Constrained torsion of thin closed composite sections
Jan Lewiński, Andrzej Wilczyński
Quarterly No. 4, 2009 pages 384-389
DOI:
keywords: polymeric composites, constrained torsion, sectorial coordinates, sectorial moments of inertia
abstract The paper presents a theoretical solution for torsion of thin, closed composite sections. Such problems, known for isotropic materials are not easily accessible for anisotropic composite structures despite quick development of these materials. This enforces use of not always justifiable laborious numeric methods. Constrained torsion problems and solutions were posed and developed to a great extent in the Soviet Union, starting at the begining of the thirties in the previous century and greatly, without the use of computers and applied mostly by the military aviation industry during the World War II. The presented solution is an exact extension of the known results, to which the reader is directed, to the case of anisotropic polymeric compo-sites, using methods of description presented in several monographs, two of which can be found in the literature list. The solution is based on formulation of analytical relations, allowing for determination of normal and shear stress distributions in the wall of the tube and the angle of torsion, taking into account the warp of the profile. To obtain the full solution the problems of pure torsion, shear by transverse forces and finally the constrained torsion had to be investigated. Analysis of free torsion (with unrestricted warp possibility) led to introduction of a new quantity - the sectorial coordinate, a convenient area description in the cases of constrained torsion, replacing the possible use of higher order moments of inertia. Solution of the shear problem gave coordinates of the axis of rotation of the profile, while the case of constrained torsion allowed for calculation of normal stresses, not existing in pure torsion. Results for composite structures differ from isotropic cases only by the influence of anisotropic elasticity constants and use these values in weighted averages describing material properties. The proposed theory is used in an exemplary solution of an engineering problem, showing the straight applicability in simple cases.