• Journal of the Korea Concrete Institute
• /
• v.15 no.4
• /
• pp.557-565
• /
• 2003

• Advances in materials Research
• /
• v.9 no.1
• /
• pp.63-98
• /
• 2020

The novelty of this paper is the use of a simple higher order shear and normal deformation theory for bending and free vibration analysis of functionally graded material (FGM) beams on two-parameter elastic foundation. To this aim, a new shear strain shape function is considered. Moreover, the proposed theory considers a novel displacement field which includes undetermined integral terms and contains fewer unknowns with taking into account the effects of both transverse shear and thickness stretching. Different patterns of porosity distributions (including even and uneven distribution patterns, and the logarithmic-uneven pattern) are considered. In addition, the effect of different micromechanical models on the bending and free vibration response of these beams is studied. Various micromechanical models are used to evaluate the mechanical characteristics of the FG beams for which properties vary continuously across the thickness according to a simple power law. Hamilton's principle is used to derive the governing equations of motion. Navier type analytical solutions are obtained for the bending and vibration problems. Numerical results are obtained to investigate the effects of power-law index, length-to-thickness ratio, foundation parameter, the volume fraction of porosity and micromechanical models on the displacements, stresses, and frequencies.

• Journal of Power System Engineering
• /
• v.15 no.6
• /
• pp.47-52
• /
• 2011

In this study, an accurate 2-noded hybrid-mixed element for continuous fiber-reinforced laminated beams is newly proposed. The present element including the effect of shear deformation is based on Hellinger-Reissner variational principle, and introduces additional consistent node less degrees for displacement field interpolation in order to enhance the numerical performance. The micromechanical and lamination theory are employed in the finite element description to consider the effects of the laminate stacking sequences, material orthotropy, and fiber volume fraction, etc. The element stiffness matrix can be explicitly derived through the stationary condition and static condensation using Mathematica program. Several numerical examples confirm the accuracy of the present hybrid-mixed element and also show in detail the effects of the continuous fiber volume fraction, stacking sequences and boundary condition on the bending behavior of laminated beams.

• Journal of the Korean Society of Manufacturing Technology Engineers
• /
• v.6 no.3
• /
• pp.89-95
• /
• 1997

A simulation to investigate the thermal behavior in short fiber or whisker reinforced composite materials has been performed for the application to the thermoelastic stress analysis using Finite Element Method (FEM). To obtain the internal field quantities of composite material, the procedure of micromechanical modeling and the principle of virtual work were implemented. For the numerical illustration, an aligned axisymmetric single fiber model has been employed to assess field quantities. It was found that the proposed simulation methodology for thermoelastic stress analysis is applicable to the complicated inhomogeneous solid for the investigation of micromechanical thermoelastic behavior.

• Steel and Composite Structures
• /
• v.39 no.3
• /
• pp.275-290
• /
• 2021

The main purpose of this research work is to investigate the critical buckling load of functionally graded (FG) porous plates with graphene platelets (GPLs) reinforcement using generalized differential quadrature (GDQ) method at thermal condition. It is supposed that the GPL nanofillers and the porosity coefficient vary continuously along the plate thickness direction. Generally, the thermal distribution is considered to be nonlinear and the temperature changing continuously through the thickness of the nanocomposite plates according to the power-law distribution. To model closed cell FG porous material reinforced with GPLs, Halpin-Tsai micromechanical modeling in conjunction with Gaussian-Random field scheme are used, through which mechanical properties of the structures can be extracted. Based on the third order shear deformation theory (TSDT) and the Hamilton's principle, the equations of motion are established and solved for various boundary conditions (B.Cs). The fast rate of convergence and accuracy of the method are investigated through the different solved examples and validity of the present study is evaluated by comparing its numerical results with those available in the literature. A special attention is drawn to the role of GPLs weight fraction, GPLs patterns through the thickness, porosity coefficient and distribution of porosity on critical buckling load. Results reveal that the importance of thermal condition on of the critical load of FGP-GPL reinforced nanocomposite plates.

