• 한국소음진동공학회논문집
• /
• 제13권12호
• /
• pp.947-955
• /
• 2003

This research analyzes the dynamic stability of stiffened plates on elastic foundations using the finite element method. For analyzing the stiffened plates, both the Mindlin plate theory and Timoshenko beam-column theory were applied. In application of the finite element method, 8-nodes serendipity element system and 3-nodes finite element system were used for plate and beam elements, respectively Elastic foundations were modeled as the Pasternak foundations in which the continuity effect of foundation is considered. In order to verify the theory of this study, solutions obtained by this analysis were compared with the classical solutions in open literature and experimental solutions. The dynamic stability legions of stiffened plates on Pasternak foundations were determined according to changes of in-plane stresses, foundation parameters and dimensions of stiffener.

• Steel and Composite Structures
• /
• 제27권2호
• /
• pp.177-184
• /
• 2018

This study contributes to evaluate multiphase topology optimization design of plate-like structures on elastic foundations by using classic plate theory. Multi-material optimal topology and shape are produced as an alternative to provide reasonable material assignments based on stress distributions. Multi-material topology optimization problem is solved through an alternative active-phase algorithm with Gauss-Seidel version as an optimization model of optimality criteria. Stiffness and adjoint sensitivity formulations linked to thin plate potential strain energy are derived in terms of multiphase design variables and Winkler-Pasternak parameters considering elastic foundation to apply to the current topology optimization. Numerical examples verify efficiency and diversity of the present topology optimization method of elastic thin plates depending on multiple materials and Winkler-Pasternak parameters with the same amount of volume fraction and total structural volume.

• 한국전산구조공학회논문집
• /
• 제18권2호
• /
• pp.151-158
• /
• 2005

본 연구에서는 유한요소법을 이용하여 Pasternak 지반 위에 놓인 보강판의 고유치해석을 수행하였다. 보강판 해석은 Mindlin 판 이론과 Timoshenko 보-기둥 이론을 적용하여 해석하였으며, 유한요소법 적용시 판요소는 8절점 Serendipity 요소계를, 보요소는 3절점 유한요소를 적용하였다. 탄성지반은 지반의 연속성을 고려한 Pasternak 지반으로 모형화하였다. 본 연구의 타당성을 검증하기 위하여 이 연구의 결과를 문헌, 실험 및 SAP 2000의 결과와 비교하였다. 이 연구의 결과로 문헌 해가 존재하지 않는 Pasternak 지반 위에 놓인 보강판의 지반 변수의 변화 및 보강재 크기에 따른 고유진동수를 산정하였다.

• Geomechanics and Engineering
• /
• 제2권1호
• /
• pp.45-56
• /
• 2010

The current study presents a mathematical model and numerical method for free vibration of tapered piles embedded in two-parameter elastic foundations. The method of Discrete Singular Convolution (DSC) is used for numerical simulation. Bernoulli-Euler beam theory is considered. Various numerical applications demonstrate the validity and applicability of the proposed method for free vibration analysis. The results prove that the proposed method is quite easy to implement, accurate and highly efficient for free vibration analysis of tapered beam-columns embedded in Winkler- Pasternak elastic foundations.

• Steel and Composite Structures
• /
• 제14권1호
• /
• pp.85-104
• /
• 2013

The present work deals with the thermomechanical bending response of functionally graded plates resting on Winkler-Pasternak elastic foundations. Theoretical formulations are based on a recently developed refined trigonometric shear deformation theory (RTSDT). The theory accounts for trigonometric distribution of transverse shear stress, and satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate without using shear correction factor. Unlike the conventional trigonometric shear deformation theory, the present refined trigonometric shear deformation theory contains only four unknowns as against five in case of other shear deformation theories. The material properties of the functionally graded plates are assumed to vary continuously through the thickness, according to a simple power law distribution of the volume fraction of the constituents. The elastic foundation is modelled as two-parameter Pasternak foundation. The results of the shear deformation theories are compared together. Numerical examples cover the effects of the gradient index, plate aspect ratio, side-to-thickness ratio and elastic foundation parameters on the thermomechanical behavior of functionally graded plates. It can be concluded that the proposed theory is accurate and efficient in predicting the thermomechanical bending response of functionally graded plates.

• 한국전산구조공학회논문집
• /
• 제15권2호
• /
• pp.367-377
• /
• 2002

이 논문은 탄성지반 위에 놓인 낮은 아치의 자유진동에 관한 연구이다. Pasternak가 제안한 두 개의 매개변수로 표현되는 지반모형을 채택하여 대상아치의 자유진동을 지배하는 미분방정식을 유도하였다. 양단회전 및 양단고정의 단부 조건을 갖는 두 종류의 아치선형을 유도된 지배방정식에 적용하여 Galerkin method로 해석함으로써 최저차 대칭 및 역대칭 고유진동수 방정식을 산출하였다 아치높이, Winkler지반계수 및 전단지반계수가 고유진동수에 미치는 영향을 분석하였으며, 아치선형이 고유진동수에 미치는 영향을 분석하였다.

