Accuracy and Convergence of Finite Element Approximations
Abstract
The paper reports on a theoretical investigation of the convergence properties of several finite element approximations in current use and assesses the magnitude of the principal errors resulting from their use for certain classes of structural problems. The method is based on classical order of error analyses commonly used to evaluate finite difference methods. Through the use of the Taylor series differential or partial differential equations are found which represent the convergence and principal error characteristics of the finite element equations. These resulting equations are then compared with known equations governing the continuum, and the error terms are evaluated for selected problems. Finite elements for bar, beam, plane stress, and plate bending problems are studied as well as the use of Straight or curved elements to approximate curved beams. The results of the study provide basic information on the effect of interelement compatibility, unequal size elements, discrepancies in triangular element approximations, flat element approximations to curved structures, and the number of elements required for a desired degree of accuracy.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1968
- Accession Number
- ADA447390
Entities
People
- Joseph E. Walz
- Nancy J. Cyrus
- Robert E. Fulton
Organizations
- National Aeronautics and Space Administration