• Computers and Concrete
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• 제31권2호
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• pp.151-161
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• 2023

This paper presents an investigation of variables that cause spurious cracking in numerical modeling of concrete fracture. Spurious cracks appear due to the approximate nature of numerical modeling. They overestimate the dissipated energy, leading to divergent results with mesh refinement. This paper is limited to quasi-static loading regime, homogeneous models, cracking as the only nonlinear mode of deformation and cracking only due to tensile loading. Under these conditions, some variables that can be related to spurious cracking are: mesh alignment, ductility, crack band width, structure size, mesh refinement and load increment size. Case studies illustrate the effect of each variable and convergence analyses demonstrate that, after all, load-increment size is the most important variable. Theoretically, a sufficiently small load increment is able to eliminate or at least alleviate the detrimental influence of the other variables. Such load-increment size might be prohibitively small, rendering the simulation unfeasible. Hence, this paper proposes two alternatives. First, it is proposed an algorithm that automatically find such small load increment size automatically, which not necessarily avoid large computations. Then, it is proposed a double simulation technique, in which the crack is forced to propagate through the localization zone.

• Structural Engineering and Mechanics
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• 제15권5호
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• pp.579-608
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• 2003

This paper deals with adaptive finite element analysis of linearly elastic structures using different error estimators based on flux projection (or best guess stress values) and residual methods. Presentations are given on a typical h-type adaptive analysis, a mesh refinement scheme and the coupling of adaptive finite element analysis with automatic mesh generation. Details about different error estimators are provided and their performance, reliability and convergence are studied using six node quadratic triangular elements. Several examples are presented to demonstrate the reliability of different error estimators.

• 대한수학회논문집
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• 제34권3호
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• pp.1015-1027
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• 2019

A class of systems of singularly perturbed convection diffusion type equations with integral boundary conditions is considered. A numerical method based on a finite difference scheme on a Shishkin mesh is presented. The suggested method is of almost first order convergence. An error estimate is derived in the discrete maximum norm. Numerical examples are presented to validate the theoretical estimates.

• Journal of applied mathematics & informatics
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• 제37권3_4호
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• pp.183-200
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• 2019

We have constructed a robust numerical method on Shishkin mesh for a class of convection diffusion type turning point problems with Robin type boundary conditions. Supremum norm is used to derive error estimates which is of order O($N^{-1}$ ln N). Theoretical results are verified by providing numerical examples.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제15권1호
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• pp.57-65
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• 2011

In this paper, a good quality mesh generation for the finite element method is investigated for artificial hip joint simulations. In general, bad meshes with a large aspect ratio or mixed elements can give rise to excessively long computational running times and extremely high errors. Typically, hexahedral elements outperform tetrahedral elements during three-dimensional contact analysis using the finite element method. Therefore, it is essential to mesh biologic structures with hexahedral elements. Four meshing schemes for the finite element analysis of an artificial hip joint are presented and compared: (1) tetrahedral elements, (2) wedge and hexahedral elements, (3) open cubic box hexahedral elements, and (4) proposed hexahedral elements. The proposed meshing scheme is to partition a part before seeding so that we have a high quality three-dimensional mesh which consists of only hexahedral elements. The von Mises stress distributions were obtained and analyzed. We also performed mesh refinement convergence tests for all four cases.

• Journal of Advanced Research in Ocean Engineering
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• 제4권2호
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• pp.78-85
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• 2018

This paper presents a study of the effects of the free surface to marine propeller including the mesh effect of the models. In the present study, we conduct the numerical simulation for propeller performance employing the openwater test. The numerical simulations compare the meshing strategies for the propeller and show the effects on both thrust and torque. OpenFOAM is applied to solve the propeller problem and then open water performances of KCS propeller (KP505) are estimated using a Reynold-averaged Navier-Stokes equations (RANS) solver and the turbulence of the $K-{\omega}$ SST model. Unstructured meshes are used in the numerical simulation employing hexahedral meshing for mesh generation. The arbitrary mesh interfacing (AMI) and multiple rotating frame (MRF) are compared to define the best meshing strategy. The meshing strategies are evaluated through 3 classifications, i.e., coarse, medium, and fine mesh. Thus, the propeller can be performed utilizing the best mesh strategy. The computational results are validated by comparison with the experimental results. The $K_T$, $K_Q$, and efficiency of the propeller are compared to an experimental result and for all of the meshing strategies. Thus, the simulations show the influence of meshing in order to perform the propeller performances.

