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1

Parametric instability of stiffened plates

Srivastava A. K. L., Datta P. K., Sheikh A. H.

International Journal of Applied Mechanics and Engineering

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2004

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Vol. 9, no 1

169-180

EN

The parametric instability behavior of a stiffened plate subjected to uniform in-plane edge loading is studied using the finite element analysis. The method of Hill's infinite determinants is applied to analyze the dynamic instability regions. Numerical results are presented to demonstrate the effects of various parameters, such as the aspect ratio, boundary condition, stiffening scheme, on the dynamic stability of stiffened plates. The results show that the location, size and number of stiffeners have a significant effect on the location of the boundaries of the principal instability regions when compared with those of a flat unstiffened plate.

2

Free vibration of isotropic thick/thin plates using a sub-parametric shear deformable element

Manna M. C., Haldar S., Sheikh A. H.

International Journal of Applied Mechanics and Engineering

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2003

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Vol. 8, no 3

441-448

EN

A free vibration analysis of isotropic plates is investigated in this paper. A sixteen node sub-parametric element having thirty-six degrees of freedom is developed for this purpose. The transverse displacement and bending rotations are taken as independent field variables. The polynomials used to express these variables are of the same order. The entire formulation is made based on the first-order shear deformation theory (FSDT). The rotary inertia is included in the consistent mass matrix for the analysis. Isotropic plates with different thickness ratios, aspect ratios and boundary conditions are analyzed. The results show an excellent agreement with the available published analytical results.

3

A new plate bending element for the analysis of thin plates of arbitrary shapes

Mukhopadhyay M., Sheikh A. H.

Applied Mechanics and Engineering

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2000

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Vol. 5, no 2

337-354

EN

It is well known that the isoparametric element has certain drawbacks when applied to thin plates subjected to bending. The specific problem which creeps up for such cases is known as the shear locking phenomenon which becomes more and more pronounced as the thickness of the plate reduces. Though this can be taken care of by techniques such as the reduced integration, problems still linger for very thin plates which occur in many practical structures. The mapping concept used in the formulation of the isoparametric element has been utilised in developing a new four-noded plate bending element. The shear deformation which is not important for the analysis for thin plates has not been considered and thus the disturbing feature of shear locking does not creep into the analysis, yet like the isoparametric element the new element is able to analyse plates having arbitrary shapes.