An efficient scheme for coupling dissimilar hexahedral meshes with the aid of variable-node transition elements

3-D local mesh refinement XFEM with variable-node hexahedron elements for extraction of stress intensity factors of straight and curved planar cracks

“…Notice that the variable-node hexahedron elements [19,22] are further extended to carry cracks in this work. In fact, unlike the problems with smoothed solutions, the problems under investigation involving cracks (or non-smoothed solutions type) require not only a regular variable-node element, but also a variable-node element that can carry crack.…”

“…[14][15][16][17][18], and the underlying idea of those methods is to impose constraints at nodes on mismatching interfaces to connect different scale meshes. Those methods however often require some modifications on the system matrix whenever the constraints are imposed [19]. Kumar et al [20,21] proposed a homogenized XFEM to simulate fatigue crack growth and a virtual node XFEM to represent kinked cracks based on a non-uniform mesh.…”

“…The Lm-XFEM associated with an adaptive process allows the users to achieve desired accuracies with some trials. Another important point is that each node of the variable-node hexahedron element has its own degree of freedom and a symmetric system matrix is constructed in the same way as the standard FEM [19].…”

“…Recently, the variable-node transition elements [19,22], which have an arbitrary number of nodes on the element sides and faces, are developed based on the generic point interpolation for solving engineering problems. By using the variable-node elements, the mismatching interfaces are converted into matching interfaces in a straightforward manner, thus the system matrix does not need to be modified, an effective feature that does not valid in some of the previous methods.…”

“…The Lm-XFEM utilizing the variable-node hexahedron elements [19,22] with an arbitrary number of nodes on each of their faces is to couple the meshes at different levels; while the enrichment scheme [10,40] for describing the discontinuities induced by the crack surfaces and the singularities because of crack front is taken. Notice that the variable-node hexahedron elements [19,22] are further extended to carry cracks in this work.…”