A new shear flexible cubic spline plate element for vibration analysis

Abstract

SUMMARYHere, a new cubic B-spline plate element is developed using ÿeld consistency principle, for vibration analysis. The formulation includes anisotropy, transverse shear deformation, in-plane and rotary inertia e ects. The element is based on a laminated reÿned plate theory, which satisÿes the interface transverse shear stress and displacement continuity, and has a vanishing shear stress on the top and bottom surfaces of the plates. The lack of consistency in the shear strain ÿeld interpolations in its constrained physical limits produces poor convergence and results in unacceptable solutions due to locking phenomenon. Hence, numerical experimentation for the evaluation of natural frequencies of plates is carried out to check this deÿciency with a series of assumed shear strain functions, redistributed in a ÿeld consistent manner.

A Higher Order Finite Element Modeling of Piezolaminated Smart Composite Plates and Its Application to Active Vibration Control

“…Patel and Ganapathi [2002] developed a new cubic-B spline plate element using field consistency principle for vibration analysis. A four-noded, 12-degreeof-freedom plate-bending element with one electrical degree-of-freedom has been proposed by Hwang and Park [1997].…”