The accuracy of Donnell's equations for axially-loaded, imperfect orthotropic cylinders

Imperfection sensitivity of laminated conical shells

“…In (10b), d 3 is a corrector or factor introduced for the external pressure load case, (see Simitses, 1986;Goldfeld et al, 2003). If the load remains normal to the deflected reference axis, d 1 = d 3 = 1.…”

Evaluation of non-linear buckling loads of geometrically imperfect composite cylinders and cones with the Ritz method

“…linear analysis covered in this paper ‫ܨ‬ , ܶ and are kept constants, if not otherwise specified, as detailed in proposed in Section 3.1 and approach through the use of elastic constraints, discussed in Section erived using the Classical Laminated Plate Theory (CLPT) and the Donnell-can be written as ( [4], [7], [8], [9], [21],…”

“…In this context, Tennyson (1975) [6] presented a thorough review about the first studies developing semi-analytical models for orthotropic materials, all of them constraining the equations for symmetric or anti-symmetric laminates. Simitses et al (1985) [7] are among the first authors investigating the effect of initial imperfections for composite cylinders, followed by Arbocz (1992) [8] and Yamada et al (2008) [9]. For conical shells the studies of Goldfeld et al (2003) [10] and Goldfeld (2007) [11] are among the most relevant taking into account an initial imperfection field using Koiter's theory with the asymptotic expansion of Budiansky and Hutchinson (1964) [12] and assuming a geometric imperfection proportional to the critical buckling mode.…”

A semi-analytical approach for linear and non-linear analysis of unstiffened laminated composite cylinders and cones under axial, torsion and pressure loads

“…Concerning the different non-linear approximations used for the kinematic relations, Simitses et al [4] presents a comparison between the Donnell [5] and the Sanders [6] approximations for the buckling of axially compressed orthotropic cylinders under axisymmetric imperfections, and the general trend observed by the authors it that Donnell's equations can overestimate the buckling load, especially for thinner and longer cylinders. Goldfeld et al [7] extended the study of Simitses et al [4] to isotropic conical shells and included the terms required for the Timoshenko and Gere's kinematic approximation [8], concluding that Sanders' approximation already gives an accuracy comparable to Timoshenko and Gere's approximation, and supporting the observation that the more accurate non-linear equations results in a lower buckling load predictions.…”