• Title/Summary/Keyword: 1-D free boundary problem

Search Result 15, Processing Time 0.021 seconds

Seismic motions in a non-homogeneous soil deposit with tunnels by a hybrid computational technique

  • Manolis, G.D.;Makra, Konstantia;Dineva, Petia S.;Rangelov, Tsviatko V.
    • Earthquakes and Structures
    • /
    • v.5 no.2
    • /
    • pp.161-205
    • /
    • 2013
  • We study seismically induced, anti-plane strain wave motion in a non-homogeneous geological region containing tunnels. Two different scenarios are considered: (a) The first models two tunnels in a finite geological region embedded within a laterally inhomogeneous, layered geological profile containing a seismic source. For this case, labelled as the first boundary-value problem (BVP 1), an efficient hybrid technique comprising the finite difference method (FDM) and the boundary element method (BEM) is developed and applied. Since the later method is based on the frequency-dependent fundamental solution of elastodynamics, the hybrid technique is defined in the frequency domain. Then, an inverse fast Fourier transformation (FFT) is used to recover time histories; (b) The second models a finite region with two tunnels, is embedded in a homogeneous half-plane, and is subjected to incident, time-harmonic SH-waves. This case, labelled as the second boundary-value problem (BVP 2), considers complex soil properties such as anisotropy, continuous inhomogeneity and poroelasticity. The computational approach is now the BEM alone, since solution of the surrounding half plane by the FDM is unnecessary. In sum, the hybrid FDM-BEM technique is able to quantify dependence of the signals that develop at the free surface to the following key parameters: seismic source properties and heterogeneous structure of the wave path (the FDM component) and near-surface geological deposits containing discontinuities in the form of tunnels (the BEM component). Finally, the hybrid technique is used for evaluating the seismic wave field that develops within a key geological cross-section of the Metro construction project in Thessaloniki, Greece, which includes the important Roman-era historical monument of Rotunda dating from the 3rd century A.D.

Analysis of 1-D Free boundary Problem Using Implicit Moving-Least-Squares Difference Method (Implicit 이동최소제곱 차분법을 이용한 1차원 자유경계문제의 해석)

  • Yoon, Young-Cheol
    • Proceedings of the Computational Structural Engineering Institute Conference
    • /
    • 2010.04a
    • /
    • pp.48-51
    • /
    • 2010
  • 본 논문에서는 자유경계문제 해석을 위해 정확도가 향상된 implicit 이동최소제곱 차분법을 제시한다. 계면경계에 대한 implicit 정의로 인해 비선형 시스템이 구성되고, 매 해석단계마다 절점해와 계면경계의 위치를 반복계산을 통해 찾는다. 계면경계 결정시 속도항을 한 단계 뒤로 지연시켜 explicit하게 근사적으로 계산하던 기존 방법에 비해 계면경계의 위치를 더 정확하게 계산할 수 있고, 결과적으로 해의 정확도가 향상되었다. 계면경계 위치값이 비교적 빠른 속도로 수렴하기 때문에 많은 반복계산이 필요치 않다. 수치예제를 통해 기존의 방법으로 계산한 결과와 비교하여 새롭게 개발한 implicit 방법의 향상된 정확도를 보였다.

  • PDF

Application of the Weak-Scatterer Hypothesis to the Wave-Body Interaction Problems

  • Kim, Yong-hwan;Sclavounos, Paul-D.
    • Journal of Ship and Ocean Technology
    • /
    • v.4 no.2
    • /
    • pp.1-12
    • /
    • 2000
  • The present study concentrates on the weak-scatterer hypothesis for the nonlinear wave-body interaction problems. In this method, the free surface boundary conditions are linearized on the incoming wave profile and the exact body motion is applied. The considered problems are the diffraction problem near a circular cylinder and the ship response in oblique waves. The numerical method of solution is a Rankine panel method. The Rankine panel method of this study adopts the higher-order B spline basis function for the approximation of physical variables. A modified Euler scheme is applied for the time stepping, which has neutral stability. The computational result shows some nonlinear behaviors of disturbance waves and wave forces. Moreover, the ship response shows very close results to experimental data.

  • PDF

Geometrically non-linear static analysis of a simply supported beam made of hyperelastic material

  • Kocaturk, T.;Akbas, S.D.
    • Structural Engineering and Mechanics
    • /
    • v.35 no.6
    • /
    • pp.677-697
    • /
    • 2010
  • This paper focuses on geometrically non-linear static analysis of a simply supported beam made of hyperelastic material subjected to a non-follower transversal uniformly distributed load. As it is known, the line of action of follower forces is affected by the deformation of the elastic system on which they act and therefore such forces are non-conservative. The material of the beam is assumed as isotropic and hyperelastic. Two types of simply supported beams are considered which have the following boundary conditions: 1) There is a pin at left end and a roller at right end of the beam (pinned-rolled beam). 2) Both ends of the beam are supported by pins (pinned-pinned beam). In this study, finite element model of the beam is constructed by using total Lagrangian finite element model of two dimensional continuum for a twelve-node quadratic element. The considered highly non-linear problem is solved by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. In order to use the solution procedures of Newton-Raphson type, there is need to linearized equilibrium equations, which can be achieved through the linearization of the principle of virtual work in its continuum form. In the study, the effect of the large deflections and rotations on the displacements and the normal stress and the shear stress distributions through the thickness of the beam is investigated in detail. It is known that in the failure analysis, the most important quantities are the principal normal stresses and the maximum shear stress. Therefore these stresses are investigated in detail. The convergence studies are performed for various numbers of finite elements. The effects of the geometric non-linearity and pinned-pinned and pinned-rolled support conditions on the displacements and on the stresses are investigated. By using a twelve-node quadratic element, the free boundary conditions are satisfied and very good stress diagrams are obtained. Also, some of the results of the total Lagrangian finite element model of two dimensional continuum for a twelve-node quadratic element are compared with the results of SAP2000 packet program. Numerical results show that geometrical nonlinearity plays very important role in the static responses of the beam.

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
    • /
    • v.22 no.1
    • /
    • pp.19-48
    • /
    • 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.

  • PDF