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The main objective of this research is to analyze the variation of minimum film thickness in the inlet zone of roll-strip interface by incorporating starvation and viscous shear heating effects at high rolling speeds (5-20 m/s), reduction ratios (0.05-0.20), and slip values (varying up to 20%). An additional objective of this paper is to develop empirical relations for predictions of minimum film thicknesses (both isothermal and thermal) and maximum film temperature rise in the inlet zone of the lubricated roll strip contact as functions of roll-speed, reduction ratio, material parameter, slip, and starvation parameter. An efficient numerical method based on Lobatto quadrature technique is adopted for rigorous analysis of the present problem. The results reveal that the existence of starvation seems to be beneficial in terms of reduction in maximum film temperature rise as well as reduction in quantity of oil required for lubrication provided thin continuous film exists at the contact. Keywords: thermohydrodynamic analysis, high-speed cold rolling, minimum film thickness, starvation, film temperature rise, empirical relations

The prebuckling and the postbuckling behaviors of the angle-ply composite laminated joined circular conical--cylindrical shells subjected to torsion, external pressure, axial compression, and thermal loading are studied considering the variation of stiffness coefficients along the meridional direction in the conical section. The analysis is carried out using the semi-analytical finite element method based on the first-order shear deformation theory. The nonlinear governing equations, derived using Sanders-type kinematic relations, are solved using the Newton--Raphson iterative technique coupled with the displacement control method to trace the prebuckling followed by the postbuckling equilibrium path. The presence of asymmetric perturbation in the form of a small magnitude load spatially proportional to the linear buckling mode shape is considered to initiate the bifurcation of the shell deformation. The influences of the semicone angle, the ply angle, and the number of circumferential waves on the prebuckling/postbuckling response of the angle-ply laminated joined circular conical--cylindrical shells are investigated. The critical buckling load shows a decreasing trend for positive semicone angle cases and an increasing one for negative semicone angle cases with the increase in the magnitude of the semicone angle of the mechanically loaded shells. The shells with a positive semicone angle mostly depict asymmetric bifurcation buckling under uniform decrease in temperature whereas the shells with a negative semicone angle depict asymmetric bifurcation buckling under a uniform rise in temperature. The ratio of the minimum load in the postbuckling path and the critical buckling load may significantly be lower than unity depending upon the shell parameters and loading situations. DOI: 10.2514/1.28358

The present study estimates the critical/buckling loads of laminated composite rectangular plates under in-plane uniaxial and biaxial loadings. The formulation is based on the first-order shear deformation theory and von-Karman-type nonlinearity. Chebyshev series is used for spatial discretisation and quadratic extrapolation is used for linearization. An incremental iterative approach is used for estimation of the critical load. Different combinations of simply supported, clamped and free boundary conditions are considered. The effects of plate aspect ratio, lamination scheme, number of layers and material properties on the critical loads are studied. DOI: 10.1061/(ASCE)0893-1321(2005)18:4(215) CE Database subject headings: Buckling; Analytical techniques; Laminates; Composite materials; Biaxial loads; Plates.

The nonlinear thermoelastic buckling/postbuckling characteristics of laminated circular conical/cylindrical shells subjected to uniform temperature rise are studied employing semi-analytical finite element approach based on first-order shear deformation theory and field consistency principle. The nonlinear governing equations, considering geometric nonlinearity based on von Karman's assumption for moderately large deformation, are solved using Newton-Raphson iteration procedure coupled with displacement control method to trace the prebuckling/postbuckling equilibrium path. The presence of asymmetric perturbation in the form of small magnitude load spatially proportional to the linear buckling mode shape is assumed to initiate the bifurcation of the shell deformation. The study is carried out to highlight the influences of semicone angle, number of layers, material properties, and number of circumferential waves on the nonlinear thermoelastic response of the laminated circular conical/cylindrical shells. The participation of axisymmetric and asymmetric modes in the total response of the shells is brought out through the deformation shape analysis. The comparison of thermoelastic pre- and postbuckling characteristics of shells with temperature-dependent material properties is made with those considering constant material properties, and the behavior is found to be significantly different depending upon the shell parameters and degradation rate of material properties. The shells exhibit softening type of prebuckling nonlinear response and snap-through-type/stable postbuckling response depending upon the geometrical/material parameters.

