• Journal of the Earthquake Engineering Society of Korea
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• v.10 no.4 s.50
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• pp.15-24
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• 2006

This work reports the results of our study on the dynamic response of various buried pipelines depending on their boundary conditions. We have studied behavior of the buried pipelines both along the axial and the transverse direction. The buried pipelines are modeled as beams on elastic foundation while the seismic wave as a ground displacement in the form of a sinusoidal wave. The natural frequency, its mode, and the effect of parameters have been interpreted in terms of free vibration. In order to investigate the response on the ground wave, the resulting frequency and the mode shape obtained from the free vibration have been utilized to derive the mathematical formula for the forced vibration. The natural frequency varies most significantly by the soil stiffness and the length of the buried pipelines in the case of free vibration. The effects of the propagation direction and velocity and the frequency of ground wave on the dynamic responses of concrete, steel, and FRP pipes have been analyzed and then dynamic responses depending on the type of pipes have been compared. Through performing dynamic analyser for various boundary conditions and estimation of the location of maximum strain has been estimated for the type of pipes and boundary conditions.

• Steel and Composite Structures
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• v.18 no.1
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• pp.187-212
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• 2015

In this paper, various four variable refined plate theories are presented to analyze vibration of temperature-dependent functionally graded (FG) plates. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations for the present model is reduced, significantly facilitating engineering analysis. These theories account for parabolic, sinusoidal, hyperbolic, and exponential distributions of the transverse shear strains and satisfy the zero traction boundary conditions on the surfaces of the plate without using shear correction factors. Power law material properties and linear steady-state thermal loads are assumed to be graded along the thickness. Uniform, linear, nonlinear and sinusoidal thermal conditions are imposed at the upper and lower surface for simply supported FG plates. Equations of motion are derived from Hamilton's principle. Analytical solutions for the free vibration analysis are obtained based on Fourier series that satisfy the boundary conditions (Navier's method). Non-dimensional results are compared for temperature-dependent and temperature-independent FG plates and validated with known results in the literature. Numerical investigation is conducted to show the effect of material composition, plate geometry, and temperature fields on the vibration characteristics. It can be concluded that the present theories are not only accurate but also simple in predicting the free vibration responses of temperature-dependent FG plates.

• The Journal of Korea Assosiation for Disability and Oral Health
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• v.5 no.2
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• pp.87-91
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• 2009

The purpose of this study were to investigate the chief complain and dental treatment needs in handicapped patient. This study examines treatment records of 1025 patients in free dental clinic for handicapped patients during 10 years from 1999 to 2008. The results were as follows : 5.8 average visit per patient; mean patient age was 25; 544 patients was younger than 20. Handicapped patients classified according to types of disability. Crippled disorder were 19.1%, brain disorder were 4.5%, visual disorder were 3.1%, auditory disorder were 4.1%, speech disorder were 0.9%, mental retardation were 67.1%, and developmental disorder were 25.1%. Performed treatments were 322 scaling, 13 fluoride varnish, 727 preventive resin restoration, 1296 resin restoration, 600 amalgam restoration, 46 GI restoration, 612 extraction, 289 pulp treatment of primary teeth, 75 pulp treatment of permanent teeth and 138 stainless steel crown restoration. Many handicapped patients have some difficulty to dental treatment. They have limited access to dental care, which is compounded by a shortage of skilled dental professionals who are willing to treat these population and financial problems.

• Steel and Composite Structures
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• v.26 no.4
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• pp.513-531
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• 2018

