• Title/Summary/Keyword: free boundary problem

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Mechanical behaviour analysis of FGM plates on elastic foundation using a new exponential-trigonometric HSDT

  • Fatima Z. Zaoui;Djamel Ouinas;Abdelouahed Tounsi;Belkacem Achour;Jaime A. Vina Olay;Tayyab A. Butt
    • Steel and Composite Structures
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    • v.47 no.5
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    • pp.551-568
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    • 2023
  • In this research, a new two-dimensional (2D) and quasi three-dimensional (quasi-3D) higher order shear deformation theory is devised to address the bending problem of functionally graded plates resting on an elastic foundation. The displacement field of the suggested theories takes into account a parabolic transverse shear deformation shape function and satisfies shear stress free boundary conditions on the plate surfaces. It is expressed as a combination of trigonometric and exponential shear shape functions. The Pasternak mathematical model is considered for the elastic foundation. The material properties vary constantly across the FG plate thickness using different distributions as power-law, exponential and Mori-Tanaka model. By using the virtual works principle and Navier's technique, the governing equations of FG plates exposed to sinusoidal and evenly distributed loads are developed. The effects of material composition, geometrical parameters, stretching effect and foundation parameters on deflection, axial displacements and stresses are discussed in detail in this work. The obtained results are compared with those reported in earlier works to show the precision and simplicity of the current formulations. A very good agreement is found between the predicted results and the available solutions of other higher order theories. Future mechanical analyses of three-dimensionally FG plate structures can use the study's findings as benchmarks.

Numerical Study on Rayleigh-Taylor Instability Using a Multiphase Moving Particle Simulation Method (다상유동형 입자법을 이용한 Rayleigh-Taylor 불안정성의 수치해석)

  • Kim, Kyung Sung;Koo, Bonguk;Kim, Moo-Hyun;Park, Jong-Chun;Choi, Han-Suk;Cho, Yong-Jin
    • Journal of the Korean Society for Marine Environment & Energy
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    • v.20 no.1
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    • pp.37-44
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    • 2017
  • Complexity of multiphase flows due to existence of more than two interface including free-surface in one system, cannot be simulated easily. Since more than two fluids affect to flows and disturb interface, non-linearities such as instabilities can be appeared. Among several instabilities on multiphase flows, one of representative is Rayleigh-taylor instability. In order to examine in importance of density disparity, several cases with numerous Atwood number are set. Moreover, investigation of influence on initial disturbance were also considered. Moving particle simulation (MPS) method, which was employed in this paper, was not widely used for multiphase problem. In this study, by adding new particle interaction models such as self-buoyance correction, surface tension, and boundary condition at interface models, MPS were developed having more strength of physics and robust. By applying newly developed multiphase MPS, considered cases are performed and compared each other. Additionally, though existence of disagreement of magnitude of rising velocity between theoretical values from linear potential theory and that of numerical simulation, agreement of tendency can be proved of similarity of result. the discordance of magnitude can be explained due to non-linear effects on numerical simulation which was not considered in theoretical result.

Study on the Viscous Roll Damping around Circular Cylinder Using Forced Oscillations (강제동요를 이용한 원형실린더 점성 롤댐핑 연구)

  • Yang, Seung-Ho
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.18 no.2
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    • pp.71-76
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    • 2017
  • The roll damping problem in the design of ships and offshore structures remains a challenge to many researchers due to the fluid viscosity and nonlinearity of the phenomenon itself. In this paper, the study on viscous roll damping of a circular cylinder was carried out using forced oscillations. The roll moment generated by forced oscillation using a torque sensor was measured for each forced oscillation period and compared with the empirical formula. Although the magnitude of the measured torque from the shear force was relatively small, the results were qualitatively similar to those obtained from the empirical formula, and showed good agreement with the quantitative results in some oscillation periods. In addition, the flow around the circular cylinder wall was observed closely through the PIV measurements. Owing to the fluid viscosity, a boundary layer was formed near the wall of the circular cylinder, and a minute wave was generated by periodical forced oscillations at the free surface through the PIV measurement. In this study, the suitability of the empirical formula for the roll moment caused by viscous roll damping was verified by model tests. The wave making phenomenon due to the fluid viscosity around the wall of a circular cylinder was testified by PIV measurements.

