• Advances in materials Research
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• 제6권3호
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• pp.279-301
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• 2017

Thermo-mechanical vibration characteristics of in homogeneousporous functionally graded (FG) micro/nanobeam subjected to various types of thermal loadings are investigated in the present paper based on modified couple stress theory with consideration of the exact position of neutral axis. The FG micro/nanobeam is modeled via a refined hyperbolic beam theory in which shear deformation effect is verified needless of shear correction factor. A modified power-law distribution which contains porosity volume fraction is used to describe the graded material properties of FG micro/nanobeam. Temperature field has uniform, linear and nonlinear distributions across the thickness. The governing equations and the related boundary conditions are derived by Extended Hamilton's principle and they are solved applying an analytical solution which satisfies various boundary conditions. A comparison study is performed to verify the present formulation with the known data in the literature and a good agreement is observed. The parametric study covered in this paper includes several parameters such as thermal loadings, porosity volume fraction, power-law exponents, slenderness ratio, scale parameter and various boundary conditions on natural frequencies of porous FG micro/nanobeams in detail.

• Steel and Composite Structures
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• 제17권4호
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• pp.535-548
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• 2014

In this paper, the exact closed-form solutions for torsional analysis of heterogeneous magnetostrictive circular cylinder are derived. The cylinder is subjected to the action of a magnetic field produced by a constant longitudinal current density. It is also acted upon by a particular kind of shearing stress at its upper base. The rigidity of the cylinder is graded through its axial direction from one material at the lower base to another material at the upper base. The distributions of circumferential displacement and shear stresses are presented through the radial and axial directions of the cylinder. The influence of the magnetostrictive parameter is discussed. The effects of additional parameters are investigated.

• Structural Engineering and Mechanics
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• 제64권5호
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• pp.527-541
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• 2017

In this work, a new hyperbolic shear deformation beam theory is proposed based on a modified couple stress theory (MCST) to investigate the bending and free vibration responses of functionally graded (FG) micro beam made of porous material. This non-classical micro-beam model introduces the material length scale coefficient which can capture the size influence. The non-classical beam model reduces to the classical beam model when the material length scale coefficient is set to zero. The mechanical material properties of the FG micro-beam are assumed to vary in the thickness direction and are estimated through the classical rule of mixture which is modified to approximate the porous material properties with even and uneven distributions of porosities phases. Effects of several important parameters such as power-law exponents, porosity distributions, porosity volume fractions, the material length scale parameter and slenderness ratios on bending and dynamic responses of FG micro-beams are investigated and discussed in detail. It is concluded that these effects play significant role in the mechanical behavior of porous FG micro-beams.

• Structural Engineering and Mechanics
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• 제71권5호
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• pp.485-502
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• 2019

In this research, the nonlinear static, buckling and vibration analysis of viscoelastic micro-composite beam reinforced by various distributions of boron nitrid nanotube (BNNT) with initial geometrical imperfection by modified strain gradient theory (MSGT) using finite element method (FEM) are presented. The various distributions of BNNT are considered as UD, FG-V and FG-X and also, the extended rule of mixture is used to estimate the properties of micro-composite beam. The components of stress are dependent to mechanical, electrical and thermal terms and calculated using piezoelasticity theory. Then, the kinematic equations of micro-composite beam using the displacement fields are obtained. The governing equations of motion are derived using energy method and Hamilton's principle based on MSGT. Then, using FEM, these equations are solved. Finally the effects of different parameters such as initial geometrical imperfection, various distributions of nanotube, damping coefficient, piezoelectric constant, slenderness ratio, Winkler spring constant, Pasternak shear constant, various boundary conditions and three material length scale parameters on the behavior of nonlinear static, buckling and vibration of micro-composite beam are investigated. The results indicate that with an increase in the geometrical imperfection parameter, the stiffness of micro-composite beam increases and thus the non-dimensional nonlinear frequency of the micro structure reduces gradually.

• 대한기계학회논문집A
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• 제33권11호
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• pp.1249-1255
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• 2009

Cord-rubber composites widely used in tires show very complicated mechanical behavior such as nonlinearity and large deformation. Three-phase(cord, rubber and the interface) modeling has been used to analyze the stress distribution in the cord-rubber composites more accurately. In this study, finite element methods were performed using two-dimensional generalized plane strain element and plane strain element to investigate the stress distribution and effective modulus of cord-rubber composites. Neo Hookean model was used for rubber property and several interface properties were assumed for various loading directions. It was found that the interface properties affect the effective modulus and the distributions of shear stress.

• 한국지반환경공학회 논문집
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• 제12권1호
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• pp.41-50
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• 2011

본 연구에서는 단독말뚝의 측면에서 시공되는 터널에 의한 말뚝의 거동에 대하여 3차원 수치해석을 통하여 분석하였다. 수치해석을 통하여 터널-말뚝-지반의 상호거동에 대한 심도 있는 분석을 실시하였다. 수치해석을 통해 말뚝의 침하, 말뚝과 주변지반 사이의 상대변위, 전단응력 및 말뚝의 축력변화를 고찰하였다. 특히 터널굴착에 의한 전단응력의 전이과정에 대한 심도 있는 분석을 실시하였다. 터널굴착에 의한 말뚝과 인근지반에서의 상대변위 변화로 인하여 말뚝에 작용하는 전단응력 및 축력의 분포가 변하게 되는 것으로 나타났다. 터널 중심부의 상부에서는 하향의 전단응력이 발생하는 반면(Z/L=0.0-0.7~0.8), 그 하부에서는 (Z/L=0.7~0.8-1.0) 상향의 전단응력이 발생하여 말뚝에 압축력이 발생된다, 이때 Z는 임의의 심도, L은 말뚝의 길이다. 터널굴착이 종료된 후 말뚝에는 최대 $0.475P_a$의 압축력이 발생하였다, 이때 $P_a$는 말뚝의 설계지지력이다. 수치해석을 통해서 도출된 터널굴착이 말뚝 거동에 미치는 영향에 대해 상세히 고찰하였다.

