Finite element computations over quadtree meshes: strain smoothing and semi-analytical formulation

Adaptive computations on conforming quadtree meshes

In this paper, the quadtree data structure and conforming polygonal interpolants are used to develop an h-adaptive finite element method. Quadtree is a hierarchical data structure that is computationally attractive for adaptive numerical simulations. Mesh generation and adaptive refinement of quadtree meshes is straight-forward. However, finite elements are non-conforming on quadtree meshes due...

Polygonal Interpolants: Construction and Adaptive Computations on Quadtree Meshes

Abstract. In this paper, recent advances in meshfree approximations, computational geometry, and computer graphics are described towards the development of polygonal interpolants. A particular and notable contribution is the use of meshfree (Laplace) basis functions that are based on the concept of natural neighbors. These are defined on a canonical element and an affine map is used to construc...

Application of Dynamic Analysis in Semi-Analytical Finite Element Method

Analyses of dynamic responses are significantly important for the design, maintenance and rehabilitation of asphalt pavement. In order to evaluate the dynamic responses of asphalt pavement under moving loads, a specific computational program, SAFEM, was developed based on a semi-analytical finite element method. This method is three-dimensional and only requires a two-dimensional FE discretizat...

A Mixed Stabilized Finite Element Formulation for Strain Localization Analysis

This work exploits the concept of stabilization techniques to improve the behaviour of either mixed or p u / mixed u / ε linear/linear triangular elements when strain localization analysis is required. Different stabilization methods suitable for either Mode-I or Mode-II structural failure are proposed and compared to check the global stability of the corresponding discrete finite element formu...

Algebraic Surface Design and Finite Element Meshes