• Advances in materials Research
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• v.9 no.1
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• pp.33-48
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• 2020

With the use of differential quadrature method (DQM), forced vibrations and resonance frequency analysis of functionally graded (FG) nano-size beams rested on elastic substrate have been studied utilizing a shear deformation refined beam theory which contains shear deformations influence needless of any correction coefficient. The nano-size beam is exposed to uniformly-type dynamical loads having partial length. The two parameters elastic substrate is consist of linear springs as well as shear coefficient. Gradation of each material property for nano-size beam has been defined in the context of Mori-Tanaka scheme. Governing equations for embedded refined FG nano-size beams exposed to dynamical load have been achieved by utilizing Eringen's nonlocal differential law and Hamilton's rule. Derived equations have solved via DQM based on simply supported-simply supported edge condition. It will be shown that forced vibrations properties and resonance frequency of embedded FG nano-size beam are prominently affected by material gradation, nonlocal field, substrate coefficients and load factors.

• Structural Engineering and Mechanics
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• v.7 no.3
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• pp.259-276
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• 1999

An analytical solution for the shape functions of a beam segment supported on a generalized two-parameter elastic foundation is derived. The solution is general, and is not restricted to a particular range of magnitudes of the foundation parameters. The exact shape functions can be utilized to derive exact analytic expressions for the coefficients of the element stiffness matrix, work equivalent nodal forces for arbitrary transverse loads and coefficients of the consistent mass and geometrical stiffness matrices. As illustration, each distinct coefficient of the element stiffness matrix is compared with its conventional counterpart for a beam segment supported by no foundation at all for the entire range of foundation parameters.

• Structural Engineering and Mechanics
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• v.81 no.1
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• pp.29-37
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• 2022

The present paper deals with the application of one dimensional piezoelectric materials in particular piezo-thermoelastic nanobeam. The generalized piezo-thermo-elastic theory with two temperature and Euler Bernoulli theory with small scale effects using nonlocal Eringen's theory have been used to form the mathematical model. The ends of nanobeam are considered to be simply supported and at a constant temperature. The mathematical model so formed is solved to obtain the non-dimensional expressions for lateral deflection, electric potential, thermal moment, thermoelastic damping and frequency shift. Effect of frequency and nonlocal parameter on the lateral deflection, electric potential, thermal moment with generalized piezothermoelastic theory are represented graphically using the MATLAB software. Comparisons are made with the different theories of thermoelasticity.

• Structural Engineering and Mechanics
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• v.70 no.6
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• pp.711-722
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• 2019

Considering stress singularities at point support locations, buckling solutions for plates with arbitrary number of point supports are hard to obtain. Thus, new Hp-Cloud shape functions with Kronecker delta property (HPCK) were developed in the present paper to examine elastic buckling of point-supported thin plates in various shapes. Having the Kronecker delta property, this specific Hp-Cloud shape functions were constructed through selecting particular quantities for influence radii of nodal points as well as proposing appropriate enrichment functions. Since the given quantities for influence radii of nodal points could bring about poor quality of interpolation for plates with sharp corners, the radii were increased and the method of Lagrange multiplier was used for the purpose of applying boundary conditions. To demonstrate the capability of the new Hp-Cloud shape functions in the domain of analyzing plates in different geometry shapes, various test cases were correspondingly investigated and the obtained findings were compared with those available in the related literature. Such results concerning these new Hp-Cloud shape functions revealed a significant consistency with those reported by other researchers.

• Magazine of the Korean Society of Agricultural Engineers
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• v.24 no.3
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• pp.73-83
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• 1982

study aims to derive a rational method for the analysis of the farm silo supported on an elastic foundation in which it is assumed that the reaction pressure of the soil at a point is proportional to the deflection at that point. In order to investigate the effects of an elastic foundation on the behaviour of the structures on it, the analysis of the farm silo resting on an elastic foundation was compared with the solution that the ground support may be assumed uniform (which was obtained from part I of this paper). To calculate the deformation of an elastic foundation, Boussinesq's solution which allows an interaction of the various parts of ground was adopted. In this case, the foundation was treated as a superparametric element additionally. In the evaluation of an element stiffness matrix, Gauss quadrature' was used. In above numerical integration, 3-point rule for the farm silo wall and the footing was introduced and 2-point rule for the evaluation of a reaction between the footing and the elastic foundation was adopted. The stresses of a farm silo on an elastic foundation were smaller than those which the distribution of contact pressure between the footing and the soil is assumed uniformly. Since the differences of stresses were remarkable in PS structures than RC structures, it is desirable that designers take into account the effect of an elastic foundation for the case of PS structures. It can be noted that while the effect of an elastic foundation was more conspicuously observed in near of the ground, the value of stresses at far from the soil was little affected by an supported soil.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2005.06a
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• pp.1695-1698
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• 2005

