Abstract
ABSTRACT ABSTRACT In this paper the optimal cross-sectional shape of a thin-walled composite tube for maximum torsional rigidity is studied. Optimality conditions are presented, using variational principles. Due to unknown end points, transver-sality conditions are used to find boundary conditions. It is shown that a circular section is the optimal shape for a tube with helically-wound reinforced composite material. For an orthotropic tube, the optimal shape is found to be C continuous only for cases in which the degree of orthotropism is less than or equal to a critical value. Otherwise, the optimal shape contains cusps at the end points.
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