Structural Engineering and Mechanics

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Shape optimization by the boundary element method with a reduced basis reanalysis technique

  • Leu, Liang-Jenq (Department of Civil Engineering, National Taiwan University)
  • Published : 1999.07.25
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Abstract

This paper is concerned with shape optimization problems by the boundary element method (BEM) emphasizing the use of a reduced basis reanalysis technique proposed recently by the author. Problems of this class are conventionally carried out iteratively through an optimizer; a sequential quadratic programming-based optimizer is used in this study. The iterative process produces a succession of intermediate designs. Repeated analyses for the systems associated with these intermediate designs using an exact approach such as the LU decomposition method are time consuming if the order of the systems is large. The newly developed reanalysis technique devised for boundary element systems is utilized to enhance the computational efficiency in the repeated system solvings. Presented numerical examples on optimal shape design problems in electric potential distribution and elasticity show that the new reanalysis technique is capable of speeding up the design process without sacrificing the accuracy of the optimal solutions.

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References

  1. Brebbia, C.A and Dominguez, J. (1992), Boundary Elements: an Introductory Course, 2nd edition, Computational Mechanics Publications, Southampton, UK.
  2. Haug, E.J., Choi, K.K. and Komkov, V. (1986), Design Sensitivity Analysis of Structural Systems, Academic Press, New York.
  3. Lekhnitski, S.G. (1968), Anisotropic Plates, 2nd edition, translated by S.W. Tsai and T. Cheron, Gordon and Breach, New York.
  4. Leu, L.J. and Mukherjee, S. (1993), "Sensitivity analysis and shape optimization in nonlinear solid mechanics", Engineering Analysis with Boundary Elements, 12, 251-260. https://doi.org/10.1016/0955-7997(93)90052-M
  5. Leu, L.J. (1994), Sensitivity Analysis and Optimization in Nonlinear Solid Mechanics, Ph.D. Dissertation, Cornell University, Ithaca, New York.
  6. Leu, L.J. and Tsai, S.F. (1995), "Boundary element reanalysis for shape optimization", Loh, C.H. ed., Proceedings of the Fifth KU-KAlST-NTU Tri-Lateral Seminar/Workshop on Civil Engineering, National Taiwan University, Taipei, Taiwan.
  7. Sadegh, A.M. (1988), "On the Green's functions and boundary integral formulation of elastic planes with cutouts", Mech. Struct. Mach., 16, 293-311. https://doi.org/10.1080/08905458808960265
  8. Schwarz, H.R. (1989), Numerical Analysis: A Comprehensive Introduction, John Wiley & Sons, New York.
  9. Timoshenko, S.P. and Goodier, J.N . (1970), Theory of Elasticity, 3rd edition, McGraw-Hill, New York.
  10. Wei, X., Chandra, A., Leu, L.J. and Mukherjee, S. (1994), "Shape optimization in elasticity and elasto-viscoplasticity by the boundary element method", Int. J. Solids Structures, 31, 533-550. https://doi.org/10.1016/0020-7683(94)90091-4
  11. Zhou, J.L. and Tits, A.L. (1994), User's Guide for FSQP version 3.4: a FORTRAN Code for Solving Constrained Inequality and Linear Constraints, SRC TR-92-107r4, System Research Center, University of Nonlinear (Minimax) Optimization Problems, Generating Iterates Satisfying All Maryland, College Park, MD, U.S.A.

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