In this article, static, buckling and free vibration analyses of a sinusoidal micro composite beam reinforced by single-walled carbon nanotubes (SWCNTs) with considering temperature-dependent material properties embedded in an elastic medium in the presence of magnetic field under transverse uniform load are presented. This system is used at micro or sub micro scales to enhance the stiffness of micro composite structures such as bar, beam, plate and shell. In the present work, the size dependent effects based on surface stress effect and modified strain gradient theory (MSGT) are considered. The generalized rule of mixture is employed to predict temperature-dependent mechanical and thermal properties of micro composite beam. Then, the governing equations of motions are derived using Hamilton's principle and energy method. Numerical results are presented to investigate the influences of material length scale parameters, elastic foundation, composite fiber angle, magnetic intensity, temperature changes and carbon nanotubes volume fraction on the bending, buckling and free vibration behaviors of micro composite beam. There is a good agreement between the obtained results by this research and the literature results. The obtained results of this study demonstrate that the magnetic intensity, temperature changes, and two parameters elastic foundations have important effects on micro composite stiffness, while the magnetic field has greater effects on the bending, buckling and free vibration responses of micro composite beams. Moreover, it is shown that the effects of surface layers are important, and observed that the changes of carbon nanotubes volume fraction, beam length-to-thickness ratio and material length scale parameter have noticeable effects on the maximum deflection, critical buckling load and natural frequencies of micro composite beams.

• Steel and Composite Structures
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• v.26 no.4
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• pp.473-484
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• 2018

Free vibration of cross-ply laminated plates using a higher-order shear deformation theory is studied. The arbitrary number of layers is oriented in symmetric and anti-symmetric manners. The plate kinematics are based on higher-order shear deformation theory (HSDT) and the vibrational behaviour of multi-layered plates are analysed under simply supported boundary conditions. The differential equations are obtained in terms of displacement and rotational functions by substituting the stress-strain relations and strain-displacement relations in the governing equations and separable method is adopted for these functions to get a set of ordinary differential equations in term of single variable, which are coupled. These displacement and rotational functions are approximated using cubic and quantic splines which results in to the system of algebraic equations with unknown spline coefficients. Incurring the boundary conditions with the algebraic equations, a generalized eigen value problem is obtained. This eigen value problem is solved numerically to find the eigen frequency parameter and associated eigenvectors which are the spline coefficients.The material properties of Kevlar-49/epoxy, Graphite/Epoxy and E-glass epoxy are used to show the parametric effects of the plates aspect ratio, side-to-thickness ratio, stacking sequence, number of lamina and ply orientations on the frequency parameter of the plate. The current results are verified with those results obtained in the previous work and the new results are presented in tables and graphs.

• Steel and Composite Structures
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• v.20 no.2
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• pp.227-249
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• 2016

The objective of this work is to present a zeroth-order shear deformation theory for free vibration analysis of functionally graded (FG) nanoscale plates resting on elastic foundation. The model takes into consideration the influences of small scale and the parabolic variation of the transverse shear strains across the thickness of the nanoscale plate and thus, it avoids the employ use of shear correction factors. Also, in this present theory, the effect of transverse shear deformation is included in the axial displacements by using the shear forces instead of rotational displacements as in available high order plate theories. The material properties are supposed to be graded only in the thickness direction and the effective properties for the FG nanoscale plate are calculated by considering Mori-Tanaka homogenization scheme. The equations of motion are obtained using the nonlocal differential constitutive expressions of Eringen in conjunction with the zeroth-order shear deformation theory via Hamilton's principle. Numerical results for vibration of FG nanoscale plates resting on elastic foundations are presented and compared with the existing solutions. The influences of small scale, shear deformation, gradient index, Winkler modulus parameter and Pasternak shear modulus parameter on the vibration responses of the FG nanoscale plates are investigated.

• Steel and Composite Structures
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• v.41 no.6
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• pp.899-910
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• 2021

A 4-unknown shear deformation theory is applied to investigate the vibration of functionally graded plates under thermal environment. The plate is fabricated from a functionally graded material mixed of ceramic and metal with continuously varying material properties through the plate thickness. Three types of thermal loadings, uniform, linear and nonlinear temperature rises along the plate thickness are taken into account. The present theory contains four unknown functions as against five or more in other higher order shear deformation theories. The through-the-thickness distributions of transverse shear stresses of the plate are considered to vary parabolically and vanish at upper and lower surfaces. The present model does not require any problem dependent shear correction factor. Analytical solutions for the free vibration analysis are derived based on Fourier series that satisfy the boundary conditions (Navier's method). Benchmark solutions are firstly considered to evaluate the accuracy of the proposed model. Comparisons with the solutions available in literature revealed the good capabilities of the present model for the simulations of vibration responses of FG plates. Some parametric studies are carried out for the frequency analysis by varying the volume fraction profile and the temperature distribution across the plate thickness.

