Linear buckling predictions of unstiffened laminated composite cylinders and cones under various loading and boundary conditions using semi-analytical models

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

“…[30] demonstrates how other types of boundary conditions can be obtained by adding elastic constraints to the edges and using different base functions for matrix g 2 Â Ã . In Eq.…”

Modelling of fibre steered plates with coupled thickness variation from overlapping continuous tows

“…The general buckling problem is derived based on the neutral equilibrium criterion of the total potential energy given in Equation 13. Following the derivation in [12,9], the general form of Equation 14 can be obtained.…”

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

“…The analytical integration of matrices ሾ‫ܭ‬ ሿ and ሾ‫ܭ‬ ሿ is performed extending the approach described by [14] in order to consider the new base functions ሾ݃ ሿ and ሾ݃ ଵ ሿ, such that the integration conditions shown in Table 4 are required. The generated matrices are approximately 99% sparse justifying the use of a sparse matrix-based implementation, and the current implementation, available in Ref.…”

“…In Table 9 the numerical and experimental results of Messager et al [39] and the predictions of Li and Lin [38] are compared with the present model (݉ ଵ = 150, ݉ ଶ = ݊ ଶ = 40), showing that for this moderately thick shell (ܴ ℎ ⁄ = 16.05) the CLPT differs from the finite element results by 5.5% and 3.3%, for the two laminates, respectively. For the analysis of Table 8 and Table 9, the computational cost associated with the proposed method is about 100 times faster than the corresponding finite element models, since only the linear stiffness matrix ሾ‫ܭ‬ ሿ and the geometric stiffness matrix of the initial stress state have to be calculated, which can be performed analytically, as presented by [14]. …”

“…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].…”