A 3-D Adaptive Mesh Refinement Using Variable-Node Solid Transition Elements

Abstract

SUMMARYAn automated three-dimensional adaptive h-refinement strategy using the solid transition elements with variable midside nodes at edges and faces of the element is presented. The basic behaviour of these transition elements were improved by addition of associated non-conforming modes. By introducing these transition elements, some difficulties associated with imposing displacement constraints on irregular nodes to enforce interelement compatibility in the conventional adaptive h-refinement are easily overcome. A superconvergent patch recovery technique is also extended to three-dimensional problem. Numerical examples show the effectiveness of the proposed adaptive mesh refinement scheme using transition elements.

An adaptive finite element/meshless coupled method based on local maximum entropy shape functions for linear and nonlinear problems

“…In [50], the SPR method was used to calculate error in three-dimensional h-adaptive analysis for linear-elastic problems. Adaptive FEA based on the modified SPR method was used to model curved cracks in three-dimensional problems in [51].…”

Polyhedral elements with strain smoothing for coupling hexahedral meshes at arbitrary nonmatching interfaces

“…That is, conditions of nodal connectivity and element compatibility are not satisfied at the nonmatching interfaces. Adaptive mesh refinement [3][4][5][6], multiscale simulations [7][8][9], and multiphysics simulations [10][11][12] can also involve nonmatching interface problems. If such nonmatching interface problems are not resolved in an appropriate manner, the convergence and accuracy of solutions obtained by the finite element method (FEM) cannot be guaranteed.…”

“…In contrast, there are methods that use nonconventional types of elements for accommodating arbitrary distributions of nodes on nonmatching interfaces. To name but a few, interface elements [21][22][23] and variable-node elements [3][4][5][6][7][8][24][25][26][27][28] have been used as transition elements for gluing dissimilar meshes. The use of these elements enables a global stiffness matrix to be assembled in a straightforward way, without modifications.…”

“…In particular, a simple and efficient scheme is proposed to manage arbitrarily shaped nonmatching interfaces resulting from dissimilar hexahedral meshes. Variable-node elements have been proposed and applied to mesh coupling, which can contain arbitrary numbers of additional nodes on a four-node quadrilateral element in two dimensions [5][6][7][8][24][25][26], and on an eight-node hexahedral element in three dimensions [3][4][5]27,28]. However, with three-dimensional mesh coupling, variable-node elements are not generally applicable for arbitrary nonmatching interfaces.…”

“…However, with three-dimensional mesh coupling, variable-node elements are not generally applicable for arbitrary nonmatching interfaces. This is because they have thus far allowed only regular distributions of additional nodes in three dimensions [3][4][5]. Recently, Sohn et al [28] further enhanced the flexibility of nodal distributions of three-dimensional variable-node elements; nonetheless, types of the nodal distributions have not been generalized completely.…”