A new computational approach to contact mechanics using variable‐node finite elements

Abstract

SUMMARYIn this paper, a new computational strategy for two-dimensional contact problems is developed with the aid of variable-node finite elements within the range of infinitesimal deformations. The variable-node elements, which are among MLS (moving least square)-based finite elements, enable us to transform node-to-surface contact problems into node-to-node contact problems. This contact formulation with variable-node elements leads to an accurate and effective solution procedure, needless to mention that the contact patch test is passed without any additional treatment. Through several numerical examples, we demonstrate its simplicity and the effectiveness of the proposed scheme.

Three-dimensional variable-node elements based upon CS-FEM for elastic–plastic analysis

“…VNEs by MLS approximation [16][17][18] have been a new tool of mesh transition to obtain high quality of meshes in mesh gradation [20,41], adaptive mesh refinement [21], and http://dx.doi.org/10.1016/j.compstruc.2015.06.005 0045-7949/Ó 2015 Elsevier Ltd. All rights reserved. contact mechanics [19], and so forth. The merit of VNEs is to use the same framework as in the conventional finite element method when constructing the stiffness matrix, and so the modification of the system matrix is not required.…”

“…The shape functions of VNEs by MLS approximation fulfill the requirements of the conventional finite elements, and the algorithm is implemented into existing finite element codes. The VNEs with rational type shape function are followed by the emergence of VNEs by point interpolation [19][20][21][22][23], wherein polynomial type of shape functions are utilized [19][20][21][22][23] and patch test is passed completely [22,23]. The outstanding features of VNEs are manifested through a variety of problems, including nonmatching meshes [16,17,43], contact mechanics [19], mesh gradation [20,41], and adaptive mesh refinement [21].…”

“…Due to these characteristics, S-FEM is widely applied to various problems for dynamics, fracture, contact, elasticity and elasto-plasticity [67][68][69]75]. Therefore this nature may link to a remarkably efficient integration scheme for VNEs [16,17,19,[41][42][43][44][45]. The details of S-FEM features may be found in the recent Liu's monograph [50].…”

An efficient three-dimensional adaptive quasicontinuum method using variable-node elements

“…In terms of the availability of an efficient alternative, what are known as variable-node elements [12][13][14][15][16][17][18] are a powerful tool for adaptive refinement. In this context, it is not necessary to use only triangular or tetrahedral elements for the implementation of the QC.…”

“…For an efficient adaptive mesh refinement, the variable-node elements [12][13][14][15][16][17][18] are employed to bridge concurrently between different scales of meshes. To test the performance of the present QC with hexahedral elements in conjunction with the variable-node elements, nanoindentation [19][20][21][22][23][24][25][26][27][28][29][30][31] simulations are conducted under various conditions.…”