In this paper we investigate characteristics of deflection for circular plate with the non-symmetric boundary condition that is the boundary condition partly supported along the width direction of plate according to the length change of supporting end. For two boundary conditions such as simple supported and completely clamped boundary conditions, this study derives the maximum deflection formula of the circular plate using differential equation of elastic curve, assuming that a circular plate is a beam with the change of width and thickness along the longitudinal direction. The deflection formula of circular plate is verified by carrying out finite element analysis with regard to the ratio of length of supporting end to radius of circular plate.

• Structural Engineering and Mechanics
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• v.66 no.6
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• pp.729-736
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• 2018

This paper studies thermal buckling and post-buckling behaviors of functionally graded materials (FGM) tubes subjected to a uniform temperature rise and resting on elastic foundations via a refined beam model. Compared to the Timoshenko beam theory, the number of unknowns of this model are the same and no correction factors are required. The material properties of the FGM tube vary continuously in the radial direction according to a power function. Two ends of the tube are assumed to be simply supported and in-plane boundary conditions are immovable. Energy variation principle is employed to establish the governing equations. A two-step perturbation method is adopted to determine the critical thermal buckling loads and post-buckling paths of the tubes with arbitrary radial non-homogeneity. Through detailed parametric studies, it can be found that the tube has much higher buckling temperature and post-buckling strength when it is supported by an elastic foundation.

• Structural Engineering and Mechanics
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• v.57 no.4
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• pp.617-639
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• 2016

In this work, an analytical formulation based on both hyperbolic shear deformation theory and stress function, is presented to study the nonlinear post-buckling response of symmetric functionally graded plates supported by elastic foundations and subjected to in-plane compressive, thermal and thermo-mechanical loads. Elastic properties of material are based on sigmoid power law and varying across the thickness of the plate (S-FGM). In the present formulation, Von Karman nonlinearity and initial geometrical imperfection of plate are also taken into account. By utilizing Galerkin procedure, closed-form expressions of buckling loads and post-buckling equilibrium paths for simply supported plates are obtained. The effects of different parameters such as material and geometrical characteristics, temperature, boundary conditions, foundation stiffness and imperfection on the mechanical and thermal buckling and post-buckling loading capacity of the S-FGM plates are investigated.

• Structural Engineering and Mechanics
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• v.83 no.4
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• pp.451-463
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• 2022

The present study deals with forced vibrations of an elastic circular plate supported along its circular edge by unilateral elastic springs. The plate is assumed to be subjected to a uniformly distributed and a concentrated load. Under the combination of these loads, equations of motion are explicitly derived for static and dynamic response analyses by assuming a series of the displacement functions of time and other unknown parameters which are to be determined by employing Lagrangian functional. The approximate solution is sought by applying the Lagrange equations of motions by using the potential energy of the external forces that includes the contributions of the edge forces and the external moments, i.e., those of the effects of the boundary condition to the analysis. For the numerical treatment of the problem in the time domain, the linear acceleration procedure is adopted. The tensionless character of the support is taken into account by using an iterative process and, the coordinate functions for the displacement field are selected to partially fulfill the boundary conditions so that an acceptable approximation can be achieved faster. Numerical results are presented in the figures focusing on the nonlinearity of the problem due to the plate lift-off from the unilateral springs at the edge support.

• Structural Engineering and Mechanics
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• v.85 no.6
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• pp.717-728
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• 2023

The effect of temperature dependent material properties on the free vibration of FG porous beams is investigated in the present paper. A quasi-3D shear deformation solution is used involves only three unknown function. The mechanical properties which are considered to be temperature-dependent as well as the porosity distributions are assumed to gradually change along the thickness direction according to defined law. The beam is supposed to be simply supported and lying on variable elastic foundation. The differential equation system governing the free vibration behavior of porous beams is derived based on the Hamilton principle. Navier's method for simply supported systems is then used to determine and compute the frequencies of FG porous beam. The results of the present formulation are validated by comparing with those available literatures. Finally, the effects of several parameters such as porosity distribution and the parameters of variable elastic foundation on the free vibration behavior of temperature-dependent FG beams are presented and discussed in detail.