K. Bhaskar

Bending of laminated orthotropic cylindrical shells—An elasticity approach

Three-dimensional elasticity solutions are obtained for finite length, cross-ply cylindrical shells, simply supported at both ends and subjected to transverse sinusoidal loading. By assuming suitable displacement functions, the boundary value problem is reduced to a set of coupled ordinary differential equations and then solved by the method of Frobenius. Displacement and stresses are presented for 90°, (90°/0°), (90°/0°/90°), (90°/0°/90°/0°/90°)s shells. Deviations from laminated plate behaviour are described. The method presented is shown to give results identical to those of a stress function approach for a plane strain problem. The paper includes extensive tabulated results to serve as a basis for assessment of improved shell theories.

Thermoelastic solutions for orthotropic and anisotropic composite laminates

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 Kirchhoffs hypothesis.

A new theory for accurate thermal/mechanical flexural analysis of symmetric laminated plates

A new displacement-based higher order theory is presented here. The theory employs realistic displacement variations and is shown to be extremely accurate for even thick laminates and for any combination of mechanical and thermal loading. The importance of various higher-order terms in the proposed theory is discussed with reference to a specific numerical example.

A higher-order theory for bending analysis of laminated shells of revolution

Abstract A new higher-order shear deformation theory is presented for the analysis of laminated anisotropic shells of revolution. The theory is based on realistic approximation of the in-plane displacements through the thickness. The accuracy of the theory is verified by comparison with three-dimensional elasticity results for a laminated orthotropic cylindrical shell. Finally, an isoparametric quadrilateral shell of revolution finite element is presented. The example problems solved illustrate the performance of the element and the effects of transverse shear deformation.

Exact elasticity solution for laminated anisotropic cylindrical shells

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.

Simple and exact series solutions for flexure of orthotropic rectangular plates with any combination of clamped and simply supported edges

Rectangular plates with arbitrary clamped edges are not easily amenable to exact analysis. Available solutions are either approximate or mathematically complex. The purpose of this paper to present an exact solution methodology for such problems based on superposition of double sine series solutions easily derived using the principle of virtual work. The paper includes tabulated results for two laminates for all possible combinations of clamped–simply supported edges, which would be valuable for future comparisons.

Benchmark Elasticity Solution for Locally Loaded Laminated Orthotropic Cylindrical Shells

Three-dimensional elasticity solutions for plate/shell structures serve as a standard benchmark for the assessment of various two-dimensional theories. Such a solution, for assessment of laminated shell theories, is presented here. The problem is that of a simply supported cross-ply cylindrical shell pinched by two diametrically opposite local patch loads. The solution is developed by using Taylor series, and results are tabulated for a three-layer shell with various radius-to-thickness ratios. Finally, these results are used to throw light on the accuracy of the classical Love-Kirchhoff hypothesis and a recently proposed higher order shear deformation theory.

Buckling under axial compression of thin-walled composite beams exhibiting extension-twist coupling

A study of the flexural buckling of single-cell extension-twist coupled beams under axial compression is presented. The analysis is based on a recently developed geometrically non-linear thin walled beam theory. The effects of direct transverse shear and the parasitic bending-transverse shear coupling as well as those of different boundary conditions and ply-angles are discussed.

Accurate flexural analysis of clamped moderately thick cross-ply rectangular plates by superposition of exact untruncated infinite series solutions

A rigorous analytical solution for the title problem is presented here using the method of superposition. The derivation of tedious Levy-type solutions, commonly used in such an approach, is obviated by the ingenious use of their infinite series counterparts, which are summed without truncation so as to retain accuracy. The methodology is fast convergent and yields accurate results without excessive computation. Tabulated results are presented for two cross-ply plates for future comparisons.

A benchmark elasticity solution for an axisymmetrically loaded angle-ply cylindrical shell

Abstract A three-dimensional elasticity solution is obtained for finite-length laminated anisotropic cylindrical shells, simply supported at both ends and subjected to axisymmetric transverse loading. Suitable displacement functions are used to reduce the problem to a set of coupled homogeneous ordinary differential equations in terms of the radial coordinate, and these are then solved by employing a Taylor series. Displacements and stresses at critical locations are tabulated for different angle-ply layups and radius-to-thickness ratios for two types of loading. These results will be useful for the assessment of various two-dimensional laminated shell theories. As an example, the accuracy of the Love-type classical shell theory is discussed.