• Structural Engineering and Mechanics
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• v.75 no.6
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• pp.685-699
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• 2020

Polygonal finite element provides a great flexibility in mesh generation of crack propagation problems where the topology of the domain changes significantly. However, the control of the discretization error in such problems is a main concern. In this paper, a polygonal-FEM is presented in modeling of crack propagation problems via an automatic adaptive mesh refinement procedure. The adaptive mesh refinement is accomplished based on the Zienkiewicz-Zhu error estimator in conjunction with a weighted SPR technique. Adaptive mesh refinement is employed in some steps for reduction of the discretization error and not for tracking the crack. In the steps that no adaptive mesh refinement is required, local modifications are applied on the mesh to prevent poor polygonal element shapes. Finally, several numerical examples are analyzed to demonstrate the efficiency, accuracy and robustness of the proposed computational algorithm in crack propagation problems.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.13 no.4
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• pp.485-500
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• 2000

In this paper the adaptive crack propagation analysis based on the estimated local and global error in the element-free Galerkin (EFG) method is presented. It is possible to keep consistency and accuracy of analysis in each propagation step by adaptive analysis. The adaptivity analysis in crack propagation is achieved by adding and removing the node along the background integration cell that are refined or recovered as estimated error. These errors are obtained by calculating the difference between the values of the projected stresses and original EFG stresses. To evaluate the performance of proposed adaptive procedure, the convergence behavior is investigated lot several examples. The results of these examples show the efficiency of proposed scheme in crack propagation analysis.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2001.04a
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• pp.84-91
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• 2001

In this study, the adaptive analysis procedure of crack propagation based on the element-free Galerkin(EFG) method is presented. The adaptivity analysis in quasi-static crack propagation is achieved by adding and/or removing the node along the background integration cell that are refined or recovered according to the estimated error. These errors are obtained basically by calculating the difference between the values of the projected stresses and original EFG stresses. To evaluate the performance of proposed adaptive procedure, the crack propagation behavior is investigated for several examples. The results of these examples show the efficiency and accuracy of proposed scheme in crack propagation analysis.

• Structural Engineering and Mechanics
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• v.12 no.5
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• pp.475-490
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• 2001

Remeshing strategies are formulated for r-adaptive and h/r-adaptive analysis of crack propagation. The relocation of the nodes, which typifies r-adaptivity, is a very cheap method to optimise a given discretisation since the element connectivity remains unaltered. However, the applicability is limited. To further improve the finite element mesh, a combined h/r-adaptive method is proposed in which h-adaptivity is applied whenever r-adaptivity is not capable of further improving the discretisation. Two and three-dimensional examples are presented. It is shown that the r-adaptive approach can optimise a discretisation at minimal computational costs. Further, the combined h/r-adaptive approach improves the performance of a fully r-adaptive technique while the number of h-remeshings is reduced compared to a fully h-adaptive technique.

• Structural Engineering and Mechanics
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• v.35 no.3
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• pp.283-299
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• 2010

This paper addresses the numerical simulation of fatigue crack growth in arbitrary 2D geometries under constant amplitude loading by the using a new finite element software. The purpose of this software is on the determination of 2D crack paths and surfaces as well as on the evaluation of components Lifetimes as a part of the damage tolerant assessment. Throughout the simulation of fatigue crack propagation an automatic adaptive mesh is carried out in the vicinity of the crack front nodes and in the elements which represent the higher stresses distribution. The fatigue crack direction and the corresponding stress-intensity factors are estimated at each small crack increment by employing the displacement extrapolation technique under facilitation of singular crack tip elements. The propagation is modeled by successive linear extensions, which are determined by the stress intensity factors under linear elastic fracture mechanics (LEFM) assumption. The stress intensity factors range history must be recorded along the small crack increments. Upon completion of the stress intensity factors range history recording, fatigue crack propagation life of the examined specimen is predicted. A consistent transfer algorithm and a crack relaxation method are proposed and implemented for this purpose. Verification of the predicted fatigue life is validated with relevant experimental data and numerical results obtained by other researchers. The comparisons show that the program is capable of demonstrating the fatigue life prediction results as well as the fatigue crack path satisfactorily.