Numerical Computations on the Hydrodynamic Forces by Internal Waves in a Sediment Pocket (퇴적 침전구에서 발생하는 내면파 유동에 의한 유체력 해석)

  • Kyoung Jo-Hyun;Kim Jang-Whan;Bai Kwang-June
    • Journal of the Korean Society for Marine Environment & Energy
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    • v.7 no.4
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    • pp.192-198
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    • 2004
  • A numerical method is developed to solve a two-dimensional diffraction problem for a body located in a sediment pocket where a heavier muddy water is trapped. In the present study, the wave exciting forces acting on a submerged body in the water-sediment interface by an incident wave is investigate. It is assumed that the heavier mud is trapped locally in a sediment pocket. A mathematical formulation is made in the scope of the potential theory. The fluid is assumed to be inviscid, incompressible and its motion irrotational. The boundary conditions on the unknown free surface and interface are linearized. As a method of solution, the localized finite-element method is adopted. In the method, the computation domain is reduced by utilizing the complete set of analytic solutions known in the infinite subdomain to be truncated by introduction of an appropriate juncture conditions. The main advantage of this method is that any complex geometry of the boundaries can be easily accommodated. Computations are carried out for mono-chromatic plane progressive surface waves normally incident on the domain. Numerical results are compared with those obtained by Lassiter based on Schwingers variational method. Good Agreements are obtained in general. Another numerical computations are made for the cases with and without a body in the sediment pocket.

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Development of a Numerical Model of Shallow-Water Flow using Cut-cell System (분할격자체계를 이용한 천수흐름 수치모형의 개발)

  • Kim, Hyung-Jun;Lee, Seung-Oh;Cho, Yong-Sik
    • Journal of the Korean Society of Hazard Mitigation
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    • v.8 no.4
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    • pp.91-100
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    • 2008
  • Numerical implementation with a Cartesian cut-cell method is conducted in this study. A Cartesian cut-cell method is an easy and efficient mesh generation methodology for complex geometries. In this method, a background Cartesian grid is employed for most of computational domain and a cut-cell grid is applied for the peculiar grids where the flow characteristics are changed such as solid boundary to enhance the accuracy, applicability and efficiency. Accurate representation of complex geometries can be obtained by using the cut-cell method. The cut-cell grids are constructed with irregular meshes which have various shape and size. Therefore, the finite volume method is applied to numerical discretization on a irregular domain. The HLLC approximate Riemann solver, a Godunov-type finite volume method, is employed to discretize the advection terms in the governing equations. The weighted average flux method applied on the Cartesian cut cell grid for stabilization of the numerical results. To validate the numerical model using the Cartesian cut-cell grids, the model is applied to the rectangular tank problem of which the exact solutions exist. As a comparison of numerical results with the analytical solutions, the numerical scheme well represents flow characteristics such as free surface elevation and velocities in x-and y-directions in a rectangular tank with the Cartesian and cut-cell grids.

A Study on the Forest Land System in the YI Dynasty (이조시대(李朝時代)의 임지제도(林地制度)에 관(關)한 연구(硏究))

