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Design optimization for truss structures under elasto-plastic loading condition

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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.

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References

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  3. Zienkiewicz, O.C. and Taylor, R.L., The Finite Element Method, London: McGraw-Hill, 1994.

    MATH  Google Scholar 

  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.

    Article  Google Scholar 

  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. 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. 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.

    Article  MathSciNet  Google Scholar 

  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.

    Article  Google Scholar 

  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. 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. 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.

    Article  Google Scholar 

  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.

    Article  MathSciNet  Google Scholar 

  13. Dreyfus, S.E., Dynamic Programming and the Calculus of Variations, New York: Academic Press, 1965.

    MATH  Google Scholar 

  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.

  15. Fletcher, R. and Leyffer, S., Numerical experience with solving MPECs as NLPs, University of Dundee Report NA/210, 2002.

  16. Arora, J.S. and Cardoso, J.B., Variational principle for shape design sensitivity analysis, AIAA Journal, Vol.30, No.2, 1992, 538–547.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Engineering Mechanics, Northwestern Polytechnical University, Xi’an, 710072, China

    Tao Liu & Ziehen Deng

  2. State Key Laboratory of Structural Analysis of Industrial Equipment, Dalian University of Technology, Dalian, 116024, China

    Ziehen Deng

Authors
  1. Tao Liu
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  2. Ziehen Deng
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Correspondence to Ziehen Deng.

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Project supported by the National Natural Sciences Foundation of China (Nos. 10372084 and 10572119), the Program for New Century Excellent Talents in University (No. NCET-04-0958), the Open Foundation of State Key Laboratory of Structural Analysis of Industrial Equipment and the Doctorate Foundation of Northwestern Polytechnical University.

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Liu, T., Deng, Z. Design optimization for truss structures under elasto-plastic loading condition. Acta Mech. Solida Sin. 19, 264–274 (2006). https://doi.org/10.1007/s10338-006-0632-6

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  • DOI: https://doi.org/10.1007/s10338-006-0632-6

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