• Structural Engineering and Mechanics
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• v.10 no.5
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• pp.441-449
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• 2000

In this study, the state equation for axisymmetric bending of laminated transversely isotropic circular plates on elastic foundation is established on the basis of three-dimensional elasticity. By using the expansions of Bessel functions, an analytical solution of the problem is presented. As a result, all the fundamental equations of three-dimensional elasticity can be satisfied exactly and all the independent elastic constants can be fully taken into account. Furthermore, the continuity conditions at the interfaces of plies can also be satisfied.

• Geomechanics and Engineering
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• v.32 no.6
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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.

• Structural Engineering and Mechanics
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• v.59 no.4
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• pp.761-774
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• 2016

Curved beams' dynamic behavior on viscoelastic foundation is the subject of the current paper. By rewritten the Timoshenko beams theory formulation for the curved and twisted spatial rods, governing equations are obtained for the circular beams on viscoelastic foundation. Using the complementary functions method (CFM), in Laplace domain, an ordinary differential equation is solved and then those results are transformed to real space by Durbin's algorithm. Verification of the proposed method is illustrated by solving an example by variating foundation parameters.

• Structural Engineering and Mechanics
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• v.64 no.5
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• pp.591-610
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• 2017

This paper is concerned with the static analysis of variable thickness of two directional functionally graded porous materials (FGPM) circular plate resting on a gradient hybrid foundation (Horvath-Colasanti type) with friction force and subjected to compound mechanical loads (e.g., transverse, in-plane shear traction and concentrated force at the center of the plate).The governing state equations are derived in terms of displacements based on the 3D theory of elasticity, assuming the elastic coefficients of the plate material except the Poisson's ratio varying continuously throughout the thickness and radial directions according to an exponential function. These equations are solved semi-analytically by employing the state space method (SSM) and one-dimensional differential quadrature (DQ) rule to obtain the displacements and stress components of the FGPM plate. The effect of concentrated force at the center of the plate is approximated with the shear force, uniformly distributed over the inner boundary of a FGPM annular plate. In addition to verification study and convergence analysis, numerical results are displayed to show the effect of material heterogeneity indices, foundation stiffness coefficients, foundation gradient indices, loads ratio, thickness to radius ratio, compressibility, porosity and friction coefficient of the foundation on the static behavior of the plate. Finally, the responses of FG and FG porous material circular plates to compound mechanical loads are compared.

• Computational Structural Engineering
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• v.10 no.1
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• pp.193-200
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• 1997

Even though there are many analysis methods of circular tanks on elastic foundation, the finite element method is widely used for that purpose. But the finite element method requires a number of memory spaces, computation time to solve large stiffness equations. In this study many the simplified methods(Analogy of Beam on Elastic Foundation, Foundation Stiffness Matrix, Finite Element Method and Transfer Matrix Method) are applied to analyze a circular tank on elastic foundation. By the given analysis methods, BEF analogy and foundation matrix method, the circular tank was transformed into the skeletonized frame structure. The frame structure was divided into several finite elements. The stiffness matrix of a finite element is related with the transfer matrix of the element. Thus, the transfer matrix of each finite element utilized the transfer matrix method to simplify the analysis of the tank. There were no significant difference in the results of two methods, the finite element method and the transfer matrix method. The transfer method applied to a circular tank on elastic foundation resulted in four simultaneous equations to solve completely.

• Smart Structures and Systems
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• v.16 no.1
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• pp.81-100
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• 2015

This paper presents nonlinear analysis of an arbitrary functionally graded circular plate integrated with two functionally graded piezoelectric layers resting on the Winkler-Pasternak foundation. Geometric nonlinearity is considered in the strain-displacement relation based on the Von-Karman assumption. All the mechanical and electrical properties except Poisson's ratio can vary continuously along the thickness of the plate based on a power function. Electric potential is assumed as a quadratic function along the thickness direction. After derivation of general nonlinear equations, as an instance, numerical results of a functionally graded material integrated with functionally graded piezoelectric material obeying two different functionalities is investigated. The effect of different parameters such as parameters of foundation, non homogenous index and boundary conditions can be investigated on the mechanical and electrical results of the system. A comprehensive comparison between linear and nonlinear responses of the system presents necessity of this study. Furthermore, the obtained results can be validated by using previous linear and nonlinear analyses after removing the effect of foundation.

• Structural Engineering and Mechanics
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• v.70 no.1
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• pp.97-112
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• 2019

Using the classical, first order and third order shear deformation plates theories the motion equations of an undrained porous FG circular plate which is located on visco-Pasternak elastic foundation have been derived and used for free vibration analysis thereof. Strains are related to displacements by Sanders relationship. Fluid has saturated the pores whose distribution varies through the thickness according to three physically probable given functions. The equations are discretized and numerically solved by the generalized differential quadrature method. The effect of porosity, pores distribution, fluid compressibility, viscoelastic foundation and aspect ratio of the plate on its vibration has been considered.

• Structural Engineering and Mechanics
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• v.15 no.6
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• pp.735-752
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• 2003

The quasi-static and dynamic responses of a linear viscoelastic circular beam on Winkler foundation are studied numerically by using the mixed finite element method in transformed Laplace-Carson space. This element VCR12 has 12 independent variables. The solution is obtained in transformed space and Schapery, Dubner, Durbin and Maximum Degree of Precision (MDOP) transform techniques are employed for numerical inversion. The performance of the method is presented by several quasi-static and dynamic example problems.

• Coupled systems mechanics
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• v.11 no.4
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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.

• Journal of the Korea institute for structural maintenance and inspection
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• v.13 no.1 s.53
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• pp.125-134
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• 2009

This paper deals with the free vibrations of circular strip foundations which have uniform solid rectangular cross-section. The ground which supports circular strips was modeled as the two parameter elastic foundation. Differential equations governing the flexural-torsional free vibrations of circular strips supported by such foundation were derived, and solved numerically for obtaining the natural frequencies and mode shapes. Boundary condition of free-free ends was considered for numerical examples. Four lowest natural frequencies according to the variations of five system parameters i.e. subtended angle, depth ratio, contact ratio, elasticity ratio and soil parameter are reported in the non-dimensional forms. Also, typical mode shapes of both deformations and stress resultants are presented in the figures. Experiment was conducted for validating the theory developed in this study.