A Novel Virtual Node Hexahedral Element with Exact Integration and Octree Meshing

Abstract

The method presented in this work is a 3-dimensional polyhedral finite element (3D PFEM) based on virtual node method. Novel virtual node polyhedral elements (termed as VPHE) are developed here, particularly virtual node hexahedral element (termed as VHE). Stiffness matrices of these polyhedral elements consist of simple polynomials. Thus, a new algorithm is introduced in this paper, which enables exact integration of monomials without a need for high number of integration points and weights. The number of nodes for VHE elements is not restricted, as opposed to the conventional hexahedral elements. This feature enables formulation of transition elements (termed as T-VHE) which are useful to adaptive computation. Performances of the new VHE elements in solid mechanics and conductive heat transfer phenomena are examined through numerical simulations. The new T-VHE elements are utilized in octree mesh. The VHE elements are found to produce good results and T-VHE elements help to reduce number of global nodes for the analysis.

Techniques for element formulation and quadtree-based triangular mesh generation for strain-based finite elements

“…In contrast, a coarse mesh is used for the rest of the region. Both fine and coarse meshed regions are then merged by using transition elements [37] . Transition elements consist of a mid-node at one of the sides of the element.…”

“…This work introduces a new approach to form strain-based triangular transition elements (denoted as SB-TTE) by using three-node triangular elements. The fourth mid-node is formed by using virtual node method [37 , 38] ; therefore, the need for more degrees of freedom is avoided. However, this approach requires formulation of the strain-based finite elements to be represented in the form of conventional displacement-based elements: by deriving shape functions.…”