T.K. Varadan

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.

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.

Nonlinear flexural vibrations of laminated orthotropic plates

Abstract Large amplitude free flexural vibrations of laminated orthotropic plates are studied using C 0 shear flexible QUAD-8 plate element. The nonlinear governing equations are solved using the direct iteration technique. Numerical results are obtained for isotropic, orthotropic and cross-ply laminated plates with simply-supported boundary conditions on immovable edges. It is observed that hardening behaviour is increased for thick plates and orthotropic plates.

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.

Lagrange-type formulation for finite element analysis of non-linear beam vibrations

Abstract A Lagrange-type formulation for finite element analysis of non-linear vibrations of immovably supported beams is presented. Two equations of motion coupled in axial and transverse displacements are derived by using Lagranges equations. By neglecting the in-plane inertial effects, these equations are written in terms of the transverse displacement alone. Upon defining certain properties for the non-linear oscillatory behaviour of the transverse displacement, the governing equation is reduced to an equation in space alone from which the eigenvalue-like quantity is computed. The governing equation is solved in two ways. A direct iteration technique is used in the first method to compute a numerically exact mode shape and the corresponding frequency. A Rayleigh quotient type of formulation, similar to linear vibration analysis, is used in the second approach to evaluate the frequency of vibration for a fundamental mode which is determined from a linear FEM model and is maintained constant at all amplitudes. Numerical results are compared with available results and they corroborate the observations of earlier research workers.

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.

Dynamic buckling of orthotropic shallow spherical shells

Abstract The dynamic axisymmetric behaviour of clamped orthotropic shallow spherical shell subjected to instantaneously applied uniform step-pressure load of infinite duration, is investigated here. The available modal equations, based on an assumed two-term mode shape for the lateral displacement, for the free flexural vibrations of an orthotropic shallow spherical shell is extended now for the forced oscillations. The resulting modal equations, two in number, are numerically integrated using Runge-Kutta method, and hence the load-deflection curves are plotted. The pressure corresponding to a sudden jump in the maximum deflection (at the apex) is considered as the dynamic buckling pressure, and these values are found for various values of geometric parameters and one value of orthotropic parameter. The numerical results are also determined for the isotropic case and they agree very well with the previous available results. It is observed here that the dynamic buckling load increases with the increase in the orthotropic parameter value. The effect of damping on the dynamic buckling load is also studied and this effect is found to increase the dynamic buckling load. It is further observed that this effect is more pronounced with increase in the rise of the shell.

Dynamic instability of laminated composite curved panels using finite element method

Abstract The dynamic instability of laminated composite cylindrical shells due to periodic loads is studied using a C0 shear flexible QUAD-9 shell element. The boundaries of the principal instability region are conveniently represented in the nondimensional excitation frequency-nondimensional load amplitude plane. The effects of various parameters such as ply-angle, number of layers, thickness and radius-to-side ratio on dynamic stability are brought out.

Nonlinear dynamic instability of laminated composite plates using finite element method

Abstract An investigation is carried out on the dynamic instability of anisotropic laminated composite plates considering geometric nonlinearity. The mathematical model is formulated using C°o shear flexible, field consistent, QUAD-9 plate elements. The nonlinear governing equations are solved using the direct iteration technique. The effect of a large amplitude on the dynamic instability is studied for a simply-supported laminated composite plate. Detailed numerical results are presented for various parameters, namely, ply-angle, number of layers and thickness of plates.

Nonlinear free flexural vibrations of laminated circular cylindrical shells

Abstract This paper deals with large-amplitude free flexural vibrations of laminated composite circular cylindrical shells. The formulation is based on first-order shear deformation theory and Lagranges equation of motion. The nonlinearity due to finite deformation of the shell is included in the formulation. Amplitude-frequency relationships are obtained through dynamic response history using the Wilson-θ numerical integration scheme. An element based on the field consistency approach is used to investigate the nonlinear behaviour of cylindrical shells. Detailed numerical results based on various parameters are presented for orthotropic, cross-ply and angle-ply laminated circular cylindrical shells with different boundary conditions.