• Computational Structural Engineering
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• v.4 no.1
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• pp.109-120
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• 1991

This paper introduces a geometric modelling system adopted in a newly developed preprocessor for finite element analysis of three dimensional structures. The formulation is characterized by hierachical construction of structural model which consists of control points, curves, surfaces and solids. Various surface and solid modelling schemes based on blending functions and boundary representation are systematized for finite element mesh generation. The modelling system is integrated with model synthesis and operations which facilitate modelling of complex structures.

• Korean Journal of Computational Design and Engineering
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• v.14 no.4
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• pp.281-289
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• 2009

Topology optimization has been widely used for the optimal structure design for weight reduction and high performance. Since the result of three-dimensional topology optimization is represented by the discrete material distribution in finite elements, it is hard to interpret from a design point of view. In this paper, the method for interpreting three-dimensional topology optimization resuIt into a series of cross-sectional curve representation is proposed and interfaced with the existing CAD system for the practical use. The concept of node density and virtual grid is introduced to transform element density values into grid density and material boundaries in each cross section are identified based on the element volume rate to satisfy the amount of material specified in the original design intent. Design exampIes show that three-dimensional topology result can be converted into a form of curve CAD model and the seamless interface with CAD software can be achieved.

• Journal of Dental Rehabilitation and Applied Science
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• v.22 no.4
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• pp.341-348
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• 2006

Accurate fit of the implant prosthesis is important in ensuring long term success of osseointegrated implant. Inaccurate fit of the implant prosthesis may give rise to complications and mechanical failure. To evaluate fite of the implant prosthesis, the development of the methods of analyzing the degree of misfit is important in clinical practice. To analyze the degree of the misfit of implant prosthesis, modal testing was used. A 2-dimensional finite element modal testing was accomplished. Four 2-dimensional finite element models with various levels of misfit of implant prostheses were constructed. Thickness gauges were simulated to make misfit in the implant prostheses. With eigenvalue analysis, the natural frequencies of the models were found in the frequency domain representation of vibration. According to the difference of degree of misfit, natural frequencies of the models were changed.

• Journal of Dental Rehabilitation and Applied Science
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• v.22 no.3
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• pp.251-260
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• 2006

Accurate fit of the implant prosthesis is important in ensuring long term success of osseointegrated implant. Inaccurate fit of the implant prosthesis may give rise to complications and mechanical failure. To evaluate fite of the implant prosthesis, the development of the methods of analyzing the degree of misfit is important in clinical practice. To analyze the degree of the misfit of implant prosthesis, modal testing was used. A 2-dimensional finite element modal testing was accomplished. Four 2-dimensional finite element models with various levels of misfit of implant prostheses were constructed. Thickness gauges were simulated to make misfit in the implant prostheses. With eigenvalue analysis, the natural frequencies of the models were found in the frequency domain representation of vibration. According to the difference of degree of misfit, natural frequencies of the models were changed.

• Geomechanics and Engineering
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• v.14 no.5
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• pp.479-489
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• 2018

In this paper, a comparative study of the effects of soil modelling on the interaction between tunnelling in soft soil and adjacent piled structure is presented. Several three-dimensional finite element analyses are performed to study the deformation of pile caps and piles as well as tunnel internal forces during the construction of an underground tunnel. The soil is modelled by two material models: the simple, yet approximate Mohr Coulomb (MC) yield criterion; and the complex, but reasonable hardening soil (HS) model with hyperbolic relation between stress and strain. For the former model, two different values of the soil stiffness modulus ($E_{50}$ or $E_{ur}$) as well as two profiles of stiffness variation with depth (constant and linearly increasing) were used in attempts to improve its prediction. As these four attempts did not succeed, a hybrid representation in which the hardening soil is used for soil located at the highly-strained zones while the Mohr Coulomb model is utilized elsewhere was investigated. This hybrid representation, which is a compromise between rigorous and simple solutions yielded results that compare well with those of the hardening soil model. The compared results include pile cap movements, pile deformation, and tunnel internal forces. Problem symmetry is utilized and, therefore, one symmetric half of the soil medium, the tunnel boring machine, the face pressure, the final tunnel lining, the pile caps, and the piles are modelled in several construction phases.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1997.10a
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• pp.17-23
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• 1997

