Convergence studies of eigenvalue solutions using two finite plate bending elements

✍ Scribed by Garry M. Lindberg; Mervyn D. Olson

• Publisher: John Wiley and Sons
• Year: 1970
• Tongue: English
• Weight: 768 KB
• Volume: 2
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/nme.1620020110

✦ Synopsis

Abstract

The convergence rates of eigenvalue solutions using two finite plate bending elements are studied. The elements considered are the well‐known 12 degree of freedom, non‐conforming rectangular element and the 16 degree of freedom, conforming rectangular element. Three problems are analysed, a square plate simply supported on two opposite sides with the other two sides clamped, simply supported, or free. Closed form, finite element solutions for these problems are obtained by using shifting E‐operators.

With few exceptions, eigenvalue solutions found with the non‐conforming element converge from below the exact answers at an asymptotic rate of n^−2^, where n is the number of elements on a side. However, since the array size needed for such convergence is very large, little can be said about the convergence rates for practical arrays. The conforming element solutions converge from above at an asymptotic rate of n^−4^. A comparison of the errors involved in using these two elements shows that the conforming element is far superior to the non‐conforming element.