Optimization of Fiber Orientation and Concentration in Composites

  • J. Thomsen
  • N. Olhoff
Part of the International Centre for Mechanical Sciences book series (CISM, volume 332)


Linearly elastic fiber reinforced composite discs and laminates in plane stress with variable local orientation and concentration of one or two fiber fields embedded in the matrix material, are considered. The thickness and the domain of the discs or laminates are assumed to be given, together with prescribed boundary conditions and in-plane loading along the edge.

The problem under study consists in determining throughout the structural domain the optimum orientations and concentrations of the fiber fields in such a way as to maximize the integral stiffness of the composite disc or laminate under the given loading. Minimization of the integral stiffness can also be carried out. The optimization is performed subject to a prescribed bound on the total cost or weight of the composite that for given unit cost factors or specific weights determines the amounts of fiber and matrix materials in the structure. Examples are presented by the end of the paper.


Design Variable Topology Optimization Fiber Orientation Fiber Concentration Total Strain Energy 
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  1. [1]
    Thomsen, J.: Optimization of Composite Discs. Rept. no. 21, Institute of Mechanical Engineering, The University of Aalborg, Aalborg, Denmark, pp. 27, June 1990. (Submitted to Structural Optimization).Google Scholar
  2. [2]
    Rasmussen, S.H.: Optimization of Fiber Reinforced Structures (in Danish), DCAMM report no. S12, The Technical University of Denmark, Lyngby, Denmark, pp. 127, 1979.Google Scholar
  3. [3]
    Niordson, F.; Olhoff, N.: Variational Methods in Optimization of Structures: Trends in Solid Mechanics 1979, Proc. W.T. Koiter Anniversary Symp. (eds.: J.F. Besseling and A.M.A. van der Heijden), Sijthoff & Noordhoff, 177–194, 1979.Google Scholar
  4. [4]
    Pedersen, P.: Bounds on Elastic Energy in Solids of Orthotropic Materials. Structural Optimization, 2, 55–63, 1990.CrossRefGoogle Scholar
  5. [5]
    Pedersen, P.: On Optimal Orientation of Orthotropic Materials. Structural Optimization. 1, 101–106, 1989.CrossRefGoogle Scholar
  6. [6]
    Pedersen, P.: Combining Material and Element Rotation in One Formula. Comm. Appl. Num. Meth. (to appear 1990 ).Google Scholar
  7. [7]
    Pedersen, P.: Energy Bounds by Material Rotation. Same issue of this JournalGoogle Scholar
  8. [8]
    Banichuk, N.V.: Problems and Methods of Optimal Structural Design. New York: Plenum Press, 181–207, 1983.Google Scholar
  9. [9]
    Sacchi Landriani, G.; Rovati, M.: Optimal Design of 2-D Structures Made of Composite Materials. (Submitted to J. Engrg. Materials and Technology).Google Scholar
  10. [10]
    Bendsoe, M.P.; Kikuchi, N.: Generating Optimal Topologies in Structural Design Using a Homogenization Method. Computer Methods in Applied Mechanics and Engineering. 71, 197–224, 1988.CrossRefMathSciNetGoogle Scholar
  11. [11]
    Bendsoe, M.P.: Optimal Shape Design as a Material Distribution problem. Structural Optimization. 4, 193–202, 1989.CrossRefGoogle Scholar
  12. [12]
    Fleury, C.; Braibant, V.: Structural Weight Optimization by Dual Methods of Convex Programming. International Journal for Numerical Methods in Engineering. 14, 1761–1783, 1986.CrossRefMathSciNetGoogle Scholar
  13. [13]
    Jones, R.M.: Mechanics of Composite Materials. New York: McGraw-Hill, 1975.Google Scholar
  14. [14]
    Tsai, S.W.; Pagano, N.J.: Invariant Properties of Composite Materials. Composite materials workshop. Technomic, Westport Com, 1968.Google Scholar
  15. [15]
    Institut National de Recherche en Informatique et en Automatique (INRIA, France). Avril 1983: Modulef, Bibliotheque D’Elasticite. 101, 1983.Google Scholar
  16. [16]
    Olhoff, N.; Taylor, J.E.: On Structural Optimization, J. Appt. Mech., 1139–1151, 1983.Google Scholar

Copyright information

© Springer-Verlag Wien 1993

Authors and Affiliations

  • J. Thomsen
    • 1
  • N. Olhoff
    • 1
  1. 1.The University of AalborgAalborgDenmark

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