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EXTENSION OF THE ZIENKIEWICZ–ZHU ERROR ESTIMATOR TO SHAPE SENSITIVITY ANALYSIS
Author(s) -
FUENMAYOR F. J.,
OLIVER J. L.,
RÓDENAS J. J.
Publication year - 1997
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19970430)40:8<1413::aid-nme118>3.0.co;2-#
Subject(s) - sensitivity (control systems) , estimator , extension (predicate logic) , mathematics , algorithm , statistics , computer science , engineering , electronic engineering , programming language
The application of the Zienkiewicz–Zhu estimator was extended to the estimation of the discretization error arising from shape sensitivity analysis using the finite element method. The sensitivity error was quantified from the sensitivity of the energy norm by using an estimator specially developed for this purpose. Sensitivity analyses were carried out using the discrete analytical approach, which introduced no additional errors other than the discretization error. In this work, direct nodal averaging was used for linear triangular elements and the SPR technique for quadratic elements in order to obtain the smoothed stress and sensitivities fields. Two examples with an exact solution are used to analyse the effectivity of the proposed estimator and its convergence with the h ‐adaptive refinement. © 1997 by John Wiley & Sons, Ltd.