Stress bounds or bars in torsion



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This investigation is concerned with bounds on the maximum shear stress in bars subjected to twisting by applied end couples. The results which are found within the framework of the Saint-Venant formulation, are applicable to bars of homogeneous, anisotropic material, having a simply connected cross section. In the case of isotropic bars we arrive at an upper bound that evidently constitutes an improvement over those available in the literature. On the other hand, there appears to be nothing in the literature concerning stress bounds for bars of anisotropic materials. The key idea involved in the derivation of the upper bound for the isotropic bars is the minimum principle for superharmonic functions. The stress bounds for anisotropic bars are found both in a manner analogous to the development to the isotropic case, and by directly applying an affine transformation to the results found in the isotropic case. Both methods are used for orthotropic and anisotropic bars.