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S. J. van den Boom, J. Zhang, F. van Keulen, A. M. Aragón^{*}
Research output: Contribution to journal › Comment/Letter to the editor › Scientific › peerreview
The published article contains a mistake in the notation of the strain–displacement matrix (Formula presented.) in Voigt notation concerning the isoparametric mapping and in the notation of the corresponding derivatives. As the mistakes relate only to the notation, and the implementation in the code was done correctly, they bear no consequences for the remainder of the manuscript and the results presented therein. The (Formula presented.) matrix defined inline after Eq. (11) on page 5 (repeated on pages 8 and 17) should be written as (Formula presented.) for an enriched element with n original shape functions and m enrichment functions. The differential operator (Formula presented.) in Eq. 12 should then have been defined in Voigt notation and in global coordinates as (Formula presented.) for elastostatics in 2D and 3D, respectively, and (Formula presented.) for heat conductivity in 2D and 3D, respectively. The derivatives in global coordinates are computed from the derivatives in local coordinates as (Formula presented.) for standard and enriched shape functions, respectively, where (Formula presented.) is the Jacobian of the intersected original element and (Formula presented.) is the Jacobian of the integration element. Furthermore, the derivative of (Formula presented.) with respect to the enriched node location (Formula presented.) in Equation 28 should be written as (Formula presented.) Note that the terms in (Formula presented.) corresponding to the standard shape functions are zero (this equation replaces Eq. 29 of the manuscript): (Formula presented.) as the Jacobian of the parent element is not influenced by the enriched node location, and the derivatives of the standard shape functions with respect to local coordinates of the parent element are constant. The components in (Formula presented.) corresponding to the enrichment functions are computed using (this equation replaces Eq. 30 in the manuscript) (Formula presented.) where the second term is zero because the derivatives of the enrichment function with respect to local coordinates are constant and independent of the enriched node location in global coordinates.
Original language  English 

Article number  184 
Number of pages  2 
Journal  Structural and Multidisciplinary Optimization 
Volume  66 
Issue number  8 
DOIs 

Publication status  Published  2023 
Research output: Contribution to journal › Article › Scientific › peerreview