Asymptotically correct, linear theory is presented for thin-walled prismatic beams made of generally anisotropic materials. Consistent use of small parameters that are intrinsic to the problem permits a natural description of all thin-walled beams within a common framework, regardless of whether cross-sectional geometry is open, closed, or strip-like. Four “classical” one-dimensional variables associated with extension, twist, and bending in two orthogonal directions are employed. Analytical formulas are obtained for the resulting cross-sectional stiffness matrix (which, in general, is fully populated and includes all elastic couplings) as well as for the strain field. Prior to this work no analytical theories for beams with closed cross sections were able to consistently include shell bending strain measures. Corrections stemming from those measures are shown to be important for certain cases. Contrary to widespread belief, it is demonstrated that for such “classical” theories, a cross section is not rigid in its own plane. Vlasov’s correction is shown to be unimportant for closed sections, while for open cross sections asymptotically correct formulas for this effect are provided. The latter result is an extension to a general contour of a result for I-beams previously published by the authors. [S0021-8936(00)03003-8]
Theory of Anisotropic Thin-Walled Beams
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, Sept. 18, 1998; final revision, Mar. 7, 2000. Associate Technical Editor: W. K. Liu. Discussion on the paper should be addressed to the Technical Editor, Professor Lewis T. Wheeler, Department of Mechanical Engineering, University of Houston, Houston, TX 77204-4792, and will be accepted until four months after final publication of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
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Volovoi, V. V., and Hodges, D. H. (March 7, 2000). "Theory of Anisotropic Thin-Walled Beams ." ASME. J. Appl. Mech. September 2000; 67(3): 453–459. https://doi.org/10.1115/1.1312806
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