Three-dimensional stress analysis of orthotropic and cross-ply laminated hollow cylinders and cylindrical panels

On the Successive Approximation Method for Three-Dimensional Analysis of Radially Inhomogeneous Tubes With an Arbitrary Cylindrical Anisotropy

“…It has been demonstrated that within the SAM approach, as far as the dimensionless thickness h of a fictitious layer may be set anyhow small, the exact formal solution may be approximated with any desired accuracy by the exponential expanded up to Oðh 2 Þ inclusive. Further to this conclusion, the actual computational performance of the method has shown [1,3,13,14] that very accurate numerical results can be obtained even with the use of h values which are not necessarily very small and/or for rather large k z and o values, such that altogether may demand extending of the series expansion in h to the higher order terms. The broader area of the SAM applicability is apparently related to the fact that any coefficient of the exponential expansion in h contains a higher power of the system matrix and hence a higher maximum power of k z and o; than the coefficient of the same order in the expansion of the approximation discrepancy.…”

“…It has been successfully employed in a series of publications that dealt with dynamic [2][3][4][5][6][7][8][9][10][11][12][13], static [6,9,14], thermoelastic [6,15] and stability analysis [6,[16][17][18] of structural components having various geometrical and/or material characteristics and subjected to a variety of lateral or edge support conditions. The method is based on treating a given hollow cylinder as consisting of N thin coaxial cylindrical layers (real or fictitious), so that for each of them the variable coefficients of the governing differential system may be replaced (truncated) by their constant values taken at an interim radial coordinate inside the layer.…”

“…Accuracy of the approximation is stipulated by smallness of the constituent layers's thickness, which may be reduced in successive steps. The efficiency of convergence has been exemplified in references [1,3,5,9,13,14] by means of successful numerical comparison with results based on other analytical methods.…”

Analysis of 2D non-axisymmetric elasticity and thermoelasticity problems for radially inhomogeneous hollow cylinders

“…Because in (1) the normal stresses are related to the shear stress by the derivative with respect to the angular coordinate ϕ, we use inverse superscripts for the shear stress and tractions in (12). By substitution of expressions (12) in (1), (9), (10) and conditions (8) or applying corresponding finite integral transformations prescribed by (13), we deduce the sets of ODEs and boundary conditions to determine the required terms of stress expansions into Fourier series (12). We shall consider below the solution construction for terms of series (12) with subscript "0" (so-called elementary solutions [1,3]) and for those with superscripts "1", "2" separately.…”

“…The numerical procedure was used in [11] for finding the non-axisymmetric thermal stresses in a inhomogeneous hollow cylinder. The successiveapproximation method has been used in [12] for a three-dimensional stress and displacement analysis of transversely loaded, laminated hollow cylinders and open cylindrical panels. In [13], the analytical solutions to plane elasticity and thermoelasticity problems for a hollow cylinder, whose properties are expressed as a power of the radial coordinate, have been presented in the form of complex Fourier series.…”