• Structural Engineering and Mechanics
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• 제45권2호
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• pp.169-182
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• 2013

The mechanical behavior of rectangular foundation plates with perimetric beams and internal stiffening beams of the plate is herein analyzed, taking the foundation design into account. A series of dimensionless parameters related to the geometry of the studied elements were defined. In order to generalize the problem statement, an initial settlements was considered. A numeric procedure was developed for the resolution by means of the Finite Differences Method that takes into account the stiffness of the plate, the perimetric and internal plate beams and the soil reaction module. Iterative algorithms were employed which, for each of the analyzed cases, made it possible to find displacements and reaction percentages taken by the plate and those that discharge directly into the perimetric beams, practically without affecting the plate. To enhance its mechanical behavior the internal stiffening beams were prestressed and the results obtained with and without prestressing were compared. This analysis was made considering the load conditions and the soil reaction module constant.

• Structural Engineering and Mechanics
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• 제27권2호
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• pp.199-222
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• 2007

Composite laminated structures supported on elastic foundations are being increasingly used in a great variety of engineering applications. Composites exhibit larger dispersion in their material properties compared to the conventional materials due to large number of parameters associated with their manufacturing and fabrication processes. And also the dispersion in elastic foundation stiffness parameter is inherent due to inaccurate modeling and determination of elastic foundation properties in practice. For a better modeling of the material properties and foundation, these are treated as random variables. This paper deals with effects of randomness in material properties and foundation stiffness parameters on the free vibration response of laminated composite plate resting on an elastic foundation. A $C^0$ finite element method has been used for arriving at an eigen value problem. Higher order shear deformation theory has been used to model the displacement field. A mean centered first order perturbation technique has been employed to handle randomness in system properties for obtaining the stochastic characteristic of frequency response. It is observed that small amount of variations in random material properties and foundation stiffness parameters significantly affect the free vibration response of the laminated composite plate. The results have been compared with those available in the literature and an independent Monte Carlo simulation.

• 한국소음진동공학회논문집
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• 제15권4호
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• pp.388-394
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• 2005

This paper has the object of investigating natural frequencies of tapered thick plate on Pasternak foundation by means of finite element method and providing kinetic design data for mat of building structures. Vibration analysis for tapered thick plate subjected to in-plane stress is presented in this paper. Finite element analysis of rectangular plate is done by use of rectangular finite element with 8-nodes. Analysis conditions of tapered thick plate are as follows each. The ratio of in-plane stress to critical load is varied with $0.2\sigma_{cr}$, $0.4\sigma_{cr}$, $0.6\sigma_{cr}$. The Winkler parameter is 0, 10, 100, 1000, the shear foundation parameter is 0, 10 and the taper ratio is 0.0, 0.2, 0.4, 0.6, 0.8.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2004년도 추계학술대회논문집
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• pp.521-525
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• 2004

This paper has the object of investigating natural frequencies of tapered thick plate on pasternak foundation by means of finite element method and providing kinetic design data for mat of building structures. vibration analysis that tapered thick plate subjected to In-plane stress is presented in this paper Finite element analysis of rectangular plate is done by use of rectangular finite element with 8-nodes. In order to analysis tapered plate which is supported on pasternak foundation. The ratio of In-plane stress to critical load is varied with $0.2\sigma_{cr},\;0.4\sigma_{cr},\;0.6\sigma_{cr}$, and the Winkler parameter is 0, 10, 100, 1000 the shear foundation parameter 0, 10. The taper ratio is applied as 0.0, 0.2, 0.4, 0.6, 0.8 respectively. This paper is analyzed varying thickness by taper ratio with In-plane stress.

• Geomechanics and Engineering
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• 제32권6호
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• pp.553-566
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• 2023

A circular tank foundation resting on the ground and subjected to axisymmetric horizontal and vertical loads and moments is analyzed using the variational principles of mechanics. The circular foundation is assumed to behave as a Kirchhoff plate with in-plane and transverse displacements. The soil beneath the foundation is assumed to be a multi-layered continuum in which the horizontal and vertical displacements are expressed as products of separable functions. The differential equations of plate and soil displacements are obtained by minimizing the total potential energy of the plate-soil system and are solved using the finite element and finite difference methods following an iterative algorithm. Comparisons with the results of equivalent two-dimensional finite element analysis and other researchers establish the accuracy of the method.

