• Structural Engineering and Mechanics
• /
• 제65권4호
• /
• pp.453-464
• /
• 2018

In this paper, an efficient higher-order shear deformation theory is presented to analyze thermomechanical bending of temperature-dependent functionally graded (FG) plates resting on an elastic foundation. Further simplifying supposition are made to the conventional HSDT so that the number of unknowns is reduced, significantly facilitating engineering analysis. These theory account for hyperbolic 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. Nonlinear thermal conditions are imposed at the upper and lower surface for simply supported FG plates. Equations of motion are derived from the principle of virtual displacements. Analytical solutions for the thermomechanical bending analysis are obtained based on Fourier series that satisfy the boundary conditions (Navier's method). Non-dimensional results are compared for temperature-dependent FG plates and validated with those of other shear deformation theories. Numerical investigation is conducted to show the effect of material composition, plate geometry, and temperature field on the thermomechanical bending characteristics. It can be concluded that the present theory is not only accurate but also simple in predicting the thermomechanical bending responses of temperature-dependent FG plates.

• 한국농공학회지
• /
• 제38권3호
• /
• pp.82-91
• /
• 1996

This is a basic study for the static and dynamic analysis on the elasto-plastic and elasto-viscoplastic of an axi-symmetric shell. The objective of this study was to investigate the mechanical characteristics of a nuclear reinforced concrete containment structure, which was selected as a model, by a numerical analysis using a finite element method. The structure was modeled with discrete ring elements of 8-noded isoparametric element rotating against the symmetrical axis, and the interaction between the foundation and the structure was modeled by Winkler's model. Also, the meridional tendon was modeled with 2-node truss elements, and the hoop tendon was done with point elements in two degrees of freedom. The effect of the tendon was considered without the increasement in total degree of freedom as the stiffness matrix of modeled tendon elements was assembled on the stiffness matrix of ring elements linked with the tendon. The results obtained from the analysis of an example were summarized as follows : 1. The stresses in the hoop direction on the interior and exterior surfaces of the structure were shown in changes of similar trend, and high stresses appeared on the structure wall 2. The stresses in the meridional direction on the interior and exterior surfaces were shown in change of different trend. Especially, the stresses at the junctions between the dome and the wall and between the wall and the bottom plate of the structure were very high, compared with those at other parts of the structure. 3. The stress changes in the direction of thickness on the crown of the dome were much linearly distributed. However, as the amount of tendon increased, the stresses in the upper and lower parts of the wall established with the tendon were shown stress concentration. 4. The stress changes in the direction of thickness on the center of the structure wall was linearly distributed in the all cases, and special stress due to the use of the tendon was not shown.

• Structural Engineering and Mechanics
• /
• 제86권4호
• /
• pp.443-459
• /
• 2023

This study investigates the theoretical thermal buckling analyses of thick porous rectangular functionally graded (FG) plates with different geometrical boundary conditions resting on a Winkler-Pasternak elastic foundation using a new higher-order shear deformation theory (HSDT). This new theory has only four unknowns and involves indeterminate integral variables in which no shear correction factor is required. The variation of material properties across the plate's thickness is considered continuous and varied following a simple power law as a function of volume fractions of the constituents. The effect of porosity with two different types of distribution is also included. The current formulation considers the Von Karman nonlinearity, and the stability equations are developed using the virtual works principle. The thermal gradients are involved and assumed to change across the FG plate's thickness according to nonlinear, linear, and uniform distributions. The accuracy of the newly proposed theory has been validated by comparing the present results with the results obtained from the previously published theories. The effects of porosity, boundary conditions, foundation parameters, power index, plate aspect ratio, and side-to-thickness ratio on the critical buckling temperature are studied and discussed in detail.

• Advances in nano research
• /
• 제16권5호
• /
• pp.509-519
• /
• 2024

In this study, the static analysis of carbon nanotube-reinforced composites (CNTRC) beams resting on a Winkler-Pasternak elastic foundation is presented. The developed theories account for higher-order variation of transverse shear strain through the depth of the beam and satisfy the stress-free boundary conditions on the top and bottom surfaces of the beam. To study the effect of carbon nanotubes distribution in functionally graded (FG-CNT), we introduce in the equation of CNT volume fraction a new exponent equation. The SWCNTs are assumed to be aligned and distributed in the polymeric matrix with different patterns of reinforcement. The rule of mixture is used to describe the material properties of the CNTRC beams. The governing equations were derived by employing Hamilton's principle. The models presented in this work are numerically provided to verify the accuracy of the present theory. The analytical solutions are presented, and the obtained results are compared with the existing solutions to verify the validity of the developed theories. Many parameters are investigated, such as the Pasternak shear modulus parameter, the Winkler modulus parameter, the volume fraction, and the order of the exponent in the volume fraction equation. New results obtained from bending and stresses are presented and discussed in detail. From the obtained results, it became clear the influence of the exponential CNTs distribution and Winkler-Pasternak model improved the mechanical properties of the CNTRC beams.