  • Lee, Mahn Woo
    • Journal of Korean Society of Forest Science
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    • v.22 no.1
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    • pp.19-48
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    • 1974
  • Land was originally communized by a community in the primitive society of Korea, and in the age of the ancient society SAM KUK-SILLA, KOKURYOE and PAEK JE-it was distributed under the principle of land-nationalization. But by the occupation of the lands which were permitted to transmit from generation to generation as Royal Grant Lands and newly cleared lands, the private occupation had already begun to be formed. Thus the private ownership of land originated by chiefs of the tribes had a trend to be gradually pervaded to the communal members. After the, SILLA Kingdom unified SAM KUK in 668 A.D., JEONG JEON System and KWAN RYO JEON System, which were the distribution systems of farmlands originated from the TANG Dynasty in China, were enforced to established the basis of an absolute monarchy. Even in this age the forest area was jointly controlled and commonly used by village communities because of the abundance of area and stocked volume, and the private ownership of the forest land was prohibited by law under the influence of the TANG Dynasty system. Toward the end of the SILLA Dynasty, however, as its centralism become weak, the tendency of the private occupancy of farmland by influential persons was expanded, and at the same time the occupancy of the forest land by the aristocrats and Buddhist temples began to come out. In the ensuing KORYO Dynasty (519 to 1391 A.D.) JEON SI KWA System under the principle of land-nationalization was strengthened and the privilege of tax collection was transferred to the bureaucrats and the aristocrats as a means of material compensation for them. Taking this opportunity the influential persons began to expand their lands for the tax collection on a large scale. Therefore, about in the middle of 11th century the farmlands and the forest lands were annexed not only around the vicinity of the capital but also in the border area by influential persons. Toward the end of the KORYO Dynasty the royal families, the bureaucrats and the local lords all possessed manors and occupied the forest lands on a large scale as a part of their farmlands. In the KORYO Dynasty, where national economic foundation was based upon the lands, the disorder of the land system threatened the fall of the Dynasty and so the land reform carried out by General YI SEONG-GYE had led to the creation of ensuing YI Dynasty. All systems of the YI Dynasty were substantially adopted from those of the KORYO Dynasty and thereby KWA JEON System was enforced under the principle of land-nationalization, while the occupancy or the forest land was strictly prohibited, except the national or royal uses, by the forbidden item in KYEONG JE YUK JEON SOK JEON, one of codes provided by the successive kings in the YI Dynasty. Thus the basis of the forest land system through the YI Dynasty had been established, while the private forest area possessed by influential persons since the previous KORYO Dynasty was preserved continuously under the influence of their authorities. Therefore, this principle of the prohibition was nothing but a legal fiction for the security of sovereign powers. Consequently the private occupancy of the forest area was gradually enlarged and finally toward the end of YI Dynasty the privately possessed forest lands were to be officially authorized. The forest administration systems in the YI Dynasty are summarized as follows: a) KEUM SAN and BONG SAN. Under the principle of land-nationalization by a powerful centralism KWA JEON System was established at the beginning of the YI Dynasty and its government expropriated all the forests and prohibited strictly the private occupation. In order to maintain the dignity of the royal capital, the forests surounding capital areas were instituted as KEUM SAN (the reserved forests) and the well-stocked natural forest lands were chosen throughout the nation by the government as BONG SAN(national forests for timber production), where the government nominated SAN JIK(forest rangers) and gave them duties to protect and afforest the forests. This forest reservation system exacted statute labors from the people of mountainious districts and yet their commons of the forest were restricted rigidly. This consequently aroused their strong aversion against such forest reservation, therefore those forest lands were radically spoiled by them. To settle this difficult problem successive kings emphasized the preservation of the forests repeatedly, and in KYEONG KUK DAI JOEN, the written constitution of the YI Dynasty, a regulation for the forest preservation was provided but the desired results could not be obtained. Subsequently the split of bureaucrats with incessant feuds among politicians and scholars weakened the centralism and moreover, the foreign invasions since 1592 made the national land devasted and the rural communities impoverished. It happned that many wandering peasants from rural areas moved into the deep forest lands, where they cultivated burnt fields recklessly in the reserved forest resulting in the severe damage of the national forests. And it was inevitable for the government to increase the number of BONG SAN in order to solve the problem of the timber shortage. The increase of its number accelerated illegal and reckless cutting inevitably by the people living mountainuos districts and so the government issued excessive laws and ordinances to reserve the forests. In the middle of the 18th century the severe feuds among the politicians being brought under control, the excessive laws and ordinances were put in good order and the political situation became temporarily stabilized. But in spite of those endeavors evil habitudes of forest devastation, which had been inveterate since the KORYO Dynasty, continued to become greater in degree. After the conclusion of "the Treaty of KANG WHA with Japan" in 1876 western administration system began to be adopted, and thereafter through the promulgation of the Forest Law in 1908 the Imperial Forests were separated from the National Forests and the modern forest ownership system was fixed. b) KANG MU JANG. After the reorganization of the military system, attaching importance to the Royal Guard Corps, the founder of the YI Dynasty, TAI JO (1392 to 1398 A.D.) instituted the royal preserves-KANG MU JANG-to attain the purposes for military training and royal hunting, prohibiting strictly private hunting, felling and clearing by the rural inhabitants. Moreover, the tyrant, YEON SAN (1495 to 1506 A.D.), expanded widely the preserves at random and strengthened its prohibition, so KANG MU JANG had become the focus of the public antipathy. Since the invasion of Japanese in 1592, however, the innovation of military training methods had to be made because of the changes of arms and tactics, and the royal preserves were laid aside consequently and finally they had become the private forests of influential persons since 17th century. c) Forests for official use. All the forests for official use occupied by government officies since the KORYO Dynasty were expropriated