• Steel and Composite Structures
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• 제45권4호
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• pp.547-554
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• 2022

This paper studies the static stability of an axially graded column with the power-law gradient varying along the axial direction. For a nonhomogeneous column with one end linked to a rotational spring and loaded by a compressive force, respectively, an Euler problem is analyzed by solving a boundary value problem of an ordinary differential equation with varying coefficients. Buckling loads through the characteristic equation with the aid of the Bessel functions are exactly given. An alternative way to approximately determine buckling loads through the integral equation method is also presented. By comparing approximate buckling loads with the exact ones, the approximate solution is simple in form and enough accurate for varying power-law gradients. The influences of the gradient index and the rotational spring stiffness on the critical forces are elucidated. The critical force and mode shapes at buckling are presented in graph. The critical force given here may be used as a benchmark to check the accuracy and effectiveness of numerical solutions. The approximate solution provides a feasible approach to calculating the buckling loads and to assessing the loss of stability of columns in engineering.

• 대한기계학회논문집A
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• 제22권1호
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• pp.16-22
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• 1998

This paper addresses a method which can be used for analyzing thermal stresses of a functionally graded material(FGM) using semi-analytical approach. FGM is a nonhomogeneous material whose composition is changed continuously from a metal surface to a ceramic surface. An infinite one dimensional FGM plate is considered. The temperature distribution in the FGM is obtained by approximate Green's function solution. To expedite the convergence of the solutions, alternative Green's function solution is derived and shows good agreement with results from finite difference method. Thermal stresses are calculated using temperature distribution of the plate.

• Structural Monitoring and Maintenance
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• 제7권1호
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• pp.27-42
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• 2020

Dynamic stability of graded nonlocal nano-dimension plates on elastic substrate due to in-plane periodic loads has been researched via a novel 3- unknown plate theory based on exact position of neutral surface. Proposed theory confirms the shear deformation effects and contains lower field components in comparison to first order and refined 4- unknown plate theories. A modified power-law function has been utilized in order to express the porosity-dependent material coefficients. The equations of nanoplate have been represented in the context of Mathieu-Hill equations and Chebyshev-Ritz-Bolotin's approach has been performed to derive the stability boundaries. Detailed impacts of static/dynamic loading parameters, nonlocal constant, foundation parameters, material index and porosities on instability boundaries of graded nanoscale plates are researched.

• 대한수학회지
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• 제48권1호
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• pp.117-132
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• 2011

By developing a linear algebra program involving many different structures associated to a three-graded H*-algebra, it is shown that if L is a Lie triple automorphism of an infinite-dimensional topologically simple associative H*-algebra A, then L is either an automorphism, an anti-automorphism, the negative of an automorphism or the negative of an anti-automorphism. If A is finite-dimensional, then there exists an automorphism, an anti-automorphism, the negative of an automorphism or the negative of an anti-automorphism F : A $\rightarrow$ A such that $\delta$:= F - L is a linear map from A onto its center sending commutators to zero. We also describe L in the case of having A zero annihilator.

• Structural Engineering and Mechanics
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• 제67권2호
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• pp.175-183
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• 2018

This research deals with the wave dispersion analysis of functionally graded double-layered nanobeam systems (FG-DNBSs) considering the piezoelectric effect based on nonlocal strain gradient theory. The nanobeam is modeled via Euler-Bernoulli beam theory. Material properties are considered to change gradually along the nanobeams' thickness on the basis of the rule of mixture. By implementing a Hamiltonian approach, the Euler-Lagrange equations of piezoelectric FG-DNBSs are obtained. Furthermore, applying an analytical solution, the dispersion relations of smart FG-DNBSs are derived by solving an eigenvalue problem. The effects of various parameters such as nonlocality, length scale parameter, interlayer stiffness, applied electric voltage, relative motions and gradient index on the wave dispersion characteristics of nanoscale beam have been investigated. Also, validity of reported results is proven in the framework of a diagram showing the convergence of this model's curve with that of a previous published attempt.