• 한국전산구조공학회:학술대회논문집
• /
• 한국전산구조공학회 1999년도 가을 학술발표회 논문집
• /
• pp.291-300
• /
• 1999

An idealized analytical model is proposed to estimate the effects of restrainer upon global response behaviors of a bridge system under seismic excitations. Pounding actions between adjacent vibration units and friction at movable supports are introduced in addition to other phenomena such as nonlinear behaviors of pier, motions of the foundation and abutment to achieve the better prediction of the bridge motion. The applied restrainer is assumed to be a dead-band system, which has the force clearance and the linear-elastic force. Using the proposed model, the dynamic characteristics of a bridge system retrofitted by restrainers is examined, and the effects of stiffness and clearance length of restrainer is also investigated. The main effect of the application of restrainers is found to reduce the relative displacements and the trend becomes greater with the shorter clearance length except between pier units. It is found that the relative displacements between abutment and adjacent pier units are decreased as the stiffness of restrainer increases, but almost independent upon the stiffness increments of restrainer. However, the relative displacements between pier units tend to be increased due to the applications of the restrainers.

• 소음진동
• /
• 제5권2호
• /
• pp.169-181
• /
• 1995

A theoretical model has been studied to describe the sound radiation analysis for structural vibration noise control of tire under the action of random moving line forces. When a tire is analyzed, it has been modeled as a curved beam with distributed springs and dash-pots which represent the radial, tangential stiffness and damping of tire, respectively. The reaction due to fluid loading on the vibratory response of the curved beam is taken into account. The curved beam is assumed to occupy the plane y = 0 and to be axially infinite. The material of curved beam and elastic foundation are assumed to be lossless, and governed by the law of Bernoulli-Euler beam theory. The expression for sound power is integrated numerically and its results examined as a function of Mach number(M), wavenumber ratio(.gamma.) and stiffness factor(.PSI.). The experimental investigation for structural vibration noise of tire under the action of random moving line forces has been made. Based on the STSF(Spatial Transformation of Sound Field) techniques, the sound power and sound radiation are measured. The experimental results show that operating condition, material properties and design factors of the tire have a great effect on the sound power and sound radiation characteristics.

• Structural Engineering and Mechanics
• /
• 제54권6호
• /
• pp.1061-1073
• /
• 2015

This paper presents a nonlocal sinusoidal shear deformation beam theory (SDBT) for the nonlinear vibration of single walled carbon nanotubes (CNTs). The present model is capable of capturing both small scale effect and transverse shear deformation effects of CNTs, and does not require shear correction factors. The surrounding elastic medium is simulated based on Pasternak foundation. Based on the nonlocal differential constitutive relations of Eringen, the equations of motion of the CNTs are derived using Hamilton's principle. Differential quadrature method (DQM) for the natural frequency is presented for different boundary conditions, and the obtained results are compared with those predicted by the nonlocal Timoshenko beam theory (TBT). The effects of nonlocal parameter, boundary condition, aspect ratio on the frequency of CNTs are considered. The comparison firmly establishes that the present beam theory can accurately predict the vibration responses of CNTs.

• Structural Engineering and Mechanics
• /
• 제72권3호
• /
• pp.329-338
• /
• 2019

In this paper, the magnetic field influence on the wave propagation characteristics of graphene nanosheets is examined within the frame work of a two-variable plate theory. The small-scale effect is taken into consideration based on the nonlocal strain gradient theory. For more accurate analysis of graphene sheets, the proposed theory contains two scale parameters related to the nonlocal and strain gradient effects. A derivation of the differential equation is conducted, employing extended principle of Hamilton and solved my means of analytical solution. A refined trigonometric two-variable plate theory is employed in Kinematic relations. The scattering relation of wave propagation in solid bodies which captures the relation of wave number and the resultant frequency is also investigated. According to the numerical results, it is revealed that the proposed modeling can provide accurate wave dispersion results of the graphene nanosheets as compared to some cases in the literature. It is shown that the wave dispersion characteristics of graphene sheets are influenced by magnetic field, elastic foundation and nonlocal parameters. Numerical results are presented to serve as benchmarks for future analyses of graphene nanosheets.

• Advances in nano research
• /
• 제13권1호
• /
• pp.29-45
• /
• 2022

The optimization for dynamic response associated with a cylindrical shell which is made of laminated composites embedded in a piezoelectric layer which is subjected to temperature rises and is resting on an elastic foundation is investigated for the first time. The first shear order theory (FSDT) is utilized in order to obtain the strain relations of the shell. Then, using the energy method, the equations of motions as well as boundary condition of the problem are attained. The formulation of this study together with the solution procedure which is a numerical solution method, differential quadrature method (DQM) is validated using other researches. This paper presents a thorough study on the parameters which impacts the vibration frequency of the laminated shell. The results of this paper shows that any type of laminated composite shell can reduce the vibration frequency providing that the angle related to layer are higher than 85 degrees. Also, in order to reduce the effect of temperature rises, the laminated composites instead of orthotropic one can be used.

• Geomechanics and Engineering
• /
• 제35권6호
• /
• pp.637-646
• /
• 2023

At present, the research on wave propagation in graphene platelet reinforced composite plates focuses on the propagation behavior of bulk waves, in which the effect of boundary condition is ignored, there is no literature report on propagation behaviors of guided waves in graphene platelet reinforced metal foams (GPLRMF) plates. In fact, wave propagation is affected by boundary conditions, so it is necessary to study the propagation characteristics of guided waves. The aim of this paper is to solve this problem. The effective performance of the material was calculated using the mixing law. Equations of motion of GPLRMF plate is derived by using Hamilton's principle. Then, the eigenvalue method is used to obtain the expressions of bending wave, shear wave and longitudinal wave, and the degradation verification is carried out. Finally, the effects of graphene platelets (GPLs) volume fraction, elastic foundation, porosity coefficient, GPLs distribution types and porosity distribution types on the dispersion relations are studied. We find that these factors play an important role in the propagation characteristics and phase velocity of guided waves.