• Steel and Composite Structures
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• v.44 no.5
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• pp.721-740
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• 2022

In this paper, an accurate kinematic model has been developed to study the mechanical response of functionally graded (FG) sandwich beams, mainly covering the bending, buckling and free vibration problems. The studied structure with homogeneous hardcore and softcore is considered to be simply supported in the edges. The present model uses a new refined shear deformation beam theory (RSDBT) in which the displacement field is improved over the other existing high-order shear deformation beam theories (HSDBTs). The present model provides good accuracy and considers a nonlinear transverse shear deformation shape function, since it is constructed with only two unknown variables as the Euler-Bernoulli beam theory but complies with the shear stress-free boundary conditions on the upper and lower surfaces of the beam without employing shear correction factors. The sandwich beams are composed of two FG skins and a homogeneous core wherein the material properties of the skins are assumed to vary gradually and continuously in the thickness direction according to the power-law distribution of volume fraction of the constituents. The governing equations are drawn by implementing Hamilton's principle and solved by means of the Navier's technique. Numerical computations in the non-dimensional terms of transverse displacement, stresses, critical buckling load and natural frequencies obtained by using the proposed model are compared with those predicted by other beam theories to confirm the performance of the proposed theory and to verify the accuracy of the kinematic model.

• Steel and Composite Structures
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• v.52 no.3
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• pp.273-291
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• 2024

This paper presents a three-dimensional displacement-based formulation to investigate the free vibration of functionally graded nanoplates resting on a Winkler-Pasternak foundation based on the nonlocal elasticity theory. The material properties of the FG nanoplate are considered to vary continuously through the thickness of the nanoplate according to the power-law distribution model. A general three-dimensional displacement field is considered for the plate, which takes into account the out-of-plane strains of the plate as well as the in-plane strains. Unlike the shear deformation theories, in the present formulation, no predetermined form for the distribution of displacements and transverse strains is considered. The equations of motion for functionally graded nanoplate are derived based on Hamilton's principle. The solution is obtained for simply-supported nanoplate, and the predicted results for natural frequencies are compared with the predictions of shear deformation theories which are available in the literature. The predictions of the present theory are discussed in detail to investigate the effects of power-law index, length-to-thickness ratio, mode numbers and the elastic foundation on the dynamic behavior of the functionally graded nanoplate. The present study presents a three-dimensional solution that is able to determine more accurate results in predicting of the natural frequencies of flexural and thickness modes of nanoplates. The effects of parameters that play a key role in the analysis and mechanical design of functionally graded nanoplates are investigated.

• Steel and Composite Structures
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• v.53 no.2
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• pp.169-194
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• 2024

Although the excellent characteristics of functionally graded materials (FGMs) cracks could be found due to manufacturing defects or extreme working conditions. The existence of these cracks may threaten the material or structural strength, reliability, and lifetime. Due to high cost and restrictions offered by practical operational features these cracked components couldn't be replaced immediately. Such circumstances lead to the requirement of assessing the dynamic performance of cracked functionally graded structural components especially under moving objects. The present study aims to comprehensively investigate the dynamic behavior of functionally graded cracked Timoshenko beams (FGCTBs) resting on Winkler foundation and subjected to moving load through shear locking free finite elements methodology. The through thickness material distribution is simulated by the exponential gradation law. The geometric discontinuity due to cracks is represented using the massless rotational spring approach. The shear locking phenomena is avoided by using the different interpolation functions orders for both deflections and rotations. Based on Timoshenko beam element, a shear locking free finite elements methodology is developed. The unconditionally stable Newmark procedure is employed to solve the forced vibration problem. Accuracy of the developed procedure is verified by comparing the obtained results with the available results and an excellent agreement is found. Parametric studies are conducted to explore effects of the geometrical, material characteristics, crack geometrical characteristics, the elastic foundation parameter, and the moving load speed on the dynamic behavior for different boundary conditions. Obtained results revealed the significant effect these parameters on the dynamic performance of FGCTBs.