]
    Dreyfus, S.E., Dynamic Programming and the Calculus of Variations, New York: Academic Press, 1965.zbMATHGoogle Scholar
  14. [14]
    Fletcher, R., Leyffer, S., Scholtes, S. and Ralph, D., Local convergence of SQP methods for mathematical programming problems with equilibrium constraints, Dundee Numerical Analysis Report NA/209, 2002.Google Scholar
  15. [15]
    Fletcher, R. and Leyffer, S., Numerical experience with solving MPECs as NLPs, University of Dundee Report NA/210, 2002.Google Scholar
  16. [16]
    Arora, J.S. and Cardoso, J.B., Variational principle for shape design sensitivity analysis, AIAA Journal, Vol.30, No.2, 1992, 538–547.CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2006

Authors and Affiliations

  1. 1.Department of Engineering MechanicsNorthwestern Polytechnical UniversityXi’anChina
  2. 2.State Key Laboratory of Structural Analysis of Industrial EquipmentDalian University of TechnologyDalianChina

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