by the YI Dynasty in 1392, and afterwards the forests were allotted on a fixed standard area to the government officies in need of firewoods, and as the forest resources became exhausted due to the depredated forest yield, each office gradually enlarged the allotted area. In the 17th century the national land had been almost devastated by the Japanese invasion and therefore each office was in the difficulty with severe deficit in revenue, thereafter waste lands and forest lands were allotted to government offices inorder to promote the land clearing and the increase in the collections of taxes. And an abuse of wide occupation of the forests by them was derived and there appeared a cause of disorder in the forest land system. So a provision prohibiting to allot the forests newly official use was enacted in 1672, nevertheless the government offices were trying to enlarge their occupied area by encroaching the boundary and this abuse continued up to the end of the YI Dynasty. d) Private forests. The government, at the bigninning of the YI Dynasty, expropriated the forests all over the country under the principle of prohibition of private occupancy of forest lands except for the national uses, while it could not expropriate completely all of the forest lands privately occupied and inherited successively by bureaucrats, and even local governors could not control them because of their strong influences. Accordingly the King, TAI JONG (1401 to 1418 A.D.), legislated the prohibition of private forest occupancy in his code, KYEONG JE YUK JEON (1413), and furthermore he repeatedly emphasized to observe the law. But The private occupancy of forest lands was not yet ceased up at the age of the King, SE JO (1455 to 1468 A.D.), so he prescribed the provision in KYEONG KUK DAI JEON (1474), an immutable law as a written constitution in the YI Dynasty: "Anyone who privately occupy the forest land shall be inflicted 80 floggings" and he prohibited the private possession of forest area even by princes and princesses. But, it seemed to be almost impossible for only one provsion in a code to obstruct the historical growing tendecy of private forest occupancy, for example, the King, SEONG JONG (1470 to 1494 A.D.), himself granted the forests to his royal families in defiance of the prohibition and thereafter such precedents were successively expanded, and besides, taking advantage of these facts, the influential persons openly acquired their private forest lands. After tyrannical rule of the King, YEON SAN (1945 to 1506 A.D.), the political disorder due to the splits to bureaucrats with successional feuds and the usurpations of thrones accelerated the private forest occupancy in all parts of the country, thus the forbidden clause on the private forest occupancy in the law had become merely a legal fiction since the establishment of the Dynasty. As above mentioned, after the invasion of Japanese in 1592, the courts of princes (KUNG BANGG) fell into the financial difficulties, and successive kings transferred the right of tax collection from fisherys and saltfarms to each KUNG BANG and at the same time they allotted the forest areas in attempt to promote the clearing. Availing themselves of this opportunity, royal families and bureaucrats intended to occupy the forests on large scale. Besides a privilege of free selection of grave yard, which had been conventionalized from the era of the KORYO Dynasty, created an abuse of occuping too wide area for grave yards in any forest at their random, so the King, TAI JONG, restricted the area of grave yard and homestead of each family. Under the policy of suppresion of Buddhism in the YI Dynasty a privilege of taxexemption for Buddhist temples was deprived and temple forests had to follow the same course as private forests did. In the middle of 18th century the King, YEONG JO (1725 to 1776 A.D.), took an impartial policy for political parties and promoted the spirit of observing laws by putting royal orders and regulations in good order excessively issued before, thus the confused political situation was saved, meanwhile the government officially permittd the private forest ownership which substantially had already been permitted tacitly and at the same time the private afforestation areas around the grave yards was authorized as private forests at least within YONG HO (a boundary of grave yard). Consequently by the enforcement of above mentioned policies the forbidden clause of private forest ownership which had been a basic principle of forest system in the YI Dynasty entireely remained as only a historical document. Under the rule of the King, SUN JO (1801 to 1834 A.D.), the political situation again got into confusion and as the result of the exploitation from farmers by bureaucrats, the extremely impoverished rural communities created successively wandering peasants who cleared burnt fields and deforested recklessly. In this way the devastation of forests come to the peak regardless of being private forests or national forests, moreover, the influential persons extorted private forests or reserved forests and their expansion of grave yards became also excessive. In 1894 a regulation was issued that the extorted private forests shall be returned to the initial propriators and besides taking wide area of the grave yards was prohibited. And after a reform of the administrative structure following western style, a modern forest possession system was prepared in 1908 by the forest law including a regulation of the return system of forest land ownership. At this point a forbidden clause of private occupancy of forest land got abolished which had been kept even in fictitious state since the foundation of the YI Dynasty. e) Common forests. As above mentioned, the forest system in the YI Dynasty was on the ground of public ownership principle but there was a high restriction to the forest profits of farmers according to the progressive private possession of forest area. And the farmers realized the necessity of possessing common forest. They organized village associations, SONGE or KEUM SONGE, to take the ownerless forests remained around the village as the common forest in opposition to influential persons and on the other hand, they prepared the self-punishment system for the common management of their forests. They made a contribution to the forest protection by preserving the common forests in the late YI Dynasty. It is generally known that the absolute monarchy expr opriates the widespread common forests all over the country in the process of chainging from thefeudal society to the capitalistic one. At this turning point in Korea, Japanese colonialists made public that the ratio of national and private forest lands was 8 to 2 in the late YI Dynasty, but this was merely a distorted statistics with the intention of rationalizing of their dispossession of forests from Korean owners, and they took advantage of dead forbidden clause on the private occupancy of forests for their colonization. They were pretending as if all forests had been in ownerless state, but, in truth, almost all the forest lands in the late YI Dynasty except national forests were in the state of private ownership or private occupancy regardless of their lawfulness.

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