• Structural Engineering and Mechanics
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• v.15 no.5
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• pp.563-578
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• 2003

Delaunay triangulation is combined with an adaptive finite element method for analysis of two-dimensional crack propagation problems. The content includes detailed descriptions of the proposed procedure which consists of the Delaunay triangulation algorithm and an adaptive remeshing technique. The adaptive remeshing technique generates small elements around the crack tips and large elements in the other regions. Three examples for predicting the stress intensity factors of a center cracked plate, a compact tension specimen, a single edge cracked plate under mixed-mode loading, and an example for simulating crack growth behavior in a single edge cracked plate with holes, are used to evaluate the effectiveness of the procedure. These examples demonstrate that the proposed procedure can improve solution accuracy as well as reduce total number of unknowns and computational time.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.10a
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• pp.607-614
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• 2002

For the accurate analysis of crack problems, considerable nodal refinement near the crack tip to capture singular stress field with sufficient accuracy to provide a useful computation of stress intensity factor is required. So, in this paper, adaptive nodal refinement scheme is proposed where nodes in restricted cell regions centered at crack tip are arranged in array for enhanced spatial resolution and adaptivity. With only cell-wise adaptive refinement scheme around crack tip fields, singularity of crack tip is sufficiently described to expect a successive crack propagate direction. Through numerical tests, accuracy of the proposed adaptive scheme is investigated and compared with the finite element and experimental results. By this implementation, it is shown that high accuracy is achieved by using iterative cell-wise solution method fur analyzing crack propagation problems.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.14 no.4
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• pp.525-535
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• 2001

In this paper, a new adaptive analysis scheme for element-free Galerkin method(EFGM) is proposed. The novel point of this scheme is that the triangular cell structure based on the Delaunay triangulation is used in the numerical integration and the node adding/removing process. In adaptive analysis with this scheme, there is no need to divide the integration cell and the memory cell structure. For the adaptive analysis of crack propagation, the reconstruction of cell structure by adding and removing the nodes on integration cells based the estimated error should be carried out at every iteration step by the Delaunay triangulation technique. This feature provides more convenient user interface that is closer to the real mesh-free nature of EFGM. The analysis error is obtained basically by calculating the difference between the values of the projected stresses and the original EFG stresses. To evaluate the performance of proposed adaptive procedure, the crack propagation behavior is investigated for several examples.

• Structural Engineering and Mechanics
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• v.59 no.5
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• pp.901-920
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• 2016

MeshFree methods have become popular owing to the ease with which high stress gradients can be identified and node density distribution can be reformulated to accomplish faster convergence. This paper presents a strategy for nodal density refinement with strain energy as basis in Element-Free Galerkin MeshFree technique. Two popular flat plate problems are considered for the demonstration of the proposed strategies. Issue of integration errors introduced during nodal density refinement have been addressed by suggesting integration cell refinement. High stress effects around two symmetrical semi-circular notches under in-plane axial load have been addressed in the first problem. The second considers crack propagation under mode I and mode II fracture loading by the way of introducing high stress intensity through line crack. The computational efficacy of the adaptive refinement strategies proposed has been highlighted.

• Journal of Mechanical Science and Technology
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• v.16 no.4
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• pp.454-467
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• 2002

It has been established that a crack has an important effect on the dynamic behavior of a structure. This effect depends mainly on the location and depth of the crack. Toidentifythelocation and depth of a crack in a structure, a method is presented in this paper which uses neuro-fuzzy-evolutionary technique, that is, Adaptive-Network-based Fuzzy Inference System (ANFIS) solved via hybrid learning algorithm (the back-propagation gradient descent and the least-squares method) and Continuous Evolutionary Algorithms (CEAs) solving sir ale objective optimization problems with a continuous function and continuous search space efficiently are unified. With this ANFIS and CEAs, it is possible to formulate the inverse problem. ANFIS is used to obtain the input(the location and depth of a crack) - output(the structural Eigenfrequencies) relation of the structural system. CEAs are used to identify the crack location and depth by minimizing the difference from the measured frequencies. We have tried this new idea on beam structures and the results are promising.