Salil Haldar

Free Flexural Vibration of Composite Plates in Different Situations Using a High Precision Triangular Element

A high precision, thick-plate element developed by D. Sengupta has been applied to the free vibration analysis of laminated composite plates with necessary addition and modification. The effect of shear deformation has been incorporated in the formulation, taking the transverse displacement and rotations of the normal as independent field variables. These are approximated with polynomials of different orders, which has made the element free from locking in shear. The element contains internal nodes. The degrees of freedom of these nodes have been eliminated through condensation in its final form. To facilitate the condensation, an efficient mass lumping scheme has been recommended to form the mass matrix having zero mass for the internal nodes. Recommendation has also been made for the inclusion of the rotary inertia in the lumped mass matrix. Numerical examples of plates having different shapes, boundary conditions, thickness ratios, fiber orientations and number of layers have been solved. Examples of plates having internal cutout and concentrated mass have also been studied. The results obtained in all cases have been compared with those obtained from other sources to show the accuracy and range of applicability of the element.

Free Vibration Analysis of Composite Right Angle Triangular Plate Using a Shear Flexible Element

A high precision triangular plate bending element proposed by the second author of this paper has been upgraded for the free vibration analysis of laminated composite right angle triangular plates. The effect of shear deformation has been incorporated. An efficient mass lumping scheme with rotary inertia has been recommended. Numerical examples of composite triangular plates having different thickness ratios, side ratios, fibre-orientations, number of layers and boundary conditions have been solved by this element. For validation of the present formulation and element few results on isotropic and orthotropic plates have been compared with those obtained from literatures. The results on composite plates have been presented as new results.

Robust genetically optimized skew laminates

The present research work explores genetically optimized skew laminates, whose stacking sequence has been varied to maximize their fundamental frequencies with the help of an efficient optimization algorithm. Genetic algorithm, rather than being applied blindly with empirical parameters, is tuned with respect to the problem at hand. Following an extensive study, genetic algorithm parameters are selected carefully so as to ensure a robust optimized stacking sequence. The sensitivity of ply angles is also investigated so as to warrant against marginal manufacturing perturbations. The safe limit for variation of ply angles without much hampering the frequency is also recommended. Validation with existing solutions illustrates the efficiency of the procedure. A wide range of results with rectangular/ skew plates of different layers having symmetric/ antisymmetric ply-orientations, subject to different boundary conditions are solved, which demonstrate the efficacy of the approach.

Free vibration analysis of rectangular plates with central cutout

Abstract A nine-node isoparametric plate element in conjunction with first-order shear deformation theory is used for free vibration analysis of rectangular plates with central cutouts. Both thick and thin plate problems are solved for various aspect ratios and boundary conditions. In this article, primary focus is given to the effect of rotary inertia on natural frequencies of perforated rectangular plates. It is found that rotary inertia has significant effect on thick plates, while for thin plates the rotary inertia term can be ignored. It is seen that the numerical convergence is very rapid and based on comparison with experimental and analytical data from literature, it is proposed that the present formulation is capable of yielding highly accurate results. Finally, some new numerical solutions are provided here, which may serve as benchmark for future research on similar problems.

A High Precision Shear Flexible Triangular Element for Vibration of Composite Shells

A high precision triangular shallow shell element is proposed and it is applied to free vibration analysis of composite and isotropic shells. The Mindlins hypothesis is followed to include the effect of shear deformation. The formulation is made in an efficient manner to make the element free from shear locking problem. The element has some internal nodes, which are eliminated through static condensation technique to improve the computational elegance of the element. In the present vibration problem, the implementation of the static condensation became possible with the help of an efficient mass lumping scheme. It is quite interesting that the effect of rotary inertia can be included in the recommended scheme for lumped mass matrix. Numerical examples covering a wide range of problems are solved and the results obtained are compared with the published results in many cases, which show the precision and range of applicability of the proposed element. The performance of the proposed technique for rotary inertia is found to be excellent. Some new results are produced, which may be useful in future research.