Combined Delaunay triangulation and adaptive finite element method for crack growth analysis

Abstract

ABSTRACT:The paper presents the utilization of the adaptive Delaunay triangulation in the finite element modeling of two dimensional crack propagation problems, including detailed description of the proposed procedure which consists of the Delaunay triangulation algorithm and an adaptive remeshing technique. The adaptive remeshing technique generates small elements around crack tips and large elements in the other regions. The resulting stress intensity factors and simulated crack propagation behavior are used to evaluate the effectiveness of the procedure. Three sample problems of a center cracked plate, a single edge cracked plate and a compact tension specimen, are simulated and their results assessed.

A Comprehensive Survey on Delaunay Triangulation: Applications, Algorithms, and Implementations Over CPUs, GPUs, and FPGAs

“…In [109] the application of adaptive Delaunay triangulation in finite element modeling for two-dimensional crack propagation problems is studied. It provides a comprehensive description of the proposed procedure, which combines the Delaunay triangulation algorithm with an adaptive remeshing technique.…”

“…The effectiveness of the procedure is evaluated by analyzing the resulting stress intensity factors and simulated crack propagation behavior. To assess its performance, [109] presents three sample problems: a center cracked plate, a single edge cracked plate, and a compact tension specimen. The results of these simulations are thoroughly examined and analyzed.…”

Nodeless variable finite element method for heat transfer analysis by means of flux-based formulation and mesh adaptation

“…Such technique generates small elements in the regions with great change in the temperature gradients to increase the analysis solution accuracy. At the same time, larger elements are generated in the other regions where the temperature profile is nearly uniform to reduce the computational time and the computer memory [6,7].…”

“…As small elements must be placed in the region where changes in the temperature gradients are drastic, the second derivatives of the temperature at a point with respect to global coordinates x and y are needed. Using the concept of principal stresses determination from a given state of stresses at a point [3,6], the maximum principal quantities are then used to compute the proper element size h i by requiring that the error should be uniform for all elements,…”

“…The solution accuracy is improved by simply using consecutively smaller elements to refine the finite element model until a required convergence is met. The solution accuracy can also be improved by using the h-method of adaptation where the mesh is globally or locally refined or coarsened [3,[5][6][7], or the p-method by increasing or decreasing the order of the element interpolation functions [8]. Recently, many researchers have proposed improved versions of the r -refinement method with moving mesh, so that mesh points are moved throughout the domain while the connectivity of the mesh is kept fixed [9][10][11].…”