• 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.44 no.3
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• pp.267-288
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• 2012

Free vibration analysis of arbitrary quadrilateral thick plates with internal columns and elastic edge supports is presented by using the powerful pb-2 Ritz method and Reddy's third order shear deformation plate theory. The computing domain of arbitrary quadrilateral planform is mapped onto a standard square form by coordinate transformation. The versatile pb-2 Ritz functions defined by the product of a two-dimensional polynomial and a basic function are taken to be the admissible functions. Substituting these displacement functions into the energy functional and minimizing the total energy by differentiation, leads to a typical eigenvalue problem, which is solved by a standard eigenvalue solver. Stiffness and mass matrices are numerically integrated over the plate by using Gaussian quadrature. The accuracy and efficiency of the proposed method are demonstrated through several numerical examples by comparison and convergency studies. A lot of numerical results for reasonable natural frequency parameters of quadrilateral plates with different combinations of elastic boundary conditions and column supports at any locations are presented, which can be used as a benchmark for future studies in this area.

• Structural Engineering and Mechanics
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• v.59 no.6
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• pp.1071-1094
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• 2016

We employ the so-called problem-dependent linked interpolation concept to develop two cubic 4-node quadrilateral plate finite elements with 12 external degrees of freedom that pass the constant bending patch test for arbitrary node positions of which the second element has five additional internal degrees of freedom to get polynomial completeness of the cubic form. The new elements are compared to the existing linked-interpolation quadratic and nine-node cubic elements presented by the author earlier and to the other elements from literature that use the cubic linked interpolation by testing them on several benchmark examples.

• Journal for History of Mathematics
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• v.33 no.3
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• pp.155-165
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• 2020

Pythagorean theorem is a proposition on the relationship between the lengths of three sides of a right triangle. It is well known that Pythagorean theorem for Euclidean geometry deforms into an interesting form in non-Euclidean geometry. In this paper, we investigate a new perspective that replaces right triangles with 'proper triangles' so that Pythagorean theorem extends to non-Euclidean geometries without any modification. This is seen from the perspective that a rectangle is an equiangular quadrilateral, and a right triangle is a half of a rectangle. Surprisingly, a proper triangle (defined by Paolo Maraner), which is a half of an equiangular quadrilateral, satisfies Pythagorean theorem in many geometries, including hyperbolic geometry and spherical geometry.

• Journal of Fashion Business
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• v.6 no.3
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• pp.1-14
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• 2002

According to Scythian tradition, many burials contained numerous artifacts, from weapons and harness to everyday objects and a multiplicity of personal adornments. Most valuable of all is the Scythian Gold often lavishly decorated with precious stones. The detailed images on these pieces make it possible for us to picture the appearance of the Scythians, their clothes and weapons. Scythian Gold Plaques were attached to the fabric in such a way that when they moved with each movement of the wearer it created what must have been a dazzling sight in bright daylight. Scythian Gold Plaques were divided into several types according to the shape, animal style(curved beast shape, profile shape, head reversed over its back shape), round shape, quadrilateral form, star shape, flower shape, crescent shape, bundle shape, human appearance. Through the antique tombs bequests of Three Kingdom States hereby describe the original forms of their source of Baekje gold plaque were influenced by Scythe style. Like nearly all Scythian ornaments, such gold pieces were designed to maximize various magical powers and to signify the owner's importance relative to his fellow tribesmen.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2005.06a
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• pp.978-981
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• 2005

In order to manufacture a doubly curved sheet metal effectively, a flexible incremental roll forming process has been developed by adopting the advantages of the incremental forming process and the roll forming process by combining inherent flexibility of the incremental forming process and continuous deformation of the roll forming process. The forming method has been further enhanced to form general quadrilateral blanks (including a square, a rectangle, a symmetrical trapezoid and an asymmetrical trapezoid, etc.) into doubly curved shapes by controlling the forming paths developed by various experiments.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.9 s.180
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• pp.2191-2201
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• 2000

End effects due to sectional deformations of thin-walled beams with closed cross section are analysed by a one-dimensional theory. In particular, end effects associated with warping (out of plane m otion) and distortion (in plane motion) are investigated. The exact solutions as a vector form are newly derived to reveal slowly-decaying nature of the end effects in a thin-walled beam loaded by a couple. Several examples of thin-walled beams under various loading conditions indicate that the local end effect zone due to warping and distortion is approximately ten times the typical beam width.

• Structural Engineering and Mechanics
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• v.40 no.1
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• pp.121-148
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• 2011

Closed form solutions for equilibrium and flexibility matrices of the Mindlin-Reissner theory based eight-node rectangular plate bending element (MRP8) using Integrated Force Method (IFM) are presented in this paper. Though these closed form solutions of equilibrium and flexibility matrices are applicable to plate bending problems with square/rectangular boundaries, they reduce the computational time significantly and give more exact solutions. Presented closed form solutions are validated by solving large number of standard square/rectangular plate bending benchmark problems for deflections and moments and the results are compared with those of similar displacement-based eight-node quadrilateral plate bending elements available in the literature. The results are also compared with the exact solutions.

• Korean Journal of Computational Design and Engineering
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• v.10 no.1
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• pp.61-69
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• 2005

In the global ship structure and vibration analysis, the FE(finite element) analysis model is required in the early design stage before the 3D CAD model is defined. And the analysis model generation process is a time-consuming job and takes much more time than the engineering work itself. In particular, ship structure has too many associated structural members such as stringers, stiffness and girders etc. These structural members should be satisfied as the constraints in analysis modeling. Therefore it is necessary to support generation of analysis model with satisfying these constraints as an automatic manner. For the effective support of the global ship analysis modeling, a method to generate analysis model using initial design information within ship design process, that hull form offset data and compartment data, is developed. In order to easily handle initial design information and FE model information, flexible data structure is proposed. An automatic quadrilateral mesh generation algorithm using initial design information to satisfy the constraints imposed on the ship structure is also proposed. The proposed data structure and mesh generation algorithm are applied for the various type of vessels for the usability test. Through this test, we have verified the stability and usefulness of this system including mesh generation algorithm.

• The Journal of Art Theory & Practice
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• no.6
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• pp.7-25
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• 2008

The following thesis has been composed with the inspiration attained from Paul Ardenne's conception on Contextual Art. In Europe and in the United States, there is a group of artists who emphasize in the importance of artist's participation in social, political, economical, environmental and moral issues. Since the 1960's, these artists have pondered on Modernism's ideas where art is contextually separated from humanly issues whereas the manners of such artists put on emphasis in the intent to participate in the real human social and ethical issues. Forerunner in this field of art such as Wolfgang Leib display hybrid or meta style in their work. His work displays a quadrilateral form of pollen which represents the simultaneous blending of two mixed ideas such as the abstract from the real. Thus heterogeneous style and philosophy which includes a range of medias and today's trend is observed in Contextual Art. Such art form is also found in landscapes where it is not seen as an observable object but rather an interactive object. It is correlated to Arte Povera of the Italian Art Movement, Support-Surface of the French Art Movement and lastly to the Fluxus. Through these art movements, we find a mutual antipathy towards putting art for sales in the capitalism market and reflect the social role of art in postmodern era.