• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.10
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• pp.1703-1711
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• 2003

An elastic-plastic finite element analysis is performed to investigate detailed closure behaviour of fatigue cracks in residual stress fields and the numerical results are compared with experimental results. The finite element analysis performed under plane stress using contact elements can predict fatigue crack closure behaviour. The mesh of constant element size along crack surface can not predict the opening level of fatigue crack. Specially, the mesh of element sizes depending upon the reversed plastic zone size included the effect of crack opening point can precisely predict the opening level. By using the concept of the mesh of element sizes depending upon the reversed plastic zone size included the effect of crack opening point, the opening level of fatigue crack can be determined very well.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2003.10a
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• pp.403-409
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• 2003

The finite element method is one of the most widely used method of structural analysis that has wide applications in diverse fields of engineering and science. The method has been proven effective and reliable in many practical problems. One of the reasons for the methods' popularity is its ease of use, but still the user has to input the finite element mesh which affects the accuracy of the results. The knowledge required to form an effective mesh for a given problem is somewhat complex and for sometime there has been research effort to automate the generation of the mesh and this is called the adaptive mesh generation scheme. A good adaptive mesh scheme seemed to require an accurate assessment of error and generally this requires some additional computation. This paper looks into the possibility of generating adaptive meshes based on representative strain values in each finite element method. The proposed adaptive scheme does not require additional computations other that looking up the data values already computed as finite element analysis results and simple manipulations of these data. Two plane stress problems, a plate with a hole and a deep beam with a concentrated load at the end are considered to show the progress of the improved generation of adaptive meshes using the scheme.

• 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.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.11
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• pp.2932-2943
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• 1994

An efficient approach to the automatic construction of effective quadrilateral finite element meshes for two-dimensional analysis is presented. The procedure is composed of, firstly, an initial mesh generation and, secondly, an h-version of adaptive refinement based on error analysis. As for an initial mesh generation scheme, a modified looping algorithm has been employed. For the adaptive refinement process, an error indicator obtained by computing the residual error of the equilibrium equations in the energy norm with a relaxation factor has been employed. Examples of mesh generation and self-adaptive mesh improvements are given. These example solutions demonstrate that an effective mesh for a given error tolerance can be obtained in a few steps of the analysis processes.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2001.05a
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• pp.224-227
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• 2001

Adaptive analysis of multilayered composite and sandwich plates is carried out. The adaptive analysis is based on a finite element error form, which measures the difference between the through-the-thickness distribution of finite element displacement and the actual displacement. The region where the error-measure exceeds the prescribed admitted error value, the finite element mesh locally refined in the thickness direction using the mesh superposition technique. Several numerical tests are conducted to validate the effectiveness of the current approach for adaptive analysis of laminated plates.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.04a
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• pp.60-67
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• 1998

This paper deals with the development of a variable-node element and its application to the adaptive h-version mesh refinement-recovery for the incompressible viscous flow analysis. The element which has variable mid-side nodes can be used in generating the transition zone between the refined and unrefined elements and efficiently used for construction of a refined mesh without generating distorted elements. A modified Gaussian quadrature is needed to evaluate the element matrices due to the discontinuity of derivatives of the shape functions used for the element. The penalty function method which can reduce the number of independent variables is adopted for the purpose of computational efficiency and the selective reduced integration is carried out for the convection and pressure terms to preserve the stability of solution. For the economical analysis of transient problems, not only the mesh refinement but also the mesh recovery is needed. The numerical examples show that the optimal mesh for the finite element analysis of a wind around the structures can be obtained automatically by the proposed scheme.

• Structural Engineering and Mechanics
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• v.25 no.1
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• pp.91-106
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• 2007

A new class of finite elements is described for dealing with mesh gradation. The approach employs the moving least square (MLS) scheme to devise a class of elements with an arbitrary number of nodal points on the parental domain. This approach generally leads to elements with rational shape functions, which significantly extends the function space of the conventional finite element method. With a special choice of the nodal points and the base functions, the method results in useful elements with polynomial shape functions for which the $C^1$ continuity breaks down across the boundaries between the subdomains comprising one element. Among those, (4 + n)-noded MLS based finite elements possess the generality to be connected with an arbitrary number of linear elements at a side of a given element. It enables us to connect one finite element with a few finite elements without complex remeshing. The effectiveness of the new elements is demonstrated via appropriate numerical examples.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2004.10a
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• pp.75-78
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• 2004

A mesh generation algorithm adapted to the mesh density map using the Delaunay mesh generation technique is developed. In the finite element analyses of the forging processes, the numerical error increases as the process goes on because of discrete property of the finite elements or severe distortion of elements. Especially, in the region where stresses and strains are concentrated, the numerical discretization error will be highly increased. However, it is too time consuming to use a uniformly fine mesh in the whole domain to reduce the expected numerical error. Therefore, it is necessary to construct locally refined mesh at the region where the error is concentrated such as at the die corner. In this study, the point insertion algorithm is used and the mesh size is controlled by moving nodes to optimized positions according to a mesh density map constructed with a posteriori error estimation. An optimization technique is adopted to obtain a good position of nodes. And optimized smoothing techniques are also adopted to have smooth distribution of the mesh and improve the mesh element quality.

• Computational Structural Engineering
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• v.9 no.4
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• pp.165-172
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• 1996

For thin elastic structures such as beams, arches, plates and shells, there may exist the boundary layer in the narrow thin region neighborhood of boundaries, where the solution displays the singular behavior exponentially decaying in the normal direction to the boundary. In the finite element analysis of these structures, finite element mesh patterns have a significant role to capture this singularity. This paper introduces the analytic study of this problem and provides a guideline to construct optimal mesh patterns together with numerical experiments.

• Proceedings of the Korea Concrete Institute Conference
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• 2004.05a
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• pp.462-465
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• 2004

Since quasi-brittle materials like concrete show strain localization behavior accompanied by strain softening, a numerical drawback such as mesh sensitivity is appeared in the finite element analysis. In this paper, the so-called homogenized crack model which was introduced for three dimensional finite element analysis of fracture in concrete is studied for the mesh size dependence problem in fracture analysis. A homogenized crack element having a velocity discontinuity. is averaged to remove the mesh sensitivity in finite element analysis of concrete fracture. Numerical examples show that softening behavior of concrete fracture is successfully predicted without mesh sensitivity using the homogenized crack model.