• 대한전자공학회논문지SP
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• 제38권6호
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• pp.599-607
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• 2001

기존의 블록 정합 알고리듬에서는 움직임 벡터로 평면적인 움직임만을 기술할 수 있었고 이로 인해 블록화 잡음이 발생하였다 이러한 문제점을 해결하기 위해서 삼각형 메쉬를 이용한 움직임 추정방법이 제안되었다. 영상을 일정한 크기의 삼각형으로 분할하고 같은 연결 상태를 가지도록 하는 정규화 메쉬는 메쉬의 구조를 기술하기 위한 추가적인 정보가 필요 없으나 움직임이 많은 영역과 작은 영역을 같은 크기의 메쉬로 분할함으로써 성능을 저하시키게 된다 본 논문에서는 정규화 메쉬의 형태를 유지하면서 움직임영역에 따라 메쉬의 크기와 연결상태가 가변될 수 있는 동적 정규화 메쉬를 사용한 움직임 추정방법을 제안한다. 실험결과를 통해 제안한 방법이 기존의 블록 정합 방법이나 정규화 메쉬 방법보다 PSNR이 향상된 결과를 얻을 수 있었고 노드의 재정렬시에도 다른 방법보다 초기 수렴속도가 우수함을 알 수 있었다.

• Journal of applied mathematics & informatics
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• 제32권1_2호
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• pp.185-201
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• 2014

In this paper, we construct a numerical method to solve singularly perturbed one-dimensional parabolic convection-diffusion problems. We use Euler method with uniform step size for temporal discretization and exponential-spline scheme on spatial uniform mesh of Shishkin type for full discretization. We show that the resulting method is uniformly convergent with respect to diffusion parameter. An extensive amount of analysis has been carried out to prove the uniform convergence with respect to the singular perturbation parameter. The obtained numerical results show that the method is efficient, stable and reliable for solving convection-diffusion problem accurately even involving diffusion parameter.

• 융복합기술연구소 논문집
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• 제10권1호
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• pp.7-12
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• 2020

We describe a efficient surface reconstruction method that reconstructs a 3D manifold polygonal mesh approximately passing through a set of 3D oriented points. Our algorithm includes 3D convex hull, octree data structure, signed distance function (SDF), and marching cubes. The 3D convex hull provides us with a fast computation of SDF, octree structure allows us to compute a minimal distance for SDF, and marching cubes lead to iso-surface generation with SDF. Our approach gives us flexibility in the choice of the resolution of the reconstructed surface, and it also enables to use on low-level PCs with minimal peak memory usage. Experimenting with publicly available scan data shows that we can reconstruct a polygonal mesh from point cloud of sizes varying from 10,000 ~ 1,000,000 in about 1~60 seconds.

• Ocean Systems Engineering
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• 제8권2호
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• pp.183-199
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• 2018

The open source software OpenFOAM is utilised to simulate the water entry and hydrodynamic impact process of 2D wedges and ship hull sections. Incompressible multiphase flow solver interDyMFoam is employed to calculate the free fall of structure from air into water using dynamically deforming mesh technique. Both vertical and oblique entry of wedges of various dead-rise angles have been examined. A convergence study of dynamics as well as kinematics of the flow problem is carried out on successively refined meshes. Obtained results are presented and compared to the experimental measurements showing good agreement and reasonable mesh convergence of the solution.