• Computers and Concrete
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• 제27권3호
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• pp.269-282
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• 2021

A dynamic analytical solution for a simply supported, rectangular functionally graded plate with a porous middle layer under time-dependent load based on a refined third-order shear deformation theory with a cubic variation of in-plane displacements according to the thickness and linear/quadratic transverse displacement is presented. The solution achieved in the trigonometric series form and rests on the Green's function method. Two porosity types and their influence on material properties, and mechanical behavior are considered. The network of pores is assumed to be empty or filled with low-pressure air, and the material properties are calculated using the power-law distribution idealization. Numerical calculations have been carried out to demonstrate the accuracy of the kinematic model for the dynamic problem, the effect of porosity, thickness of porous layers, power-law index, and type of loading on the dynamic response of an imperfect functionally graded material plate.

• Structural Engineering and Mechanics
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• 제70권3호
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• pp.325-337
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• 2019

In the present article, cross ply laminated composite plates are considered and a simple sinusoidal shear deformation model is tested for analyzing their flexural, stability and dynamic behaviors. The model contains only four unknown variables that are five in the first order shear deformation theory (FSDT) or other higher order models. The in-plane kinematic utilizes undetermined integral terms to quantitatively express the shear deformation influence. In the proposed theory, the conditions of zero shear stress are respected at bottom and top faces of plates without considering the shear correction coefficient. Equations of motion according to the proposed formulation are deduced by employing the virtual work principle in its dynamic version. The analytical solution is determined via double trigonometric series proposed by Navier. The stresses, displacements, natural frequencies and critical buckling forces computed using present method are compared with other published data where a good agreement between results is demonstrated.

• Advances in materials Research
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• 제12권2호
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• pp.161-177
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• 2023

This paper proposes an analytical method to investigate the free vibration behaviour of new functionally graded (FG) carbon nanotubes reinforced composite beams based on a higher-order shear deformation theory. Cosine functions represent the material gradation and material properties via the thickness. The kinematic relations of the beam are proposed according to trigonometric functions. The equilibrium equations are obtained using the virtual work principle and solved using Navier's method. A comparative evaluation of results against predictions from literature demonstrates the accuracy of the proposed analytical model. Moreover, a detailed parametric analysis checks for the sensitivity of the vibration response of FG nanobeams to nonlocal length scale, strain gradient microstructure-scale, material distribution and geometry.

• 복합신소재구조학회 논문집
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• 제1권3호
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• pp.1-9
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• 2010

본 연구에서는 Lagrangian 및 Hermite 보간함수를 혼합정식화한 유한요소법과 다양한 전단변형함수로 등방성, 대칭 적층 및 샌드위치판 모델을 제시하였다. 제시된 전단변형이론은 판의 상하면에서 전단응력이 0이 되는 다항식, 삼각함수, 쌍곡삼각함수 및 지수함수로 구성되어 있다. 모든 전단변형함수는 해석해, 정해 및 기발표된 유한요소 결과치와 비교하였으며, 합리적인 정확도를 갖는 것으로 예측되었다. 특히, 지수형태의 전단변형함수(Karama et al. 2003; Aydogu 2009)가 적층 및 샌드위치판 해석에 있어서 상대적으로 가장 우수한 결과를 보였다.

• 한국산학기술학회논문지
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• 제12권11호
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• pp.5347-5356
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• 2011

본 연구에서는 Lagrangian/Hermite 보간함수를 혼합정식화한 유한요소법과 다양한 전단변형함수로 역대칭 앵글-플라이 샌드위치판 모델을 비교하였다. 제시된 전단변형함수는 판의 상하면에서 전단응력이 0이 되는 다항식, 삼각함수, 쌍곡삼각함수 및 지수함수로 구성되어 있다. 모든 전단변형함수는 해석해(Analytical solution)와 비교하였으며, 합리적인 정확도를 갖는 것으로 예측되었다. 특히, 지수형태의 전단변형함수가 복합면재를 갖는 샌드위치판 해석에 있어서 상대적으로 가장 우수한 결과를 보였다.

