Optimized Mesh-free Analysis for the Singularity Subtraction Technique of Linear Elastic Fracture Mechanics

Autor: Tiago Oliveira, Artur Portela
Rok vydání: 2022
Zdroj: Global Journal of Researches in Engineering. :23-50
ISSN: 2249-4596
0975-5861
DOI: 10.34257/gjreivol21is1pg23
Popis: In linear elastic fracture mechanics, the stress field is singular at the tip of a crack. Since the representation of this singularity in a numerical model raises considerable numerical difficulties, the paper uses a strategy that regularizes the elastic field, subtracting the singularity from the stress field, known as the singularity subtraction technique (SST). In this paper, the SST is implemented in a local mesh-free numerical model, coupled with modern optimization schemes, used for solving two-dimensional problems of the linear elastic fracture mechanics. The mesh-free numerical model (ILMF) considers the approximation of the elastic field with moving least squares (MLS) and implements a reduced numerical integration. Since the ILMF model implements the singularity subtraction technique that performs a regularization of the stress field, the mesh-free analysis does not require a refined discretization to obtain accurate results and therefore, is a very efficient numerical analysis. Mesh-free numerical methods control the accuracy and efficiency of the model through the size of compact supports, the size of integration domains and the distribution of nodes in the body, which are usually heuristically determined through an expensive and time consuming calibration effort. The leading innovation of this paper is the automatic definition of these parameters and the nodal distribution by means of a multi-objective optimization, based on genetic algorithms (GA), with reliable and efficient objective functions. The optimization scheme effectively automates the whole pre-processing phase of a numerical analysis with mesh-free methods. Benchmark problems were analyzed to assess the accuracy and efficiency of the modeling strategy. The results presented in the paper are in perfect agreement with those of reference solutions and therefore, make reliable and robust this mesh-free numerical analysis, coupled with a multi-objective optimization,for linear elastic fracture mechanics problems.
Databáze: OpenAIRE
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