• Geomechanics and Engineering
• /
• 제31권1호
• /
• pp.99-112
• /
• 2022

The present study examines the natural frequencies (NFs) of perfect/imperfect functionally graded sandwich beams (P/IP-FGSBs), which are composed of a porous core constructed of functionally graded materials (FGMs) and a homogenous isotropic metal and ceramic face sheets resting on elastic foundations. To accomplish this, the material properties of the FGSBs are assumed to vary continuously along the thickness direction as a function of the volume fraction of constituents expressed by the modified rule of the mixture, which includes porosity volume fraction represented using four distinct types of porosity distribution models. Additionally, to characterize the reaction of the two-parameter elastic foundation to the Perfect/Imperfect (P/IP) FGSBs, the medium is assumed to be linear, homogeneous, and isotropic, and it is described using the Winkler-Pasternak model. Furthermore, the kinematic relationship of the P/IP-FGSBs resting on the Winkler-Pasternak elastic foundations (WPEFs) is described using trigonometric shear deformation theory (TrSDT), and the equations of motion are constructed using Hamilton's principle. A closed-form solution is developed for the free vibration analysis of P/IP-FGSBs resting on the WPEFs under four distinct boundary conditions (BCs). To validate the new formulation, extensive comparisons with existing data are made. A detailed investigation is carried out for the effects of the foundation coefficients, mode numbers (MNs), porosity volume fraction, power-law index, span to depth ratio, porosity distribution patterns (PDPs), skin core skin thickness ratios (SCSTR), and BCs on the values of the NFs of the P/IP-FGSBs.

• 한국소음진동공학회논문집
• /
• 제22권8호
• /
• pp.763-770
• /
• 2012

The free vibration characteristics of fluid-filled cylindrical shells on partial elastic foundations are investigated by an analytical method. The cylindrical shell is fully or partially surrounded by the elastic foundations, these are represented by the Winkler or Pasternak model. The motion of shell is represented by the first order shear deformation theory to account for rotary inertia and transverse shear strains. The steady flow of fluid is described by the classical potential flow theory. The fluid-structure interaction is considered in the analysis. The effect of internal fluid can be considered by imposing a relation between the fluid pressure and the radial displacement of the structure at the interface. To validate the present method, the numerical example is presented and compared with the available existing results.

• Geomechanics and Engineering
• /
• 제36권2호
• /
• pp.183-204
• /
• 2024

In current investigation, a novel beam finite element model is formulated to analyze the buckling and free vibration responses of functionally graded porous beams resting on Winkler-Pasternak elastic foundations. The novelty lies in the formulation of a simplified finite element model with only three degrees of freedom per node, integrating both C⁰ and C¹ continuity requirements according to Lagrange and Hermite interpolations, respectively, in isoparametric coordinate while emphasizing the impact of z-coordinate-dependent porosity on vibration and buckling responses. The proposed model has been validated and demonstrating high accuracy when compared to previously published solutions. A detailed parametric examination is performed, highlighting the influence of porosity distribution, foundation parameters, slenderness ratio, and boundary conditions. Unlike existing numerical techniques, the proposed element achieves a high rate of convergence with reduced computational complexity. Additionally, the model's adaptability to various mechanical problems and structural geometries is showcased through the numerical evaluation of elastic foundations, with results in strong agreement with the theoretical formulation. In light of the findings, porosity significantly affects the mechanical integrity of FGP beams on elastic foundations, with the advanced beam element offering a stable, efficient model for future research and this in-depth investigation enriches porous structure simulations in a field with limited current research, necessitating additional exploration and investigation.

• Structural Engineering and Mechanics
• /
• 제83권6호
• /
• pp.771-788
• /
• 2022

This research investigates the free vibration of porous advanced composite plates resting on Winkler/Pasternak/ Kerr foundations by using a new hyperbolic quasi three dimensional (quasi-3D) shear deformation theory. The present theory, which does not require shear correction factor, accounts for shear deformation and thickness stretching effects by parabolic variation of all displacements across the thickness, and satisfies the stress-free boundary conditions on the upper and lower surfaces of the plate. In this work, we consider imperfect FG plates with porosities embedded within elastic Winkler, Pasternak or Kerr foundations. Implementing an analytical approach, the obtained governing equations from Hamilton's principle according to FG plates are derived. The closed form solutions are obtained by using Navier technique, and natural frequencies of FG plates are found, for simply supported plates, by solving the results of eigenvalue problems. A comprehensive parametric study is presented to evaluate effects of the geometry of material, mode numbers, porosity volume fraction, Power-law index and stiffness of foundations parameters on free vibration characteristics of FG plates.