• Journal of the Korean Society for Precision Engineering
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• v.11 no.1
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• pp.157-165
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• 1994

A general-purpose program for automatic two-dimensional finite-element modelling with quadrilateral elements was developed in this research. The conventional looping method employed in the program was introduced with emphasis on a new splitting criterion and a splitting scheme developed for improving the method. Some application examples were given, which show versatility and applicability of the developed program.

• Korean Journal of Computational Design and Engineering
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• v.11 no.1
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• pp.41-48
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• 2006

This paper describes hexahedral mesh generation for various shell structures, such as automobile bodies, plastic injection mold components and sheet metal parts by using chordal surfaces. After generaling one-layered tetrahedral mesh by an advancing front algorithm, the chordal surfaces are constructed by cutting of tetrahedral elements. Since the choral surfaces are composed of tri/quad elements with poor quality, they are transformed into quadrilateral elements with good quality. Hexahedral elements are then generated by offsetting these quadrilateral elements. The boundary nodes of hexahedral elements are generated on the outer surfaces of the original shell structures. Sample models including nonuniform thickness have been tested to validate the proposed algorithm.

• Structural Engineering and Mechanics
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• v.14 no.6
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• pp.699-712
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• 2002

In this paper, a new quadrilateral 5-node non-conforming membrane element with drilling degrees of freedom is presented. The main advantage of these elements is the relatively small number of integration points to evaluate a stiffness matrix comparing to the existing transition membrane elements (CLM elements). Moreover, the presented elements pass the patch test by virtue of the Direct Modification Method incorporated into the element formulation. The presented 5-node elements are proved to be very efficient when used in the local mesh refinement for the in-plane structures which have stress concentrations. And some numerical studies also show the good performance of the new element developed in this study.

• Nuclear Engineering and Technology
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• v.49 no.1
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• pp.29-42
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• 2017

The purpose of the present study is the presentation of the appropriate element and shape function in the solution of the neutron diffusion equation in two-dimensional (2D) geometries. To this end, the multigroup neutron diffusion equation is solved using the Galerkin finite element method in both rectangular and hexagonal reactor cores. The spatial discretization of the equation is performed using unstructured triangular and quadrilateral finite elements. Calculations are performed using both linear and quadratic approximations of shape function in the Galerkin finite element method, based on which results are compared. Using the power iteration method, the neutron flux distributions with the corresponding eigenvalue are obtained. The results are then validated against the valid results for IAEA-2D and BIBLIS-2D benchmark problems. To investigate the dependency of the results to the type and number of the elements, and shape function order, a sensitivity analysis of the calculations to the mentioned parameters is performed. It is shown that the triangular elements and second order of the shape function in each element give the best results in comparison to the other states.

• Computational Structural Engineering
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• v.3 no.4
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• pp.91-104
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• 1990

Static performance of quadrilateral plate elements was compared through numerical experiments. Sixteen plate elements were selected for comparison from the literature, which were displacement elements, equilibrium elements, mixed elements or hybrid elements based on the Kirchhoff theory or the Mindlin theory. Thin plate bending problems, such as square plate problems, rhombic plate problems, circular plate problems and cantilevered plate problems, were modeled by various meshes and solved under various kinds of boundary conditions. Kirchhoff elements were not so good as Mindlin elements in view of efficiency and convergence. Hinton's elements resulted in the best results for the problems considered with respect to efficiency, convergence and reliability but in some problems they also resulted in more or less inaccurate solutions.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.10
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• pp.1762-1771
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• 2003

In part of mechanical design analysis, quadrilateral mesh is usually used because it provides less approximate errors than triangular mesh. Over the decades, Paving method has been considered as the most robust method among existing automatic quadrilateral element mesh generation methods. However, it also has some problems such as unpredictable node projection and relatively large element generation. In this study, the aforementioned problems are corrected by updating the Paving method. In so doing, a part of node projection process is modified by classifying nodes based on the interior angles. The closure check process is also modified by adding more nodes while generating elements. The result shows well shaped element distribution in the final mesh without any aforementioned problems.

• Korean Journal of Computational Design and Engineering
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• v.14 no.3
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• pp.197-206
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• 2009

In a finite element analysis of the metal forming processes having large plastic deformation, largely distorted elements are unstable and hence they influence upon the result toward negative way so that adaptive remeshing is required to avoid a failure in the numerical computation. Therefore automatic mesh generation and regeneration is very important to avoid a numerical failure in a finite element analysis. In case of generating quadrilateral mesh, the automation is more difficult than that of triangular mesh because of its geometric complexity. However its demand is very high due to the precision of analysis. Thus, in this study, an automatic quadrilateral mesh generation and regeneration method using grid-based approach is developed. The developed method contains decision of grid size to generate initial mesh inside a two dimensional domain, classification of boundary angles and inner boundary nodes to improve element qualities in case of concave domains, and boundary projection to construct the final mesh.

• International Journal of CAD/CAM
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• v.11 no.1
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• pp.11-17
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• 2011

A new method has been developed in this paper for automatic quadrilateral mesh generation for a two-dimensional domain. The method is named 'centering method' because it centers a point at the domain and then divides it into sub-domains using cutting lines from the center point. Each of the cutting lines is selected based on the criterion using the angles between the boundary of the domain and the cutting line. The decomposition of the domain into sub-domains is repeated until every subdomain has four or six nodes. Pre-defined splitters are used to divide six-node domains into quadrilateral elements depending on their configuration and presence on the boundary of the initial domain. Arbitrary domains are meshed as examples to verify the robustness of the new method.

• Structural Engineering and Mechanics
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• v.26 no.1
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• pp.43-68
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• 2007

Using the Mindlin-Reissner plate theory, many quadrilateral plate bending elements have been developed so far to analyze thin and moderately thick plate problems via displacement based finite element method. Here new formulation has been made to analyze thin and moderately thick plate problems using force based finite element method called Integrated Force Method (IFM). The IFM is a novel matrix formulation developed in recent years for analyzing civil, mechanical and aerospace engineering structures. In this method all independent/internal forces are treated as unknown variables which are calculated by simultaneously imposing equations of equilibrium and compatibility conditions. In this paper the force based new bilinear quadrilateral plate bending element (MQP4) is proposed to analyze the thin and moderately thick plate bending problems using Integrated Force Method. The Mindlin-Reissner plate theory has been used in the formulation of this element which accounts the effect of shear deformation. Standard plate bending benchmark problems are analyzed using the proposed element MQP4 via Integrated Force Method to study its performance with respect to accuracy and convergence, and results are compared with those of displacement based 4-node quadrilateral plate bending finite elements available in the literature. The results are also compared with the exact solutions. The proposed element MQP4 is free from shear locking and works satisfactorily in both thin and moderately thick plate bending situations.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.8 no.2
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• pp.25-32
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• 1988

A formulation of an isoparametric quadrilateral higher-order plate bending finite element is presented. The 8-noded 28-d.o.f. plate element has been degenerated from the three-dimensional continuum by introducing the plate assumptions and considering higher-order in-plane displacement profile. The element characteristics have been derived by the Galerkin's weighted residual method and computed by using the selective reduced integration technique to avoid shear-locking phenomenon. Several numerical examples are given to demonstrate the accuracy and versatility of the proposed quadrilateral higher-order plate bending element over the other existing plate finite elements in both static and dynamic analyses.