This study presents a simple analytical formulation for the eigenvalue problem of buckling and free-vibration analysis of Mindlin sector plates. The nonaxisymmetric formulation in cylindrical coordinates is discretized in the space domain in terms of two-dimensional Chebyshev polynomials. The formulation facilitates application of several combinations of simply supported, clamped, and free-edge conditions. Convergence study has been carried out, and the obtained results are compared with those available in the literature. Extensive results pertaining to critical buckling loads and natural frequencies are presented. Effects of boundary conditions, plate thickness, and annularity are studied.

The paper deals with the theoretical investigation of the postbuckling of laminated composite rectangular plates subjected to uniform in-plane temperature. An analytical method based on Chebyshev polynomial is employed. The formulation is based on Reissner-Mindlin plate theory and von Karman nonlinear kinematics. The resulting nonlinear coupled differential equations are linearized using quadratic extrapolation technique. Double Chebyshev finite series is used to discretize the differential equations. An incremental iterative approach is employed for the solution. The effects of temperature dependent mechanical and thermal properties on the limiting/critical temperature and the postbuckling response are studied. The numerical results for different boundary conditions and lamination schemes are presented. Analysis results indicate that temperature dependent properties reduce the critical/limiting temperature and postbuckling strength. CE Database subject headings: Postbuckling; Laminated materials; Composite materials; Plates; Thermal factors; Temperature.

This paper deals with the nonlinear dynamic buckling of laminated composite rectangular plates subjected to uniform time-dependent in-plane temperature-induced loading. The dynamic post-buckling deflection response is obtained and dynamic critical temperatures are estimated. The nonlinear governing equations of motion are solved analytically using fast Chebyshev series technique. The numerical results for CCCC, CCCS, CCSS, CSCS, CSSS and SSSS boundary conditions are presented. [DOI: 10.1115/1.1485755]

Postbuckling analysis is presented for shear deformable cross-ply laminated composite rectangular plates subjected to the combination of in-plane edge compressive mechanical loading and thermal loads due to a linearly varying temperature across the thickness. The formulation is based on the first-order shear deformation theory and von-Karman-type nonlinearity. The analysis uses a quadratic extrapolation technique for linearization and Chebyshev polynomials for spatial discretization. An incremental iterative approach is employed to estimate the critical load. The boundary conditions consisting of clamped, simply supported, free edge, and their combinations are considered. The effects of the thinness ratio, aspect ratio, lamination scheme, the number of layers, and the modulus ratio on the critical load/limit load and postbuckling behavior are studied. DOI: 10.1061/(ASCE)0733-9399(2002)128:1(93) CE Database keywords: Postbuckling behavior; Thermal factors; Plates; Shear deformation; Geometric nonlinearity.

Analytical solutions to the geometrically nonlinear boundary value problems of laminated-composite plate undergoing moderately large deformations and subjected to various boundary conditions are presented in this paper. The nonlinear coupled partial differential equations are linearized using a quadratic extrapolation technique. The spatial discretization of the linear differential equations is carried out using fast-converging Chebyshev polynomials. A convergence study reveals that 8-10 terms of expansion of the function is sufficient to yield quite accurate results. The results for uniformly loaded, moderately thick laminated-composite plates with simply supported immovable edges, clamped immovable edges, free edges, and their combinations are presented. Some new results are presented, and it is observed that the present method is efficient and less expensive.

This paper deals with the Chebyshev series solution technique to the non-linear static and dynamic response of cylindrically orthotropic, symmetrically laminated, cross-ply moderately thick plates. Considering the transverse shear and rotatory inertia, the governing equations of motion for the axisymmetric deformation of circular plates are expressed in terms of normal deflection [bar W], slope [bar [Phi]], and the stress function [bar [Psi]]. The effects of transverse shear, rotatory inertia, material properties, number of layers, and boundary conditions on static and dynamic response of plates to uniformly distributed normal loads are studied, and the results are shown graphically. The effects of transverse shear and rotatory inertia on the central response are greatly influenced by the ratio of base radius to thickness, the materials, and the type of loadings.