• Advances in aircraft and spacecraft science
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• 제7권2호
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• pp.115-134
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• 2020

This paper proposes a bending analysis for a functionally graded piezoelectric (FGP) plate through utilizing a two-variable shear deformation plate theory under simply-supported edge conditions. The number of unknown functions used in this theory is only four. The electric potential distribution is assumed to be a combination of a cosine function along the cartesian coordinate. Applying the analytical solutions of FGP plate by using Navier's approach and the principle of virtual work, the equilibrium equations are derived. The paper also discusses thoroughly the impact of applied electric voltage, plate's aspect ratio, thickness ratio and inhomogeneity parameter. Results are compared with the analytical solution obtained by classical plate theory, first-order-shear deformation theory, higher-order shear deformation plate theories and quasi-three-dimensional sinusoidal shear deformation plate theory.

• Steel and Composite Structures
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• 제32권2호
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• pp.281-292
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• 2019

Nonlocal elasticity and Reddy plant theory are used to study the vibration response of functionally graded (FG) nanoplates resting on two parameters elastic medium called Pasternak foundation. Nonlocal higher order theory accounts for the effects of both scale and the effect of transverse shear deformation, which becomes significant where stocky and short nanoplates are concerned. It is assumed that the properties of FG nanoplate follow a power law through the thickness. In addition, Poisson's ratio is assumed to be constant in this model. Both Winkler-type and Pasternak-type foundation models are employed to simulate the interaction of nanoplate with surrounding elastic medium. Using Hamilton's principle, size-dependent governing differential equations of motion and corresponding boundary conditions are derived. A differential quadrature approach is being utilized to discretize the model and obtain numerical solutions for various boundary conditions. The model is validated by comparing the results with other published results.

• Structural Engineering and Mechanics
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• 제68권6호
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• pp.701-711
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• 2018

Herein, the thermo-magneto-elastic wave dispersion answers of functionally graded (FG) double-nanobeam systems (DNBSs) are surveyed implementing a nonlocal strain gradient theory (NSGT). The kinematic relations are derived employing the classical beam theory. Also, scale influences are covered precisely in the framework of NSGT. Moreover, Mori-Tanaka homogenization model is introduced in order to obtain the effective material properties of FG nanobeams. Meanwhile, effects of external forces such as thermal and Lorentz forces are included in this research. Also, based upon the Hamilton's principle, the Euler-Lagrange equations are developed; afterwards, these equations are incorporated with those of NSGT to reach the nonlocal governing equations of FG-DNBSs. Furthermore, according to an analytical approach, the governing equations are solved to obtain the wave frequencies and phase velocities of FG-DNBSs. At the end, some illustrations are rendered to clarify the influences of a wide range of involved parameters.

• Structural Engineering and Mechanics
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• 제78권1호
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• pp.103-116
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• 2021

In this work, a model of a functionally graded (FG) nanotube conveying fluid embedded in an elastic medium is developed based on the nonlocal strain gradient theory (NSGT) in conjunction with Euler-Bernoulli beam theory (EBT). The main objective of this research is to investigate the nonlinear vibration and stability analysis of fluid-conveying nanotubes. The governing equations of motion are derived by means of Hamiltonian principle. The analytical expressions of nonlinear frequencies and critical flow velocities for two different types of boundary conditions including pinned-pinned (P-P) and clamped-clamped (C-C) conditions are obtained by employing Galerkin method as well as Hamiltonian Approach (HA). Comparison of the obtained results with the published works show the acceptable accuracy of the current solutions. The effects of the power-law index, the nonlocal and material length scale parameters and the elastic medium on the stability and nonlinear responses of FG nanotubes are thoroughly investigated and discussed.

• Structural Engineering and Mechanics
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• 제78권4호
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• pp.379-386
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• 2021

A numerical and computer simulation for dynamic stability analysis of graded porous nanoplates has been provided using a Chebyshev-Ritz-Bolotin approach. The nanoplate has been formulated according to the nonlocal elasticity and a 3-unkown plate model capturing neutral surface location. All of material properties are assumed to be dependent of porosity factor which determines the amount or volume of pores. The nano-size plate has also been assumed to be under temperature and moisture variation. It will be shown that stability boundaries of the nanoplate are dependent on static and dynamical load factors, porosity factor, temperature variation and nonlocal parameter.