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Error Norm vs. Uncertainty Metric in Assessing Accuracy of the Finite Element Method

[+] Author Affiliations
Pedro V. Marcal

MPACT, Corp., Oak Park, CA

Jeffrey T. Fong, Li Ma

National Institute of Standards & Technology, Gaithersburg, MD

Robert Rainsberger

XYZ Scientific Applications, Inc., Pleasant Hill, CA

Paper No. PVP2017-65817, pp. V002T02A011; 7 pages
doi:10.1115/PVP2017-65817
From:
  • ASME 2017 Pressure Vessels and Piping Conference
  • Volume 2: Computer Technology and Bolted Joints
  • Waikoloa, Hawaii, USA, July 16–20, 2017
  • Conference Sponsors: Pressure Vessels and Piping Division
  • ISBN: 978-0-7918-5793-9
  • Copyright © 2017 by ASME

abstract

In most finite-element-analysis codes, accuracy is achieved through the use of the hexahedron hexa-20 elements (a node at each of the 8 corners and 12 edges of a brick element). Unfortunately, without an additional node in the center of each of the element’s 6 faces, nor in the center of the hexa, the hexa-20 elements are not fully quadratic such that its truncation error remains at h(0), the same as the error of a hexa-8 element formulation.

To achieve an accuracy with a truncation error of h3(0), we need the fully-quadratic hexa-27 formulation. A competitor of the hexa-27 element in the early days was the so-called serendipity cubic hexa-32 solid elements (see Ahmad, Irons, and Zienkiewicz, Int. J. Numer. Methods in Eng., 2:419-451 (1970) [1]). The hexa-32 elements, unfortunately, also suffer from the same lack of accuracy syndrome as the hexa20’s.

In recent work, we have developed methods to test the errors and the rate of convergence in FEA [2,3,4].

In this paper, we propose a new metric for determining the quality of isoparametric elements a priori. Significance of the highly accurate hexa-27 formulation and a comparison of its results with similar solutions using ABAQUS hexa-20 elements, are presented and discussed. Guidelines are proposed for selection of better elements.

Copyright © 2017 by ASME

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