• 한국전산구조공학회논문집
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• 제14권3호
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• pp.401-411
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• 2001

본 논문은 등분포 면내응력을 받고 비균질 Pasternak지반에 의해 지지된 장방형판의 진동해석을 다룬 것이다. Winkler 지반계수와 전단지반계수가 고려된 2 변수지반을 Pasternak 지반이라 불리운다. 판의 중앙부분과 가장자리부분의 Winkler 지반계수값을 각각 k₁과 k₂로 선택하였고 전단지반계수값은 판의 전지역에 대해 일정한 값을 취하였다. 전체 휨강성행렬, 기하강성행렬, 질량 행렬 및 Pasternak 지반의 강성행렬을 조합하고 이 행렬들로 이루어지는 고유값 문제를 푼다. 그 결과 지반강성을 고려할 때 전단지반계수가 무시되면 안된다는 것으로 나타났다.

• 한국강구조학회 논문집
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• 제15권3호
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• pp.291-298
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• 2003

최근 건축물의 대형화로 구조물의 기초는 비균질지반에 지지된다. 본 연구는 면내력을 받는 후판의 진동해석을 한 것이다. 장방 형판은 등방, 균질의 선형 탄성재료로 구성되었다. 장방형 후판의 진동해석은 8절점과 9절점을 이용한 장방형 유한요소를 사용하여 행하였다. 본 연구에서 기초를 수직스프링으로 이상화한 Winkler지반에 전단지반층을 추가한 Pasternk지반으로 이상화하였다. 지반의 강성을 달리한 비균질 Pasternak지반에 지지된 판을 해석하기 위해 중앙부분과 가장자리 부분의 Winkler지반계수를 WFP1과 WFP2로 선택하였다. (그림 4.) Winkler지반계수 WFP1과 WFP2는 0, 10, $10^2$, $10^3$으로 변환시키고 전단지반강성은 0, 5, 10으로 하였다. 후판의 좌굴응력(${\sigma}_{cr}$)에 대한 면내력의 비는 각각 0.4, 0.8에 대해 적용하였다.

• 한국전산구조공학회논문집
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• 제17권4호
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• pp.351-363
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• 2004

비보존력을 받는 보-부재의 질량행렬, 탄성강도행릴, circulatory비보존력의 방향변화로 인한 load correction강도행력, 그리고 Winkler 및 Pasternak지반강도행렬을 고려한 운동방정식을 유도하고 divergence 및 flutter에 의한 안정성 해석을 수행한다. 또한 내적 및 외적 감쇠계수를 운동방정식에 포함시킴으로써 감쇠효과를 고려하고, 2차 고유치문제의 해법(quadratic eigen problem solution)을 적용하여 flutter에 미치는 영향을 조사한 후, Beck's column, Leipholz's column 및 Hauger's column에 대하여 비보존력의 방향파라미터 ${\alpha}$에 대한 임계하중의 영향, 내적 및 외적 감쇠계수 및 Winkler 및 Pasternak지반에 의한 임계하중의 영향을 각각 조사한다.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2003년도 춘계학술대회논문집
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• pp.852-857
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• 2003

This paper has the object of investigating natural frequencies of thick plates on inhomogeneous Pasternak foundation by means of finite element method and providing kinematic design data lot mat of building structures. This analysis was applied for design of substructure on elastic foundation. Mat of building structure may be consisdered as a thick plate on elastic foundation. Recently, as size of building structure becomes larger, mat area of building structure also tend to become target and building structure is supported on inhomogeneous foundation. In this paper, vibration analysis or rectangular thick plate is done by use or serendipity finite element with 8 nodes by considering shearing strain of plate. The solutions of this paper are compared with existing solutions and finite element solutions with 4${\times}$4 meshes of this analysis are shown the error of maximum 0.083% about the existing solutions. It is shown that natrural frequencies depend on not only Winkler foundation parameter but also shear foundation parameter.

• Advances in nano research
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• 제4권4호
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• pp.309-326
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• 2016

The buckling response of a single-layered graphene sheet (SLGS) embedded in visco-Pasternak's medium is presented. The nonlocal first-order shear deformation elasticity theory is used for this purpose. The visco-Pasternak's medium is considered by adding the damping effect to the usual foundation model which characterized by the linear Winkler's modulus and Pasternak's (shear) foundation modulus. The SLGS be subjected to distributive compressive in-plane edge forces per unit length. The governing equilibrium equations are obtained and solved for getting the critical buckling loads of simply-supported SLGSs. The effects of many parameters like nonlocal parameter, aspect ratio, Winkler-Pasternak's foundation, damping coefficient, and mode numbers on the buckling analysis of the SLGSs are investigated in detail. The present results are compared with the corresponding available in the literature. Additional results are tabulated and plotted for sensing the effect of all used parameters and to investigate the visco-Pasternak's parameters for future comparisons.

