Imperfection sensitivity of laminated conical shells

Abstract

The sensitivity of laminated conical shells to imperfection is considered, via the initial post-buckling analysis, on the basis of three different shell theories: Donnell's, Sanders', and Timoshenko's. Unlike isotropic conical shells or laminated cylindrical shells, in the case of laminated conical shells the thickness and the material properties vary with the shell coordinates, which complicates the problem considerably. The main objective of the study is to investigate the influence of the variation of the stiffness coefficients on the buckling behavior and on the imperfection sensitivity of laminated conical shells. It is felt that by finding the various parameters that influence the shell's imperfection sensitivity, it is possible to improve the behavior of the whole structure.A special Level-1 computer code ISOLCS (Imperfection Sensitivity of Laminated Conical Shells) had been developed. ISOLCS calculates the classical buckling load and the imperfection sensitivity via Koiter's theory of laminated conical shells with consideration to the variation of the material properties in the shell's coordinates. The range of validity of the Level-1 predictions by ISOLCS is verified by the Level-3 code STAGS-A.

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

“…Kinematic relations using the Sanders equations and [11]. The strain vector can be defined and separated as…”

“…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. Sofiyev and Kuruoglu (2011) [13] use a modified Donnell-type of equations and propose an analytical solution for the axial buckling of laminated cones restricted to orthotropic laminates, which results in the limitations already pointed out in [14].…”

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

“…(13) [9]. The matrix B L ½ can be defined for the Donnell-type of nonlinear equations as shown in Eq.…”

“…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. In 2007, Goldfeld [9] used a model with variable thickness for laminated composite cones and verified that the imperfection sensitivity is not reduced for a wider semi-vertex angle and observed that the most accurate non-linear equations result in lower buckling loads and less imperfection sensitivity.…”

“…In the approaches of Simitses et al [3,4] and of Goldfeld et al [7,9] only symmetric and axisymmetric imperfection patterns can be used, and more general imperfection patterns cannot be used, such as those obtained using perturbation loads or geometric imperfections from advanced data acquisition systems [10]. Such general imperfection patterns are not necessarily symmetric and can only be represented by appropriate Fourier series such as the half-cosine function proposed by Arbocz [11].…”