• Advances in materials Research
• /
• 제11권4호
• /
• pp.279-298
• /
• 2022

In this paper, the important novelty and the defining a physical phenomenon of the resent research is the development of nonlocal stress and strain parameters on the porous sandwich beam with functionally graded materials in the top and bottom face sheets.Also, various beam models including Euler-Bernoulli, Reddy and the generalized formulation of two-variable beam theories are obtained in this research. According to a nonlocal strain elasticity theory, the strain at a reference point in the body is dependent not only on the stress state at that point, but also on the stress state at all of the points throughout the body. Thus, the nonlocal stress-strain elasticity theory is defined that can be actual at micro/nano scales. It can be seen that the critical buckling load and transverse deflection of sandwich beam by considering both nonlocal stress-strain parameters is higher than the nonlocal stress parameter. On the other hands, it is noted that by considering the nonlocal stress-strain parameters simultaneously becomes the actual case.

• 대한기계학회논문집
• /
• 제15권3호
• /
• pp.735-750
• /
• 1991

본 연구에서는 적층 복합판의 충격 해석을 위하여 Reddy의 고차 전단 변형 이 론에 기초를 두고, 정적 압입 실험에 의한 접촉 법칙을 고려한 동적 유한 요소 해석 (dynamic finite element analysis)을 행하여 충격 실험에 의한 결과와 1차 전단변형 이론에 의한 해와 비교 검토하므로서, 그 유용성과 우수성을 입증하고, 적층 복합재의 충격 응력 및 응력파 전파 특성에 대하여 연구하고자 한다.

• Advances in concrete construction
• /
• 제6권6호
• /
• pp.585-610
• /
• 2018

In this study, vibration analysis of a concrete foundation-reinforced by $SiO_2$ nanoparticles resting on soil bed is investigated. The soil medium is simulated with spring constants. Furthermore, the Mori-Tanaka low is used for obtaining the material properties of nano-composite structure and considering agglomeration effects. Using third order shear deformation theory or Reddy theory, the total potential energy of system is calculated and by means of the Hamilton's principle, the coupled motion equations are obtained. Also, based an analytical method, the frequency of system is calculated. The effects of volume percent and agglomeration of $SiO_2$ nanoparticles, soil medium and geometrical parameters of structure are shown on the frequency of system. Results show that with increasing the volume percent of $SiO_2$ nanoparticles, the frequency of structure is increased.

• Steel and Composite Structures
• /
• 제32권2호
• /
• pp.281-292
• /
• 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
• /
• 제61권6호
• /
• pp.721-736
• /
• 2017

In this paper, free vibration characteristics of functionally graded (FG) nanobeams embedded on elastic medium are investigated based on third order shear deformation (Reddy) beam theory by presenting a Navier type solution for the first time. The material properties of FG nanobeam are assumed to vary gradually along the thickness and are estimated through the power-law and Mori-Tanaka models. A two parameters elastic foundation including the linear Winkler springs along with the Pasternak shear layer is in contact with beam. The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. The nonlocal equations of motion are derived based on third order shear deformation beam theory through Hamilton's principle and they are solved applying analytical solution. According to the numerical results, it is revealed that the proposed modeling can provide accurate frequency results of the FG nanobeams as compared to some cases in the literature. The obtained results are presented for the vibration analysis of the FG nanobeams such as the influences of foundation parameters, gradient index, nonlocal parameter and slenderness ratio in detail.

