K.Kanaka Raju

Finite element formulation for the large amplitude free vibrations of beams and orthotropic circular plates

A finite element formulation for the large amplitude free oscillations of beams and orthotropic circular plates is presented in this paper. The present formulation does not need the knowledge of longitudinal/inplane forces developed due to large displacements and thus avoids the use of corresponding geometric stiffness matrices, which were used in earlier finite element formulations. The convergence of the results obtained by using the present formulation is very good. Comparison of the present results with the earlier work wherever possible confirms the reliability and effectiveness of the present finite element formulation.

Effect of longitudinal or inplane deformation and inertia on the large amplitude flexural vibrations of slender beams and thin plates

Large amplitude flexural vibrations of slender beams, and thin circular and rectangular plates have been studied when a compatible longitudinal or inplane mode is coupled with the fundamental flexural mode. It is shown that the effect of longitudinal or inplane deformation and inertia is to reduce the non-linearity in the flexural frequency-amplitude relationship. Further, for slender beams and thin plates, the effect of longitudinal or inplane inertia is negligible.

Non-linear vibrations of simply supported rectangular cross-ply plates

A method of direct numerical integration of the frequency-ratio expression is proposed to study the non-linear free vibration behaviour of rectangular cross-ply laminates. The proposed method, even with single-term approximations for the admissible functions, yields results that agree very well with the existing perturbation solutions. Non-linear behaviour of the cross-ply laminates is also studied with the harmonic oscillations assumption, by using the conservation of energy and the modal equation. The results are found to be lower and upper bounds to those obtained from the direct numerical integration method. It is also observed that the arithmetic mean of the two solutions with the harmonic oscillations assumption matches very well with that of the direct numerical integration method. Non-linear vibration characteristics are obtained for several configurations of cross-ply plates. Results for orthotropic and isotropic plates are also obtained as special cases.

A reinvestigation of post-buckling behaviour of elastic circular plates using a simple finite element formulation

A modified finite element formulation to study the post-buckling behaviour of elastic circular plates is presented in this paper. A discussion on the derivation of nonlinear stiffness matrix for post-buckling analysis is included and the present results are compared with continuum solutions.

A finite element formulation for large amplitude flexural vibrations of thin rectangular plates

Large amplitude flexural vibrations of rectangular plates are studied in this paper using a direct finite element formulation. The formulation is based on an appropriate linearisation of strain displacement relations and uses an iterative method of solution. Results are presented for rectangular plates with various boundary conditions using a conforming rectangular element. Whenever possible the present solutions are compared with those of earlier work. This comparison brings out the superiority of the proposed formulation over the earlier finite element formulation.

Axisymmetric vibrations of circular plates including the effects of geometric non-linearity, shear deformation and rotary inertia

In this paper, axisymmetric vibrations of circular plates are studied, with inclusion of the effects of geometric non-linearity, shear deformation and rotatory inertia. The finite element method is employed to formulate the problem. Both simply supported and clamped plates are considered. The results indicate that the influence of geometric non-linearity is greater when the effects of shear deformation and rotatory inertia are included than when they are neglected.

Thermal post-buckling of a square plate resting on an elastic foundation by finite element method

A simple finite element formulation is presented for evaluating the thermal post-buckling behaviour of rectangular plates. The results are presented in the form of linear thermal loads and ratios of nonlinear to linear thermal loads for various values of the central deflection and for three sets of boundary conditions. The effect of elastic foundation on the thermal post-buckling behaviour is also evaluated for various values of foundation stiffness parameter.

Finite-element analysis of post-buckling behaviour of cylindrically orthotropic circular plates

Abstract A simple finite-element formulation for the study of post-buckling behaviour of orthotropic circular plates is presented in detail. The results in the form of radial load ratios along with their corresponding empirical formulae in terms of central deflection to thickness ratios of the plates are presented for the first time in the literature for various values of the orthotropic parameter.

Stability of moderately thick rectangular plates using a high precision triangular finite element

Stability of moderately thick rectangular plates is studied in this paper. A high precision triangular finite element is used in the present formulation. Explicit expressions for elastic stiffness and geometric stiffness matrices are presented; the use of numerical integration is avoided. The effect of transverse shear on the critical loads is brought out through two typical examples.

Post-buckling of a square plate resting on an elastic foundation under biaxial compression

A simple finite element formulation is presented to study the post-buckling behaviour of a square plate resting on an elastic foundation subjected to a biaxial compression. Linear critical loads and ratios of nonlinear to linear loads for various values of central deflection and for three sets of boundary conditions with different values of foundation stiffness parameters are presented, bringing out the effect of elastic foundation on the post-buckling behaviour.