• Steel and Composite Structures
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• 제30권6호
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• pp.517-534
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• 2019

In this paper, the effects of inevitable out-of-plane defects on the postbuckling behavior of single-layered graphene sheets (SLGSs) under in-plane loadings are investigated based on nonlocal first order shear deformation theory (FSDT) and von-Karman nonlinear model. A generic imperfection function, which takes the form of the products of hyperbolic and trigonometric functions, is employed to model out-of-plane defects as initial geometrical imperfections of SLGSs. Nonlinear equilibrium equations are derived from the principle of virtual work and variational formulation. The postbuckling equilibrium paths of imperfect graphene sheets (GSs) are presented by solving the governing equations via isogeometric analysis (IGA) and Newton-Raphson iterative method. Finally, the sensitivity of the postbuckling behavior of GS to shape, amplitude, extension on the surface, and location of initial imperfection is studied. Results showed that the small scale and initial imperfection effects on the postbuckling behavior of defective SLGS are important and cannot be ignored.

• Steel and Composite Structures
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• 제49권5호
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• pp.503-516
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• 2023

In the current examination, a trigonometric shear deformation theory is hired to govern natural frequencies of a functionally graded porous microplate which is covered by two nanocomposite layers. The properties of the structure are varied based on the specified patterns. Utilizing the modified form of couple stress theory for taking the scale effect into account in conjunction with Hamilton's principle, the motion equations are obtained. Then, they are solved via Fourier series functions as an analytical approach. After confirming the results' accuracy, various parameters' effect on the results is investigated. Designing and manufacturing more efficient structures, especially those that are subjected to multi-physical loads can be accounted as findings of this work.

• Geomechanics and Engineering
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• 제21권5호
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• pp.471-487
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• 2020

In this work, the buckling analysis of material sandwich plates based on a two-parameter elastic foundation under various boundary conditions is investigated on the basis of a new theory of refined trigonometric shear deformation. This theory includes indeterminate integral variables and contains only four unknowns in which any shear correction factor not used, with even less than the conventional theory of first shear strain (FSDT). Applying the principle of virtual displacements, the governing equations and boundary conditions are obtained. To solve the buckling problem for different boundary conditions, Galerkin's approach is utilized for symmetric EGM sandwich plates with six different boundary conditions. A detailed numerical study is carried out to examine the influence of plate aspect ratio, elastic foundation coefficients, ratio, side-to-thickness ratio and boundary conditions on the buckling response of FGM sandwich plates. A good agreement between the results obtained and the available solutions of existing shear deformation theories that have a greater number of unknowns proves to demonstrate the precision of the proposed theory.

• Steel and Composite Structures
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• 제34권4호
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• pp.615-623
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• 2020

In this paper, free vibration analysis of a functionally graded cylindrical nanoshell resting on Pasternak foundation is presented based on the nonlocal elasticity theory. A two-dimensional formulation along the axial and radial directions is presented based on the first-order shear deformation shell theory. Hamilton's principle is employed for derivation of the governing equations of motion. The solution to formulated boundary value problem is obtained based on a harmonic solution and trigonometric functions for various boundary conditions. The numerical results show influence of significant parameters such as small scale parameter, stiffness of Pasternak foundation, mode number, various boundary conditions, and selected dimensionless geometric parameters on natural frequencies of nanoshell.

• Steel and Composite Structures
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• 제19권5호
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• pp.1259-1277
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• 2015

In this work, a trigonometric refined beam theory for the bending, buckling and free vibration analysis of carbon nanotube-reinforced composite (CNTRC) beams resting on elastic foundation is developed. The significant feature of this model is that, in addition to including the shear deformation effect, it deals with only 3 unknowns as the Timoshenko beam (TBM) without including a shear correction factor. The single-walled carbon nanotubes (SWCNTs) are aligned and distributed in polymeric matrix with different patterns of reinforcement. The material properties of the CNTRC beams are assessed by employing the rule of mixture. To examine accuracy of the present theory, several comparison studies are investigated. Furthermore, the effects of different parameters of the beam on the bending, buckling and free vibration responses of CNTRC beam are discussed.