Abstract
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.
Highlights
In a linear elastic analysis, it is well known that, at the tip of a crack the stress field becomes infinite and is singular
In the linear elastic fracture mechanics, the stress field is singular at a crack tip and it is convenient to modify the original problem before its solution by the ILMF numerical model
We present numerical results to demonstrate the accuracy and efficiency of the mesh-free numerical method with optimization, through different linear fracture mechanics problems previously presented by Oliveira and Portela [26]
Summary
In a linear elastic analysis, it is well known that, at the tip of a crack the stress field becomes infinite and is singular. The paper considers the SST, a very efficient and accurate technique for solving twodimensional problems of linear elastic fracture mechanics, as reported by Oliveira et al [27], implemented in the ILMF mesh-free model of numerical analysis. This paper considers a domain mesh-free method of analysis, with the MLS approximation of the elastic field, coupled with a multi-objective optimization process that automatically generates optimal nodal arrangements of the mesh-free discretization, to compute the SIF of two-dimensional linear elastic fracture mechanics problems. The discretization process of local mesh-free methods has been heuristically implemented, which requires an expensive and time consuming calibration of the nodal arrangements or parameters of the discretization that refer to the size of the compact supports and the size of the integration domain of each node.
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