A LOCK-FREE MATERIAL FINITE ELEMENT FOR NON-LINEAR OSCILLATIONS OF LAMINATED PLATES

✍ Scribed by GAJBIR SINGH; G. VENKATESWARA RAO

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 185 KB
• Volume: 230
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1999.2617

✦ Synopsis

The objective of the present paper is to propose an e$cient, accurate and robust four-node shear #exible composite plate element with six degrees of freedom per node to investigate the non-linear oscillatory behavior of unsymmetrical laminated plates. The degrees of freedom considered are three displacement (u, v, w) along x-, y-and z-axis, two rotations ( V , W ) about y-and x-axis and twist VW . The element employs coupled displacement "eld, which is derived using moment-shear equilibrium and in-plane equilibrium of composite strips along the x-and y-axis. The displacement "eld so derived not only depend on the element co-ordinates but are a function of extensional, bending}extensional, bending and transverse shear sti!ness coe$cients as well. A bi-cubic polynomial distribution with 16 generalized undetermined coe$cients for the transverse displacement is assumed. The element sti!ness and mass matrices are computed numerically by employing 3;3 Gauss Legendre product rules. The element is found to be free of shear locking and does not exhibit any spurious modes. The element is found to be free of shear locking and does not exhibit any spurious modes. In order to compute the non-linear frequencies, linear mode shape corresponding to fundamental frequency is assumed as the spatial distribution and non-linear "nite element equations are reduced to a single non-linear second order ordinary di!erential equation. This equation is solved by employing direct numerical integration method. A series of numerical examples is solved to demonstrate the e$cacy of the proposed material "nite element.