Alavandi Bhimaraddi

Free vibration analysis of doubly curved shallow shells on rectangular planform using three-dimensional elasticity theory

Abstract The free vibration analysis of homogeneous and laminated doubly curved shells on rectangular planform and made of an orthotropic material has been presented using the three-dimensional elasticity equations. A solution is obtained utilizing the asumption that the ratio of the shell thickness to its middle surface radius is negligible, as compared to unity. However, it is shown that by dividing the shell thickness into layers of smaller thickness and matching the interface displacement and stress continuity conditions, very accurate results can be obtained even for very thick shells. The two-dimensional shell theories have been compared for their accuracy in the light of the present three-dimensional elasticity analysis.

FINITE ELEMENT ANALYSIS OF LAMINATED SHELLS OF REVOLUTION WITH LAMINATED STIFFENERS

Abstract A finite element analysis of orthogonally stiffened shells of revolution has been presented by combining a recently proposed shell of revolution element and a curved beam element. These two elements are isoparametric elements in which the effects of shear deformation and rotary inertia have been taken into account. They are meant to be used for arbitrarily laminated structures and are based on the higher-order theories presented recently by Bhimaraddi for plates, shells and beams.

Non-linear free vibration analysis of composite plates with initial imperfections and in-plane loading

Abstract In this paper the non-linear response of layered composite plates with initial imperfections and subjected to in-plane preload is considered. The basic equations used in the analysis are those corresponding to an accurate shear deformation theory which employs parabolic shear strain variations across the thickness and requires no correction factors. The five governing non-linear equilibrium equations of the problem are reduced to a single non-linear ordinary differential equation (ODE) using a single mode approach in conjunction with the Galerkin method. Numerical results are obtained tor two problems: 1. (i) large amplitude vibration of imperfect plates and 2. (ii) small oscillations in the vicinity of a static buckled position of an in-plane loaded two-layered (0 90) plate.

Generalized finite element analysis of laminated curved beams with constant curvature

Abstract A 24-dofisoparametric finite element has been presented for the analysis of generally laminated curved beams. The effects of shear deformation and rotary inertia have been accounted for using the shear deformation theory which employs nonlinear shear strain variation across the section. Thus it is not necessary to specify the shear correction factors in the present element. The torsional response has been incorporated according to the elementary theory of torsion. It is shown that for certain unsymmetrically laminated curved beams the in-plane and out-of-plane motions are coupled. The numerical results presented illustrate the performance of the element and the effect of coupling.

A shear deformable finite element for the analysis of general shells of revolution

A 64-dof isoparametric quadrilateral finite element is presented for the analysis of generally laminated shells of revolution. The effects of shear deformation and rotary inertia are accounted for by using shear deformation theory that employs the parabolic shear strain variation across the thickness. The classical thin shell theory is the special case of shear deformation theory used in the present study. Thus, the thin shell element also can be obtained from the present thick shell element by simply having the displacement parameters (u1 and v1,) associated with the shear rotations as zeros. The numerical results presented illustrate the performance of the element and the effects of shear deformation.

Generalized analysis of shear deformable rings and curved beams

Abstract An accurate shear deformable theory for the analysis of the complete dynamic response of curved beams of constant curvature is presented. The equations presented here are very general in the sense that any problem of curved beam and circular rings can be addressed. It is indicated that the classical thin beam theory and the Timoshenko-type shear deformation theory are obtainable from the present theory as special cases. The present formulation accounts for shear deformation and rotary inertia and hence is applicable to the analysis of thick curved beams and rings. The theory assumes parabolic variation for shear strains (hence obviates the use of shear correction factors as usually done in the case of Timoshenko-type theory) and involves six displacement parameters of the centre-line—three translations and three rotations. It is pointed out that for certain composite curved beams and rings the in-plane and out-of-plane vibrations are coupled. In such cases complete analysis, rather than separate in-plane and out-of-plane analyses, is required. The numerical results presented illustrate the effect of coupling on various vibrational frequencies.

Nonlinear vibrations of in-plane loaded, imperfect, orthotropic plates using the perturbation technique

Abstract A perturbation technique is used to study the effects of in-plane inertia, rotary inertia, and shear deformation on the nonlinear free vibration response of an imperfect, in-plane loaded orthotropic plate. The von Karman type governing equilibrium equations of the plate correspond to those of a recently proposed shear deformation theory which employs parabolic shear strain variation across the thickness. The perturbation parameter is taken as the thickness to side length ratio of the plate. By expressing the generalized displacements in the form of a truncated power series of the perturbation parameter, the five governing equations of the problem under consideration are reduced to a single second order ordinary differential equation in terms of the transverse displacement. The solution of this equation is obtained by the method of multiple scales. Numerical results illustrate the influence of various parameters under consideration.

Out-of-plane vibrations of thick rings

Abstract Natural out-of-plane vibrations of thick circular rings are considered using an accurate shear deformable theory of which the classical and the Timoshenko-type shear deformation theory are special cases. The present formulation uses no shear correction factors since the assumed shear strain variations are nonlinear across the cross-section. The numerical results presented illustrate the accuracy of the present formulation.