• Computers and Concrete
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• v.31 no.2
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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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• v.15 no.5
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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.

• Communications of the Korean Mathematical Society
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• v.34 no.3
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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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• v.37 no.3_4
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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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• v.15 no.1
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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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• v.4 no.2
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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.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.38 no.6
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• pp.599-607
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• 2001

In Conventional BMA, the motion vector can describe only translational movement and blocking noise is generated. To overcome this defect, motion estimation using triangular mesh has been proposed. The regular mesh is the method of dividing the image area into equal size triangle and haying the same node connection. It has no additional information about mesh structure, but do not reflect the real motion because it represents the regions by equal mesh structure regardless of the amount of motion. In this paper, motion estimation using dynamic regular mesh is proposed, In this method, the mesh structure is varied from the amount of motion and maintain the form of regular mesh. By the simulation, proposed method have better performance in PSNR and is superior to the other method in convergence rate.

• Journal of applied mathematics & informatics
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• v.32 no.1_2
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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.

• Journal of Institute of Convergence Technology
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• v.10 no.1
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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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• v.8 no.2
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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.