Optimization of Fiber Orientation and Concentration in Composites
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 lami
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J. Thomsen and N. Olhoff The University of Aalborg, Aalborg, Denmark Abstract - 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 inplane 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.
1. INTRODUCTION This paper gives a brief account of recent research reported by the first author in [1) on optimization of fiber orientation and concentration in composite discs and laminates. The research is inspired by the initial work in the field by Rasmussen [2) (reported in Danish, account in English available in Niordson and Olhoff [3)) and by important recent developments of Pedersen [4-7). Problems concerning optimization of fiber orientation have earlier been considered by Banichuk (8], and we refer to Sacchi Landriani and Rovati (9] for other current research activities in the area. Since the present research also comprises optimization of fiber concentration, and allows for more than one field of fibers, our development can be easily augmented with appropriate constitutive material models applicable for Bends0e
topology optimization,
cf.
[10-11], and results for problems of this type have already
been obtained. The motivatipn for the work described in this paper is that fiber G. S. Landriani et al. (eds.), Evaluation of Global Bearing Capacities of Structures © Springer-Verlag Wien 1993
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J. Thomsen and N. Olhoff
reinforced composite materials are ideal for structural applications, where high stiffness and strength are required at low weight. Aircraft and spacecraft are typical weight sensitive structures, in which composite materials are cost effective. To obtain the full advantage of the fiber reinforcement, fibers must be distributed and oriented optimally with respect to the actual strain field. Hence, transfer of fiber material from initially lowly stressed parts of the body in order to strengthen the parts and directions that are subjected to large internal forces is the general idea of optimization of composite structures. Thus,
relative to refs.
[4-9], we in this paper both use fiber
orientations and -concentrations as design variables.
Based on the
strain field deteranined by finite element analysis we construct an iterative two-level optimization procedu
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