Effect of lamination sequence on the localization and shear crippling instability in thick imperfect cross-ply rings under external pressure

Effect of lamination sequence on the compressive response of a thick plane strain cross-ply ring (very long cylindrical shell) weakened by the presence of a modal imperfection is investigated. A fully nonlinear finite element analysis, that employs a cylindrically curved 16-node layer-element, and is based on the assumption of layer-wise linear displacements distribution through thickness (LLDT), is utilized in the analysis of the afore-mentioned cross-ply ring. Hitherto unavailable numerical results pertaining to the influence of lamination sequence on the localization of buckling patterns and the ensuing shear crippling instability are also presented.     

Effects of fiber misalignment and transverse shear modulus on localization and shear crippling instability in thick imperfect cross-ply rings under external pressure

The effect of transverse shear modulus on the compressive response of a thick plane strain cross-ply ring (very long cylindrical shell) weakened by the presence of a modal imperfection is investigated. The present study is primarily motivated to obtain the hitherto unavailable results pertaining to the effect of reduced transverse shear modulus, , of a lamina weakened by the presence of randomly distributed fiber misalignments. A simple expression for the reduced transverse shear modulus, , of a layer material is derived in terms of the average fiber misalignment angle. A fully nonlinear finite element analysis, that employs a cylindrically curved 16-node layer-element and is based on the assumption of layer-wise linear displacement distribution through thickness (LLDT), is utilized in the analysis of the afore-mentioned cross-ply ring. The interaction of a micro-structural defect in the form of initial fiber misalignments with its macro-structural counterpart represented by a modal imperfection is a key to understanding this meso-structural level phenomenon. Hitherto unavailable numerical results pertaining to the influence of this effect on the localization of buckling patterns and the ensuing shear crippling instability are also presented.     

Effect of thickness on buckling of perfect cross-ply rings under external pressure

Effect of thickness on the buckling of a perfect thick plane strain cross-ply ring (very long cylindrical shell) is investigated. A linearized version of a fully nonlinear finite element analysis, that employs a cylindrically curved 16-node layer-element, and is based on the assumption of layer-wise linear displacements distribution through thickness (LLDT), is utilized for computation of hydrostatic buckling pressure of the afore-mentioned cross-ply ring. Numerical results pertaining to the effect of thickness (interlaminar shear/normal deformation) on the hydrostatic buckling pressure of cross-ply rings and comparison with their classical lamination theory (CLT) counterparts are also presented.     

On a three-dimensional axisymmetric boundary-value problem of nonlinear elastic deformation: Asymptotic solution and exponentially small error

In this paper, we study a three-dimensional axisymmetric boundary-value problem of a slender cylinder composed of a nonlinearly elastic material subjected to an axial force. Starting from the field equations, after a transformation and proper scalings, we identify a small variable and two small parameters, which characterize the present problem. Then, by an approach involving compound series-asymptotic expansions, a nonlinear ODE is derived, which governs the axial strain (the first-term in the series expansion). By imposing the zero radial displacement conditions at two ends, we manage to get the analytical solution of the axial strain, from which all other physical quantities can be deduced and thus the three-dimensional displacement field can be determined. Graphical results are presented, which show that there are two boundary layers near the two ends while the middle part is in a state of almost uniform extension. The asymptotic structure of the analytical solution is derived, which offers clear explanations to the structure of the deformed configuration and shows that the thickness of both boundary layers is of the order of the radius. We also point out the relevance of the present results to the St. Venant’s problem. In particular, we obtain the explicit uniformly-valid exponentially small error term, when the obtained deformed configuration is compared to the configuration of a uniform extension.     

Effects of wall thickness and material property on inverse heat conduction analysis of a hollow cylindrical tube

In this study, we examined the effects of a hollow cylindrical tube’s thickness and material properties on estimated time delay and waveform distortion in a one-dimensional inverse heat transfer analysis model using the thermal resistance method and an input estimation algorithm. Results indicated a persistent time delay for various heat flux amounts applied to different tube thicknesses. As the tube thickness increased, the numerically determined temperature data also experienced a time delay, which affected the inverse heat transfer response curve. Results also indicated that the transient heat flux waveform estimated for different material properties showed higher levels of distortion for materials having relatively low thermal conductivity. These materials also exhibited greater time delays. To address these issues, we applied a Fourier number (a dimensionless number representing the tube’s thickness and material properties) and proposed an equation to calculate sharpness, which can subsequently be used to predict probable time delays and heat flux waveform distortion. In conclusion, a correction is required when a low Fourier number is used in inverse heat transfer analysis.