21-node hexahedral isoparametric element for analysis of contact problems

Abstract

SUMMARYBecause the 20-node solid element of the serendipity family does not ful®l the physical contact requirements properly (the equivalent nodal forces include negative values) a 21-node three-dimensional transient element for the non-linear contact/friction problem is investigated. Construction of the shape functions is described. The proposed transition element is established by adding one node to the top or bottom face of the basic 20-node solid serendipity element for an eective connection between the contact region (21-node elements) and the rest of the structure (20-node elements) with minimum degrees of freedom possible. Comparisons with results calculated for the 3D-contact problem using the combinations of the 8-node element connected to 20-node ®nite elements prove the high accuracy and overall superiority of the present method. The numerical examples are shown to illustrate the validity and eciency of the developed technique. The approach may be employed easily in existing computer codes. #

Enhancement of a high‐cycle accumulation model by an adaptive strain amplitude and its application to monopile foundations

“…This leads to an inferior convergence behaviour of u20p8 elements in contact analyses. 56 A solution to that has been proposed by Buczkowski,57 adding a node to the mid of the face(s) of the serendipity element being in contact. Both the shape functions used for the integration of stress of this surface and the shape functions of the element have to be modified in this case.…”

“…As has been outlined in Section 5.1, integration of the shape functions used for quadratically interpolated serendipity elements can lead to a negative area. 56,57 This is especially problematic in contact analyses using this element type as the convergence rate is strongly influenced by the error in integration. numgeo therefore uses elements with 27 nodes in case of 3D contact analyses, which do not suffer from the shortcomings of the serendipity element.…”

Analysis of Bolt Joint Using the Finite Element Method

“…Thus, the elements do not represent the contact phenomenon properly. Because the standard second-order brick elements of the Serendipity family can not be used in modelling of the contact zone, special 21-or 28-node hexahedral elements were employed in the present analysis [13,14]. The dimensions and shape of the joint comply with the following standards: JIS B (Japanese standard) and ANSI B 16.5 (American standard).…”

“…The model presented in Fig. 2 is composed of: -the flange (red colour -3425 20-node finite elements beyond the contact zone, and 21-node (denotation: C3D21 [13]) or 28-node (denotation: C3D28 [14]) solid finite elements in the contact zone), -the gaskets (white colour -192 21-or 28-node solid finite elements), -the bolts (green colour -626 20-or 21-node solid finite elements, Fig. 3).…”

3D analysis of the influence of specimen dimensions on fretting stresses

“…Elements used in the contact area are 21-node special elements [24]. A 2% global error in energy norm has been defined as the target error for all the analyses performed.…”