K Bhaskar

Reissner’s new mixed variational theorem, which allows independentinterpolation, through the thickness, of the three transverse stresses besides that of the three displacements, is applied here to derive a higher-order theory of laminated orthotropic cylindrical shells. The accuracy of the theory is verified by comparison with three-dimensional elasticity solutions. It is shown that Reissner’s principle does not directly lead to accuratetransverse shear stress predictions, but requires the use of the equilibrium equations of three-dimensional elasticity as is common in the conventional displacement approach. © 1992 ASME.

The non-classical problem of buckling of a simply-supported rectangular plate due to various types of non-uniform compressive edge loads is analysed here. For each case, the elasticity solution for the internal in-plane stress field is obtained rigorously using a superposition of Airy's stress functions and also approximately using extended Kantorovich method. Subsequently, the convergent buckling loads are obtained using Galerkin's method. Results are presented to highlight the dependence of the total buckling load and the corresponding buckled shape on the edge load distribution, as well as to illustrate the applicability of the approximate plane stress solutions. © 2006 Elsevier Ltd. All rights reserved.

Solutions, within the framework of linear uncoupled thermoelasticity, are presented for certain problems of flexure of composite laminates. Benchmark numerical results, useful for the validation or otherwise of approximate laminate models, are tabulated. Finally, these results are used to examine the accuracy of the classical lamination theory based on Kirchhoff's hypothesis. Copyright © 1996 Elsevier Science Limited.

A simple two-dimensional elasticity solution is presented here for flexure of an infinite sandwich strip with rigidly clamped ends; it is based on the superposition of a strong form solution for a simply supported strip under transverse loading and a Ritz solution for end-loading. Results useful for future comparisons are presented in tabular form. On the basis of these results, the accuracy of classical plate theory and first-order shear deformation theory is critically examined. Finally, the difference between rigidly clamped end conditions and a softer version of clamped conditions is highlighted with reference to far-field response.

The paper deals with the vibration and thermal buckling behavior of sandwich beams with composite facings and viscoelastic core. Sandwich plate and beam elements are compared in this context. Each composite laminate is modeled as an equivalent single layer. Steady state temperature field is assumed. The formulation is a decoupled thermo mechanical formulation where in the temperatures in the domain of the beam are calculated first and made use in further calculations. The effect of fiber angle, the effect of aspect ratio and the effect of the core thickness on the performance of the elements is studied. The study reveals that there is a considerable difference between the predictions of plate and beam elements for some fiber angles. © 2006 Elsevier Ltd. All rights reserved.

Rigorous analytical solutions are obtained for the plane stress problem of a rectangular plate subjected to non-linearly distributed bending loads on two opposite edges. They are then used in a Galerkin type solution to obtain the corresponding convergent buckling loads. It is shown that the critical bending moment depends significantly on the actual edge load distribution and further the number of nodal lines of the buckled configuration can also be different from that corresponding to a linear antisymmetric distribution of the bending stresses. Results are tabulated for future use while judging approximate numerical solutions.

An exact three-dimensional elasticity solution is obtained for cylindrical bending of simply-supported laminated anisotropic cylindrical shell strips subjected to transverse loading. Displacements and stresses are presented for different angle-ply layups and radius-to-thickness ratios, so as to serve as useful benchmark results for the assessment of various two-dimensional shell theories. Finally, in the light of these results, the accuracy of the Love-type classical shell theory is examined. © 1993 by ASME.

Large amplitude vibrations of a rectangular plate with parabolically varying rotational constraints on two opposite edges are studied. The problem has been solved by both Berger's approach and the more rigorous von Kármán approach. Galerkin's method is used to obtain an ordinary differential equation in the modal function, the solution to which is given in terms of elliptic functions. © 1985.

The title problems, considered difficult hitherto, are solved here using a rigorous superposition method comprising of elegant and exact infinite series counterparts of the conventional Levy-type solutions. The infinite series are summed without truncation to avoid any loss of accuracy. After due validation studies, numerical results are tabulated for some typical plate problems for use as baseline solutions in the future. © SAGE Publications 2008.

An analytical approach is presented here for simply supported blade-stiffened rectangular plates wherein important non-classical effects such as transverse shear deformation and rotary inertia are carefully accounted for. The analysis differs from full three-dimensional modelling of both the plate and the stiffener in that a plane stress idealization is used to model the kinematics of transverse bending of the stiffener while simple one-dimensional classical models are employed for lateral bending and torsion. Parametric studies are used to highlight the importance of non-classical effects in plate and stiffener kinematics and to finally lead to certain recommendations for accurate modelling of stiffened plates.