• 한국농공학회지
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• 제34권1호
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• pp.49-56
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• 1992

This study was carried out to investigate the mechanical behaviour of the plate on a Winkler's foundation according to the soil-structures relative stiffness and the applicability of the conventional analysis method. For the above purpose, Winkler's constant of 4, 15, 25 and 100kg/$cm^2$/cm was considered and the plate thickness of 20, 30, 50, 100 and 150cm was adopted. Results obtained from the numerical examples are summarized as follow: 1. The effects of elastic foundation is considerable for plates with small flexural rigidity. 2. As the Winkler's constant increases, the bending moment in the plate becomes localized near the loading point. 3. The stresses evaluated by the conventional method not correct even for rigid ground such as rock. 4. If the relative stiffness of the plate is very large, for example the plate thickness is larger than 100cm, the conventional analysis method can be justified for the design purposes. 5. On assumption the flexural rigidity of the plate is infinite, the interaction of soil and plate can be ignored in design consideration. The numerical examples in this paper show that when the plate thickness is more than 100cm, the effects of elastic foundation almost disappear. In practical design, soil-plate interaction should be taken into account, because the 100cm-thickness of the plate will not be practical value in usual sites.

• Structural Engineering and Mechanics
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• 제4권2호
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• pp.149-162
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• 1996

A postbuckling analysis is presented for a simply supported, moderately thick rectangular plate subjected to combined axial compression and uniform temperature loading and resting on a two-parameter elastic foundation. The two cases of thermal postbuckling of initially compressed plates and of compressive postbuckling of initially heated plates are considered. The initial geometrical imperfection of the plate is taken into account. The formulations are based on the Reissner-Mindlin plate theory considering the first order shear deformation effect, and including the plate-foundation interaction and thermal effect. The analysis uses a deflection-type perturbation technique to determine the buckling loads and postbuckling equilibrium paths. Numerical examples cover the performances of perfect and imperfect, moderately thick plates resting on Winkler or Pasternak-type elastic foundations. Typical results are presented in dimensionless graphical form.

• Coupled systems mechanics
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• 제11권4호
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• pp.357-371
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• 2022

This paper presents a parametric study on the free vibration analysis of a functionally graded material (FGM) circular plate with non-uniform thickness resting on a variable Pasternak elastic foundation. The mechanical properties of the material vary in the transverse direction through the thickness of the plate according to the power-law distribution to represent the constituent components. The equation of motion of the circular plate has been carried out based on the classical plate theory (CPT), and the differential quadrature method (DQM) is employed to solve the governing equations as a semi-analytical method. The grid points are chosen based on Chebyshev-Gauss-Lobatto distribution to achieve acceptable convergence and better accuracy. The influence of geometric parameters, variable elastic foundation, and functionally graded variation for clamped and simply supported boundary conditions on the first three natural frequencies are investigated. Comparisons of results with similar studies in the literature have been presented and two-dimensional mode shapes for particular plates have been plotted to illustrate the effect of variable thickness profile.

• Interaction and multiscale mechanics
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• 제5권1호
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• pp.13-26
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• 2012

In this paper, the wave propagation in a generalized thermo elastic plate embedded in an elastic medium (Winkler model) is studied based on the Lord-Schulman (LS) and Green-Lindsay (GL) generalized two dimensional theory of thermo elasticity. Two displacement potential functions are introduced to uncouple the equations of motion. The frequency equations that include the interaction between the plate and foundation are obtained by the traction free boundary conditions using the Bessel function solutions. The numerical calculations are carried out for the material Zinc and the computed non-dimensional frequency and attenuation coefficient are plotted as the dispersion curves for the plate with thermally insulated and isothermal boundaries. The wave characteristics are found to be more stable and realistic in the presence of thermal relaxation times and the foundation parameter. A comparison of the results for the case with no thermal effects shows well agreement with those by the membrane theory.

• Structural Engineering and Mechanics
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• 제34권1호
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• pp.135-138
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• 2010