In the two-dimensional Finite Element Method for forming simulation, mesh generation and remeshing process are very significant. In this paper, using the modified splitting mesh generation algorithm, we can overcome the limitation of existing techniques and acquire mesh, which has optimal mesh density. A modified splitting algorithm for automatically generating quadrilateral mesh within a complex domain is described. Unnecessary meshing process for density representation is removed. Especially, during the mesh generation with high gradient density like as shear band representation, the modified mesh density scheme, which will generate quadrilateral mesh with the minimized error, which takes effect on FEM solver, is introduced.

• Korean Journal of Computational Design and Engineering
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• v.1 no.1
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• pp.76-83
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• 1996

A three dimensional FE mesh generation scheme based on mapping approach is proposed in this study. A volume in Eucledian space is represented by composite hyperpatches which are piecewise cubic functions in parameters u, v, w. A key idea in the proposed approach is that I sampled grid data points lying only on the boundary surfaces are needed for the shape representation. Inner points which are necessary to form a hyperpatch are internally generated by Coons patches. This approach is most appropriate for the shapes which are compositions of hexahedronlike shapes and also severely curved.

• Structural Engineering and Mechanics
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• v.17 no.5
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• pp.671-690
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• 2004

A meshless method with novel variation of point collocation by finite mixture approximation is developed in this paper, termed the meshless finite mixture (MFM) method. It is based on the finite mixture theorem and consists of two or more existing meshless techniques for exploitation of their respective merits for the numerical solution of partial differential boundary value (PDBV) problems. In this representation, the classical reproducing kernel particle and differential quadrature techniques are mixed in a point collocation framework. The least-square method is used to optimize the value of the weight coefficient to construct the final finite mixture approximation with higher accuracy and numerical stability. In order to validate the developed MFM method, several one- and two-dimensional PDBV problems are studied with different mixed boundary conditions. From the numerical results, it is observed that the optimized MFM weight coefficient can improve significantly the numerical stability and accuracy of the newly developed MFM method for the various PDBV problems.

• Bulletin of the Korean Mathematical Society
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• v.60 no.6
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• pp.1687-1695
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• 2023

In this paper, we study the Green ring r(𝔴⁰_n) of the weak Hopf algebra 𝔴⁰_n based on Taft Hopf algebra H_n(q). Let R(𝔴⁰_n) := r(𝔴⁰_n) ⊗_ℤ ℂ be the Green algebra corresponding to the Green ring r(𝔴⁰_n). We first determine all finite dimensional simple modules of the Green algebra R(𝔴⁰_n), which is based on the observations of the roots of the generating relations associated with the Green ring r(𝔴⁰_n). Then we show that the nilpotent elements in r(𝔴⁰_n) can be written as a sum of finite dimensional indecomposable projective 𝔴⁰_n-modules. The Jacobson radical J(r(𝔴⁰_n)) of r(𝔴⁰_n) is a principal ideal, and its rank equals n - 1. Furthermore, we classify all finite dimensional non-simple indecomposable R(𝔴⁰_n)-modules. It turns out that R(𝔴⁰_n) has n² - n + 2 simple modules of dimension 1, and n non-simple indecomposable modules of dimension 2.

• Journal of Mechanical Science and Technology
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• v.18 no.7
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• pp.1107-1120
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• 2004

This study proposes a new scheme for the sampled-data representation of nonlinear systems with time-delayed multi-input. The proposed scheme is based on the Taylor-series expansion and zero-order hold assumption. The mathematical structure of a new discretization scheme is explored. On the basis of this structure, the sampled-data representation of nonlinear systems including time-delay is derived. The new scheme is applied to nonlinear systems with two inputs and then the delayed multi-input general equation is derived. The resulting time-discretization provides a finite-dimensional representation of nonlinear control systems with time-delay enabling existing controller design techniques to be applied to them. In order to evaluate the tracking performance of the proposed scheme, an algorithm is tested for some of the examples including maneuvering of an automobile and a 2-DOF mechanical system.