• 대한기계학회논문집A
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• 제31권1호
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• pp.121-128
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• 2007

Enhanced lower order shear deformation theory is developed in this study. Generally, lower order theories are not adequate to predict accurate deformation and stress distribution through the thickness of laminated plate. For the accurate prediction of detailed stress and deformation distributions through the thickness, higher order zigzag theories have been proposed. However, in most cases, simplified zigzag higher order theory requires $C_1$, shape functions in finite element implementation. In commercial FE softwares, $C_1$, shape functions are not so common in plate and shell analysis. Thus zigzag theories are useful for the highly accurate prediction of thick composite behaviors but they are not practical in the sense that they cannot be used conveniently in the commercial package. In practice, iso-parametric $C_0$ plate model is the standard model for the analysis and design of composite laminated plates and shells. Thus in the present study, an enhanced lower order shear deformation theory is developed. The proposed theory requires only $C_0$ shape function in FE implementation. The least-squared energy error between the lower order theory and higher order theory is minimized. An enhanced lower order shear deformation theory(ELSDT) in this paper is proposed for smart structure under complex loadings. The ELSDT is constructed by the strain energy transformation and fully coupled mechanical, electric loading cases are studied. In order to obtain accurate prediction, zigzag in-plane displacement and transverse normal deformation are considered in the deformation Held. In the electric behavior, open-circuit condition as well as closed-circuit condition is considered. Through the numerous examples, the accuracy and robustness of present theory are demonstrated.

• Steel and Composite Structures
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• 제47권5호
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• pp.551-568
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• 2023

In this research, a new two-dimensional (2D) and quasi three-dimensional (quasi-3D) higher order shear deformation theory is devised to address the bending problem of functionally graded plates resting on an elastic foundation. The displacement field of the suggested theories takes into account a parabolic transverse shear deformation shape function and satisfies shear stress free boundary conditions on the plate surfaces. It is expressed as a combination of trigonometric and exponential shear shape functions. The Pasternak mathematical model is considered for the elastic foundation. The material properties vary constantly across the FG plate thickness using different distributions as power-law, exponential and Mori-Tanaka model. By using the virtual works principle and Navier's technique, the governing equations of FG plates exposed to sinusoidal and evenly distributed loads are developed. The effects of material composition, geometrical parameters, stretching effect and foundation parameters on deflection, axial displacements and stresses are discussed in detail in this work. The obtained results are compared with those reported in earlier works to show the precision and simplicity of the current formulations. A very good agreement is found between the predicted results and the available solutions of other higher order theories. Future mechanical analyses of three-dimensionally FG plate structures can use the study's findings as benchmarks.

• Structural Engineering and Mechanics
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• 제89권3호
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• pp.225-238
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• 2024

In this paper, a quasi-3D hyperbolic shear deformation theory for the bending responses of a functionally graded (FG) porous micro-beam is based on a modified couple stress theory requiring only one material length scale parameter that can capture the size influence. The model proposed accounts for both shear and normal deformation effects through an illustrative variation of all displacements across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the micro-beam. The effective material properties of the functionally graded micro-beam are assumed to vary in the thickness direction and are estimated using the homogenization method of power law distribution, which is modified to approximate the porous material properties with even and uneven distributions of porosity phases. The equilibrium equations are obtained using the virtual work principle and solved using Navier's technique. The validity of the derived formulation is established by comparing it with the ones available in the literature. Numerical examples are presented to investigate the influences of the power law index, material length scale parameter, beam thickness, and shear and normal deformation effects on the mechanical characteristics of the FG micro-beam. The results demonstrate that the inclusion of the size effects increases the microbeams stiffness, which consequently leads to a reduction in deflections. In contrast, the shear and normal deformation effects are just the opposite.

• Structural Engineering and Mechanics
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• 제44권2호
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• pp.139-161
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• 2012

In this paper, the static behavior of bi-directional functionally graded (FG) non-uniform thickness circular plate resting on quadratically gradient elastic foundations (Winkler-Pasternak type) subjected to axisymmetric transverse and in-plane shear loads is carried out by using state-space and differential quadrature methods. The governing state equations are derived based on 3D theory of elasticity, and assuming the material properties of the plate except the Poisson's ratio varies continuously throughout the thickness and radius directions in accordance with the exponential and power law distributions. The stresses and displacements distribution are obtained by solving state equations. The effects of foundation stiffnesses, material heterogeneity indices, geometric parameters and loads ratio on the deformation and stress distributions of the FG circular plate are investigated in numerical examples. The results are reported for the first time and the new results can be used as a benchmark solution for future researches.