Yu, Wenbin; Hodges, Dewey H.; Volovoi, Vitali; Cesnik, Carlos E. S. On Timoshenko-like modeling of initially curved and twisted composite beams. (English) Zbl 1087.74581 Int. J. Solids Struct. 39, No. 19, 5101-5121 (2002). Summary: A generalized, finite-element-based, cross-sectional analysis for nonhomogeneous, initially curved and twisted, anistropic beams is formulated from geometrically nonlinear, three-dimensional (3-D) elasticity. The 3-D strain field is formulated based on the concept of decomposition of the rotation tensor and is given in terms of one-dimensional (1-D) generalized strains and a 3-D warping displacement that is obtained from the formulation, not assumed. The warping is found in terms of the 1-D strains via the variational asymptotic method (VAM). In this paper a Timoshenko-like model is presupposed for a beam with cross-sectional characteristic length \(h\), wavelength of deformation given by \(l\), and the magnitude of the radius of initial curvature and/or twist is taken to be of the order \(R\). First, a solution for the asymptotically correct refinement of classical anisotropic beam theory for initially curved and twisted beams through \(O(h^2/R^2)\) is obtained. Next, the \(O(h^2/l^2)\) correction is computed. It is known that Timoshenko-like theory is not capable of capturing all the \(O(h^2/l^2)\) corrections for generally anisotropic beams. However, if all the \(O(h^2/l^2)\) terms are known, then the corresponding Timoshenko-like theory is uniquely defined. Numerical results are presented to illustrate the trends of the various classical (extension-twist, bending-twist, and extension-bending) and nonclassical couplings (extension-shear, bending-shear, and shear-torsion) as the initial twist and curvatures are varied. Cited in 1 ReviewCited in 33 Documents MSC: 74K10 Rods (beams, columns, shafts, arches, rings, etc.) 74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics Keywords:Beams; composite; transverse shear; Timoshenko; asymptotic; warping; cross section; VABS PDFBibTeX XMLCite \textit{W. Yu} et al., Int. J. Solids Struct. 39, No. 19, 5101--5121 (2002; Zbl 1087.74581) Full Text: DOI