Comments on “Development of two-dimensional elements with a central circular hole”, A.K. Soh, Z.F. Long [Comput. Methods Appl. Mech. Engrg. 188 (2000) 431–440]

✍ Scribed by R Piltner

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 35 KB
• Volume: 191
• Category: Article
• ISSN: 0045-7825
• DOI: 10.1016/s0045-7825(01)00345-0

✦ Synopsis

The authors Soh and Long discuss a derivation of a ®nite element with a circular hole. They published an almost identical version of the paper in another journal in 1999 [1]. In both versions of the paper reference to previously published work on the subject matter has been omitted. Special ®nite elements with circular and elliptical holes as well as internal cracks have been already introduced in 1982 [2±6] (Fig. 1). The special ®nite elements of [3] have been cited by several authors (see e.g. [7±13]).

In [3] the special trial functions for the hole elements have been derived using the Kolosov/Muskhelishvili solution representation of stresses and displacements in complex form. Because the trial functions used for the ®nite element domain satisfy the governing dierential equations, the special hole elements can be considered as Tretz-type ®nite elements. In [3], a mixed variational formulation with piecewise linear or quadratic displacements assumed on the ®nite element boundary has been used for an appropriate coupling with linear or quadratic standard displacement elements.

The authors Soh and Long do not mention any contributions from the literature on the Tretz method [7,8,13,14], and introduce in their description of a ®nite element with a hole a variational crime: for the coupling of a hole element with standard elements they require displacement continuity only at the element nodal points and express the free parameters of the assumed Tretz functions in terms of the nodal displacements. Comput. Methods Appl. Mech. Engrg. 191 (2001) 503±504 www.elsevier.com/locate/cma Fig. 1. Special ®nite elements with holes and internal crack and piece-wise linear or quadratic boundary displacements [2±6].