• Structural Engineering and Mechanics
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• v.4 no.4
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• pp.415-424
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• 1996

This paper presents a newly suggested calculation method in which an arbitrary quadrilateral element with curved sides is transformed to a normal rectangular one by mapping of coordinates, then the two-dimensional spline is adopted to approach the displacement function of this element. Finally the solution can be obtained by the least-energy principle. Thereby, the application field of Spline Finite Element Method will be extended.

• 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.

• Journal of applied mathematics & informatics
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• v.40 no.5_6
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• pp.949-958
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• 2022

The aim of this papaer is to prove the discrete compactness property for modified Raviart-Thomas element(MRT) of lowest order on quadrilateral meshes. Then MRT space can be used for eigenvalue problems, and is more efficient than the lowest order ABF space since it has less degrees of freedom.

• International Journal of CAD/CAM
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• v.1 no.1
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• pp.11-21
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• 2002

This paper presents a triangular-to-quadrilateral mesh conversion method that can control the directionality of the output quadrilateral mesh according to a user-specified vector field. Given a triangular mesh and a vector field, the method first scores all possible quadrilaterals that can be formed by pairs of adjacent triangles, according to their shape and directionality. It then converts the pairs into quadrilateral elements in order of the scores to form a quadrilateral mesh. Engineering analyses with finite element methods occasionally require a quadrilateral mesh well aligned along the boundary geometry or the directionality of some physical phenomena, such as in the directions of a streamline, shock boundary, or force propagation vectors. The mesh conversion method can control the mesh directionality according to any desired vector fields, and the method can be used with any existing triangular mesh generators.

• 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.

• 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.

• Structural Engineering and Mechanics
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• v.83 no.2
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• pp.273-282
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• 2022

In this paper, we propose a new concept for error estimation in finite element solutions, which we call mode-based error estimation. The proposed error estimation predicts a posteriori error calculated by the difference between the direct finite element (FE) approximation and the recovered FE approximation. The mode-based FE formulation for the recently developed self-updated finite element is employed to calculate the recovered solution. The formulation is constructed by searching for optimal bending directions for each element, and deep learning is adopted to help find the optimal bending directions. Through various numerical examples using four-node quadrilateral finite elements, we demonstrate the improved predictive capability of the proposed error estimator compared with other competitive methods.

• Structural Engineering and Mechanics
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• v.26 no.1
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• pp.69-86
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• 2007

A four-noded plate bending quadrilateral (PBQ4) and an eight-noded plate bending quadrilateral (PBQ8) element based on Mindlin plate theory have been adopted for modeling the thick plates on elastic foundations using Winkler model. Transverse shear deformations have been included, and the stiffness matrices of the plate elements and the Winkler foundation stiffness matrices are developed using Finite Element Method based on thick plate theory. A computer program is coded for this purpose. Various loading and boundary conditions are considered, and examples from the literature are solved for comparison. Shear locking problem in the PBQ4 element is observed for small value of subgrade reaction and plate thickness. It is noted that prevention of shear locking problem in the analysis of the thin plate is generally possible by using element PBQ8. It can be concluded that, the element PBQ8 is more effective and reliable than element PBQ4 for solving problems of thin and thick plates on elastic foundations.

• Proceedings of the KSME Conference
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• 2008.11a
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• pp.402-407
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• 2008

We suggest a linear elastic flat shell element based on the HT(hybrid Trefftz) method. We formulate the membrane part of the proposed element as an HT plane element with the drilling DOF. For the bending part, we developed a thick HT plate element that can represent transverse shear deformations accurately. Because we derive both the membrane and the bending parts consistently using the HT functional, we can easily construct the triangular and the quadrilateral elements in a unified way. In addition, warping of quadrilateral element is compensated by force and moment equilibrium equations. We evaluate the performance of the new element in terms of accuracy and convergence.

• Structural Engineering and Mechanics
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• v.37 no.6
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• pp.633-648
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• 2011

This paper investigates the aspect-ratio locking of the isoparametric 8-node quadrilateral (QUAD8) element. An important finding is that, if finite element solution is carried out with in exact arithmetic (i.e., with no truncation and round off errors), the locking tendency of the element is completely avoided even for aspect-ratios as high as 100000. The current finite element codes mostly use floating point arithmetic. Thus, they can only avoid this locking for aspect-ratios up to 100 or 1000. A novel method is proposed in the paper to avoid aspect-ratio locking in floating point computations. In this method, the offending terms of the strain-displacement matrix (i.e., $\mathbf{B}$-matrix) are multiplied by suitable scaling factors to avoid ill-conditioning of stiffness matrix. Numerical examples are presented to demonstrate the efficacy of the method. The examples reveal that aspect-ratio locking is avoided even for aspect-ratios as high as 100000.