• 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.

• Geomechanics and Engineering
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• v.6 no.6
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• pp.561-575
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• 2014

Estimating seismic displacements has a great importance for foundations on or adjacent to slope surfaces. However, dynamic solution of the problem has received little attention by previous researchers. This paper presents a new analytical model to determine seismic displacements of the shallow foundations adjacent to slopes. For this purpose, a dynamic equilibrium equation is written for the foundation with failure wedge. Stiffness and damping at the sliding surface are considered variable and a simple method is proposed for its estimation. Finally, for different failure surfaces, the calculated dynamic displacement and the surfaces with maximum strain are selected as the critical failure surface. Analysis results are presented as curves for different slope angles and different foundation distances from edge of the slope and are then compared with the experimental studies and software results. The comparison shows that the proposed model is capable of estimating seismic displacement of the shallow foundations adjacent to slopes. Also, the results demonstrate that, with increased slope angle and decreased foundation distances from the slope edge, seismic displacement increases in a non-linear trend. With increasing the slope angle and failure wedge angle, maximum strain of failure wedge increases. In addition, effect of slope on foundation settlement could be neglected for the foundation distances over 3B to 5B.

• Journal of applied mathematics & informatics
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• v.41 no.5
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• pp.1071-1084
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• 2023

We consider inviscid, incompressible homogeneous shear flows of variable cross section known as extended Rayleigh problem. For this extended Rayleigh problem, we derived instability region which intersect with semi-circle instability region under some condition. Also we derived condition for stability, upper bound for amplification factor and growth rate of an unstable mode.

• Geomechanics and Engineering
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• v.22 no.4
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• pp.361-374
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• 2020

This paper is concerned with the thermoelastic bending of FG beams resting on two-layer elastic foundations. One of these layers is Winkler springs with a variable modulus while the other is considered as a shear layer with a constant modulus. The beams are considered simply supported and subjected to thermo-mechanical loading. Temperature-dependent material properties are considered for the FG beams, which are assumed to be graded continuously across the panel thickness. The used theories contain undetermined integral terms which lead to a reduction of unknowns functions. Several micromechanical models are used to estimate the effective two-phase FG material properties as a function of the particles' volume fraction considering thermal effects. Analytical solutions for the thermo-mechanical bending analysis are obtained based on Navier's method that satisfies the boundary conditions. Finally, the numerical results are provided to reveal the effect of explicit micromechanical models, geometric parameters, temperature distribution and elastic foundation parameters on the thermoelastic response of FG beams.

• Earthquakes and Structures
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• v.17 no.5
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• pp.447-462
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• 2019

This present paper concerned with the analytic modelling for vibration of the functionally graded (FG) plates resting on non-variable and variable two parameter elastic foundation, based on two-dimensional elasticity using higher shear deformation theory. Our present theory has four unknown, which mean that have less than other higher order and lower theory, and we denote do not require the factor of correction like the first shear deformation theory. The indeterminate integral are introduced in the fields of displacement, it is allowed to reduce the number from five unknown to only four variables. The elastic foundations are assumed a classical model of Winkler-Pasternak with uniform distribution stiffness of the Winkler coefficient (kw), or it is with variables distribution coefficient (kw). The variable's stiffness of elastic foundation is supposed linear, parabolic and trigonometry along the length of functionally plate. The properties of the FG plates vary according to the thickness, following a simple distribution of the power law in terms of volume fractions of the constituents of the material. The equations of motions for natural frequency of the functionally graded plates resting on variables elastic foundation are derived using Hamilton principal. The government equations are resolved, with respect boundary condition for simply supported FG plate, employing Navier series solution. The extensive validation with other works found in the literature and our results are present in this work to demonstrate the efficient and accuracy of this analytic model to predict free vibration of FG plates, with and without the effect of variables elastic foundations.