• Advances in aircraft and spacecraft science
• /
• v.5 no.1
• /
• pp.21-49
• /
• 2018

In this paper, geometric nonlinear bending characteristics of single wall carbon nanotube reinforced composite (SWCNTRC) doubly curved shell panels subjected to uniform transversely loadings are investigated. The nonlinear mathematical model is developed for doubly curved SWCNTRC shell panel on the basis of higher-order shear deformation theory and Green- Lagrange nonlinearity. All nonlinear higher order terms are included in the mathematical model. The effective material properties of SWCNTRC are estimated by using Eshelby-Mori-Tanaka micromechanical approach. The governing equation of the shell panel is obtained using the total potential energy principle and a Newton-Raphson iterative method is employed to compute the nonlinear displacement and stresses. The present results are compared with published literature. The effect of SWCNT volume fraction, width-to-thickness ratio, radius-to-width ratio (R/a), boundary condition, linear and nonlinear deflection, stresses and different types of shell geometry on nonlinear bending response is investigated.

• Coupled systems mechanics
• /
• v.6 no.2
• /
• pp.207-227
• /
• 2017

In this paper Timoshenko beam theory is employed to investigate the vibration characteristics of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) Beams with a stiff core in thermal environment. The material characteristic of carbon nanotubes (CNT) are supposed to change in the thickness direction in a functionally graded form. They can also be calculated through a micromechanical model where the CNT efficiency parameter is determined by matching the elastic modulus of CNTRCs calculated from the rule of mixture with those gained from the molecular dynamics simulations. The differential transform method (DTM) which is established upon the Taylor series expansion is one of the effective mathematical techniques employed to the differential governing equations of sandwich beams. Effects of carbon nanotube volume fraction, slenderness ratio, core-to-face sheet thickness ratio, different thermal environment and various boundary conditions on the free vibration characteristics of FG-CNTRC sandwich beams are studied. It is observed that vibration response of FG-CNTRC sandwich beams is prominently influenced by these parameters.

• Steel and Composite Structures
• /
• v.18 no.3
• /
• pp.693-709
• /
• 2015

In this article, nonlinear free vibration behaviour of functionally graded spherical panel is analysed. A nonlinear mathematical model is developed based on higher order shear deformation theory for shallow shell by taking Green-Lagrange type of nonlinear kinematics. The material properties of functionally graded material are assumed to be varying continuously in transverse direction and evaluated using Voigt micromechanical model in conjunction with power-law distribution. The governing equation of the shell panel is obtained using Hamilton's principle and discretised with the help of nonlinear finite element method. The desired responses are evaluated through a direct iterative method. The present model has been validated by comparing the frequency ratio (nonlinear frequency to linear frequency) with those available published literatures. Finally, the effect of geometrical parameters (curvature ratio, thickness ratio, aspect ratio and support condition), power law indices and amplitude of vibration on the frequency ratios of spherical panel have been discussed through numerical experimentations.

• Steel and Composite Structures
• /
• v.32 no.5
• /
• pp.687-699
• /
• 2019

In this paper, free and force vibration behaviors of graphene-reinforced composite functionally graded (GRC-FG) cylindrical shells in thermal environments are investigated based on Reddy's third-order shear deformation theory (HSDT). The GRC-FG cylindrical shells are composed of piece-wise pattern graphene-reinforced layers which have different volume fraction. Based on the extended Halpin-Tsai micromechanical model, the effective material properties of the resulting nanocomposites are evaluated. Using the Hamilton's principle and the assumed mode method, the motion equation of the GRC-FG cylindrical shells is formulated. Using the time- and frequency-domain methods, free and force vibration properties of the GRC-FG cylindrical shell are analyzed. Numerical cases are provided to study the effects of distribution of graphene, shell radius-to-thickness ratio and temperature changes on the free and force vibration responses of GRC-FG cylindrical shells.

• Advances in nano research
• /
• v.7 no.3
• /
• pp.181-190
• /
• 2019

The thermal buckling temperature values of the graded carbon nanotube reinforced composite shell structure is explored using higher-order mid-plane kinematics and multiscale constituent modeling under two different thermal fields. The critical values of buckling temperature including the effect of in-plane thermal loading are computed numerically by minimizing the final energy expression through a linear isoparametric finite element technique. The governing equation of the multiscale nanocomposite is derived via the variational principle including the geometrical distortion through Green-Lagrange strain. Additionally, the model includes different grading patterns of nanotube through the panel thickness to improve the structural strength. The reliability and accuracy of the developed finite element model are varified by comparison and convergence studies. Finally, the applicability of present developed model was highlight by enlighten several numerical examples for various type shell geometries and design parameters.