• Structural Engineering and Mechanics
• /
• 제87권5호
• /
• pp.461-473
• /
• 2023

This study aims to solve for nonlinear cylindrical shell systems with a semi-analytical and numerical approach implementing the P-T method. The procedures and conditions for such a study are presented in practically solving and analyzing the cylindrical shell systems. An analytical model for a nonlinear thick cylindrical shell (TCS) is established on the basis of the stress function and Reddy's higher-order shear deformation theory (HSDT). According to Reddy's HSDT, Hooke's law in three dimensions, and the von-Kármán equation, the stress-strain relations are developed for the thick cylindrical shell systems, and the three coupled nonlinear governing equations are thus established and discretized as per the Galerkin method, for implementing the P-T method. The solution generated with the approach is continuous everywhere in the entire time domain considered. The approach proposed can also be used to numerically solve and analyze the nonlinear shell systems. The procedures and recurrence relations for numerical solutions of shell systems are presented. To demonstrate the application of the approach in numerically solving for nonlinear cylindrical shell systems, a specific nonlinear cylindrical shell system subjected to an external excitation is solved numerically. In numerically solving for the system, the present approach shows higher efficiency, accuracy, and reliability in comparison with that of the Runge-Kutta method. The approach with the P-T method presented is practically sound especially when continuous and high-quality numerical solutions for the shell systems are considered.

• Advances in nano research
• /
• 제4권3호
• /
• pp.229-249
• /
• 2016

In this paper, buckling characteristics of nonhomogeneous functionally graded (FG) nanobeams embedded on elastic foundations are investigated based on third order shear deformation (Reddy) without using shear correction factors. Third-order shear deformation beam theory accounts for shear deformation effects by a parabolic variation of all displacements through the thickness, and verifies the stress-free boundary conditions on the top and bottom surfaces of the FG nanobeam. A two parameters elastic foundation including the linear Winkler springs along with the Pasternak shear layer is in contact with beam in deformation, which acts in tension as well as in compression. The material properties of FG nanobeam are supposed to vary gradually along the thickness and are estimated through the power-law and Mori-Tanaka models. The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. Nonlocal equations of motion are derived through Hamilton's principle and they are solved applying analytical solution. Comparison between results of the present work and those available in literature shows the accuracy of this method. The obtained results are presented for the buckling analysis of the FG nanobeams such as the effects of foundation parameters, gradient index, nonlocal parameter and slenderness ratio in detail.

• Advances in nano research
• /
• 제12권2호
• /
• pp.167-183
• /
• 2022

In this paper, the free and forced vibration analysis of rotating cantilever nanoscale cylindrical beams and tubes is investigated under the external dynamic load to examine the nonlocal effect. A couple of nonlocal strain gradient theories with different beams and tubes theories, involving the Euler-Bernoulli, Timoshenko, Reddy beam theory along with the higher-order tube theory, are assumed to the mathematic model of governing equations employing the Hamilton principle in order to derive the nonlocal governing equations related to the local and accurate nonlocal boundary conditions. The two-dimensional functional graded material (2D-FGM), made by the axially functionally graded (AFG) in conjunction with the porosity distribution in the radial direction, is considered material modeling. Finally, the derived Partial Differential Equations (PDE) are solved via a couple of the generalized differential quadrature element methods (GDQEM) with the Newmark-beta techniques for the time-dependent results. It is indicated that the boundary conditions equations play a crucial task in responding to nonlocal effects for the cantilever structures.

• Journal of applied mathematics & informatics
• /
• 제26권3_4호
• /
• pp.689-706
• /
• 2008

In this paper, a fifth order numerical method is presented for solving singularly perturbed two point boundary value problems with a boundary layer at one end point. The two point boundary value problem is transformed into general first order ordinary differential equation system. A discrete approximation of a fifth order compact difference scheme is presented for the first order system. An asymptotically equivalent first order equation of the original singularly perturbed two point boundary value problem is obtained from the theory of singular perturbations. It is used in the fifth order compact difference scheme to get a two term recurrence relation and is solved. Several linear and non-linear singular perturbation problems have been solved and the numerical results are presented to support the theory. It is observed that the present method approximates the exact solution very well.

• Structural Engineering and Mechanics
• /
• 제6권6호
• /
• pp.583-612
• /
• 1998

A unified third-order laminate plate theory that contains classical, first-order and third-order theories as special cases is presented. Analytical solutions using the Navier and L$\acute{e}$vy solution procedures are presented. The Navier solutions are limited to simply supported rectangular plates while the L$\acute{e}$vy solutions are restricted to rectangular plates with two parallel edges simply supported and other two edges having arbitrary combination of simply supported, clamped, and free boundary conditions. Numerical results of bending and vibration for a number of problems are discussed in the second part of the paper.