• Geotechnical Engineering
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• v.9 no.3
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• pp.77-90
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• 1993

In the settlement analysis of shallow foundation soil properties, loads and soil strata involve many uncertainties so it is necessary to do analysis of settlement that considers the probabilistic properties of each variable. This study is performed to probabilistic analysis for settlement of shallow foundation consisted of individual footings by using Monte Carlo Method. To consider the uncertainty of variables, both the soil properties and loads are assumed to be normal distribution random variables and get settlement mean and coefficient of variation of individual footing. And the settlement of each individual footing is also assumed to be normal distribution. Settlement of each individual footing which considers the probability of soft soil pockets in soil strata follows Markov process. Then it is performed to do sensitivity analysis which is involved to excess probability of allowable criteria of maxi mum settlement and differential settlement according to varity of each variable. It is thought to be proper that the settlement analysis of shallow foundation should be analyzed considering uncertainty of variables and soil stratum conditions.

• Journal of computational fluids engineering
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• v.8 no.1
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• pp.30-37
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• 2003

The post-processor for two-dimensional flow visualization has been developed by using OOP(object-oriented programming) of Visual C++. User-friendly GUI(graphic user interface) has been built on the base of MFC(Microsoft Foundation Class). The number and order of variables can be specified by user because the input style is the free-format. The new variable can be defined and added to the variable list by using the various operators and functions.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.16 no.6 s.111
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• pp.609-618
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• 2006

This study is undertaken for the vibration analysis of tapered thick plate with concentrated mass on elastic foundation. The boundary condition of the plate is analyzed with the 4-sides simply supported and 4-fixed basis. This study find out the frequency following the change in size for each foundational variable on Pasternak foundation, one of the two-parameter elastic foundation parameter that considered the shear layer to the Winkler foundation parameter. The concentrated mass is applied with the consideration of mass of the entire plate, and the change of frequency is studies on each location with the consideration of reacting for the three locations for concentrated mass. And, in order to find out the change of frequency on the thickness of the plate, it considered tapered ratio that linearly changes depending on the length of the plate with the thickness of the plate in x-direction, and the tapered ratio has changes with 4 types ($\alpha$=0.25, 0, 5, 0.75, and 1.0). For the interpretation, the program using finite element method (F.E.M.) is used and the element coordination is used the 8-node serendipity element. Therefore, the purpose of this study is to find out the characteristics of plate vibration under the mechanica vibration or external vibration factor to facilitate as the basic data of the design to secure the stability.

• Geomechanics and Engineering
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• v.11 no.6
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• pp.805-820
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• 2016

A fully coupled non-linear effective stress response finite difference (FD) model is built to survey the counter-intuitive recent findings on the reliance of pore water pressure ratio on foundation contact pressure. Two alternative design scenarios for a benchmark problem are explored and contrasted in the light of construction emission rates using the EFFC-DFI methodology. A strain-hardening effective stress plasticity model is adopted to simulate the dynamic loading. A combination of input motions, contact pressure, initial vertical total pressure and distance to foundation centreline are employed, as model variables, to further investigate the control of permanent and variable actions on the residual pore pressure ratio. The model is verified against the Ghosh and Madabhushi high acceleration field test database. The outputs of this work are aimed to improve the current computer-aided seismic foundation design that relies on ground's packing state and consistency. The results confirm that on seismic excitation of shallow foundations, the likelihood of effective stress loss is greater in deeper depths and across free field. For the benchmark problem, adopting a shallow foundation system instead of piled foundation benefitted in a 75% less emission rate, a marked proportion of which is owed to reduced materials and haulage carbon cost.

• Journal of Power Electronics
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• v.14 no.1
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• pp.156-164
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• 2014

The power-voltage (P-V) characteristic of a photovoltaic (PV) array is nonlinear and time varying with the change in atmospheric conditions. As a result, the maximum power point tracking (MPPT) technique must be applied in PV systems to maximize the generated energy. The incremental conductance (INC) algorithm, one of the MPPT strategies, is widely used for its high tracking accuracy, good adaptability to rapidly changing atmospheric conditions, and easy implementation. This paper presents a modified asymmetrical variable step size INC MPPT method that is based on the asymmetrical feature of the P-V curve. Compared with conventional fixed or variable step size method, the proposed method can effectively improve tracking accuracy and speed. The theoretical foundation and design principle of the proposed approach are validated by the simulation and experimental results.