• Computers and Concrete
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• 제34권3호
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• pp.297-305
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• 2024

This study investigates the buckling behavior of CNTRC beams on a Winkler-Pasternak elastic foundation, considering their stiffness. To achieve the highest accuracy, the shear stiffness is taken into account based on the Higher-order Shear Deformation Theory (HSDT). A novel exponential power-law distribution of the CNT volume fraction across the beam thickness is employed to model CNTRC beams. Various reinforcement patterns are incorporated into the polymer matrix, featuring single-walled carbon nanotubes (SWCNT) that are both aligned and distributed. The effective mechanical properties of the CNTRC beam are predicted using the rule of mixtures. Hamilton's principle is applied to derive the differential equations of motion. This theoretical framework enables the validation of the approach by comparing numerical simulation results with previous studies. The impact of the exponent order (n), CNT volume fraction, geometrical ratio, and Winkler-Pasternak parameters on buckling analysis is thoroughly presented and discussed. The results indicate that, among the different types of analyzed CNTRC beams, the X-Beam pattern demonstrates the highest buckling load capacity.

• Coupled systems mechanics
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• 제9권6호
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• pp.499-519
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• 2020

The effect of porosity on the thermo-mechanical behavior of simply supported functionally graded plate reposed on the Winkler-Pasternak foundation is investigated analytically in the present paper using new refined hyperbolic shear deformation plate theory. Both even and uneven distribution of porosity are taken into account and the effective properties of FG plates with porosity are defined by theoretical formula with an additional term of porosity. The present formulation is based on a refined higher order shear deformation theory, which is based on four variables and it still accounts for parabolic distribution of the transverse shearing strains and stresses through the thickness of the FG plate and takes into account the various distribution shape of porosity. The elastic foundation is described by the Winkler-Pasternak model. Anew modified power-law formulation is used to describe the material properties of FGM plates in the thickness direction. The closed form solutions are obtained by using Navier technique. The present results are verified in comparison with the published ones in the literature. The results show that the dimensionless and stresses are affected by the porosity volume fraction, constituent volume fraction, and thermal load.

• Steel and Composite Structures
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• 제44권3호
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• pp.353-369
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• 2022

This study attempts to shed light on the coupled impact of types of loading, thickness stretching, and types of variation of Winkler-Pasternak foundations on the flexural behavior of simply- supported FG plates according to the new quasi-3D high order shear deformation theory, including integral terms. A new function sheep is used in the present work. In particular, both Winkler and Pasternak layers are non-uniform and vary along the plate length direction. In addition, the interaction between the loading type and the variation of Winkler-Pasternak foundation parameters is considered and involved in the governing equilibrium equations. Using the virtual displacement principle and Navier's solution technique, the numerical results of non-dimensional stresses and displacements are computed. Finally, the non-dimensional formulas' results are validated with the existing literature, and excellent agreement is detected between the results. More importantly, several complementary parametric studies with the effect of various geometric and material factors are examined. The present analytical model is suitable for investigating the bending of simply-supported FGM plates for special technical engineering applications.

• 한국소음진동공학회논문집
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• 제13권4호
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• pp.281-289
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• 2003

Recently, as high-rise buildings increase steeply, sub-structures of them are often supported on in-homogeneous foundation. And there are many machines in sub-structures of buildings, and slabs of sub-structures are affected by vibration which they make. This paper deals with vibration of plates with concentrated masses on in-homogeneous foundation. Machines on plates are considered as concentrated masses. In-homogeneous foundation is considered as assigning $k_{w1}$ and $k_{w2}$ to Winkler foundation parameters of central region and side region of plate respectively, and foundation is idealized to use Pasternak foundation model which considered both of Winkler foundation parameter and shear foundation parameter. In this paper, applying Winkler foundation parameters which $k_{w1}$and $k_{w2}$ are 10, $10^2$, $10^3$ and shear foundation parameter which are 10, 20 respectively, first natural frequencies of thick plates with concentrated masses on in-homogeneous foundations are calculated.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2005년도 춘계학술대회논문집
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• pp.711-714
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• 2005

This paper is for the vibration analysis of thick plate with concentrated mass on a inhomogeneous pasternak foundation. the thick rectangular plate resting on a inhomogeneous pasternak foundation is isotropic, homogeneous and composite with linearly elastic material. In order to analyize plat which is supported on inhomogeneous pasternak foundation, the value of winkler foundation parameter(WFP) of centural and border zone of plate are chosen as Kw1 and Kw2 respectively. The value of Kw1 and Kw2 can be changed as 0, 10, $10^2,\;10^3$ and the value of SFP(shear foundation parameter) also be changed 0, 5, 10, 15 respectively. Finally, In this paper, vibration of retangular plate on the inhomogeneous pasternak foundation, natural frequency of this plate with Concentrated Mass are calculated