EXTENSION OF THE ZIENKIEWICZ-ZHU ERROR ESTIMATOR TO SHAPE SENSITIVITYANALYSIS

The application of the Zienkiewicz-Zhu estimator was extended to the e stimation of the discretization error arising from shape sensitivity a nalysis using the finite element method. The sensitivity error was qua ntified from the sensitivity of the energy norm by using an estimator specially developed for this purpose. Sensitivity analyses were carrie d out using the discrete analytical approach, which introduced no addi tional errors other than the discretization error. In this work, direc t nodal averaging was used for linear triangular elements and the SPR( 18) technique for quadratic elements in order to obtain the smoothed s tress and sensitivities fields. Two examples with an exact solution ar e used to analyse the effectivity of the proposed estimator and its co nvergence with the h-adaptive refinement. (C) 1997 by John Wiley & Son s, Ltd.