• Steel and Composite Structures
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• 제19권1호
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• pp.93-110
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• 2015

The thermomechanical bending response of anti-symmetric cross-ply composite plates is investigated by the use of the simple four variable sinusoidal plate theory. The theory accounts for sinusoidal distribution of transverse shear stress, and satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate without using shear correction factor. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations for the present theory is reduced, significantly facilitating engineering analysis. The validity of the present theory is demonstrated by comparison with solutions available in the literature. Numerical results are presented to demonstrate the behavior of the system. The influences of aspect ratio, side-to-thickness ratio, thermal expansion coefficients ratio and stacking sequence on the thermally induced response are studied. The present study is relevant to aerospace, chemical process and nuclear engineering structures which may be subjected to intense thermal loads.

• Structural Engineering and Mechanics
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• 제55권5호
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• pp.1001-1014
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• 2015

Bending analysis of functionally graded (FG) nano-plates is investigated in the present work based on a new sinusoidal shear deformation theory. The theory accounts for sinusoidal distribution of transverse shear stress, and satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate without using shear correction factor. The material properties of nano-plate are assumed to vary according to power law distribution of the volume fraction of the constituents. The size effects are considered based on Eringen's nonlocal theory. Governing equations are derived using energy method and Hamilton's principle. The closed-form solutions of simply supported nano-plates are obtained and the results are compared with those of first-order shear deformation theory and higher-order shear deformation theory. The effects of different parameters such as nano-plate length and thickness, elastic foundation, orientation of foundation orthtotropy direction and nonlocal parameters are shown in dimensionless displacement of system. It can be found that with increasing nonlocal parameter, the dimensionless displacement of nano-plate increases.

• Earthquakes and Structures
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• 제17권3호
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• pp.257-270
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• 2019

The purpose of this work is to analyze the bending behavior of laminated composite plates using the refined fourvariable theory and the finite element method approach using an ANSYS 12 computational code. The analytical model is based on the multilayer plate theory of shear deformation of the nth-order proposed by Xiang et al 2011 using the theory principle developed by Shimpi and Patel 2006. Unlike other theories, the number of unknown functions in the present theory is only four, while five or more in the case of other theories of shear deformation. The formulation of the present theory is based on the principle of virtual works, it has a strong similarity with the classical theory of plates in many aspects, it does not require shear correction factor and gives a parabolic description of the shear stress across the thickness while filling the condition of zero shear stress on the free edges. The analysis is validated by comparing results with those in the literature.

• Coupled systems mechanics
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• 제5권3호
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• pp.269-283
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• 2016

A two new high-order shear deformation theory for bending analysis is presented for a simply supported, functionally graded plate with porosities resting on an elastic foundation. This porosities may possibly occur inside the functionally graded materials (FGMs) during their fabrication, while material properties varying to a simple power-law distribution along the thickness direction. Unlike other theories, there are only four unknown functions involved, as compared to five in other shear deformation theories. The theories presented are variationally consistent and strongly similar to the classical plate theory in many aspects. It does not require the shear correction factor, and gives rise to the transverse shear stress variation so that the transverse shear stresses vary parabolically across the thickness to satisfy free surface conditions for the shear stress. It is established that the volume fraction of porosity significantly affect the mechanical behavior of thick function ally graded plates. The validity of the two new theories is shown by comparing the present results with other higher-order theories. The influence of material parameter, the volume fraction of porosity and the thickness ratio on the behavior mechanical P-FGM plate are represented by numerical examples.

• Structural Engineering and Mechanics
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• 제54권4호
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• pp.693-710
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• 2015

This paper presents a nonlocal shear deformation beam theory for bending, buckling, and vibration of functionally graded (FG) nanobeams using the nonlocal differential constitutive relations of Eringen. The developed theory account for higher-order variation of transverse shear strain through the depth of the nanobeam, and satisfy the stress-free boundary conditions on the top and bottom surfaces of the nanobeam. A shear correction factor, therefore, is not required. In addition, this nonlocal nanobeam model incorporates the length scale parameter which can capture the small scale effect and it has strong similarities with Euler-Bernoulli beam model in some aspects such as equations of motion, boundary conditions, and stress resultant expressions. The material properties of the FG nanobeam are assumed to vary in the thickness direction. The equations of motion are derived from Hamilton's principle. Analytical solutions are presented for a simply supported FG nanobeam, and the obtained results compare well with those predicted by the nonlocal Timoshenko beam theory.

• Structural Engineering and Mechanics
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• 제55권4호
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• pp.703-717
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• 2015

In this paper, a simple n-order refined theory based on neutral surface position is developed for bending and frees vibration analyses of functionally graded beams. The present theory is variationally consistent, uses the n-order polynomial term to represent the displacement field, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. The governing equations are derived by employing the Hamilton's principle and the physical neutral surface concept. The accuracy of the present solutions is verified by comparing the obtained results with available published ones.

• Advances in materials Research
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• 제5권4호
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• pp.223-244
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• 2016

In this paper, a higher order shear and normal deformation theory is presented for functionally graded material (FGM) plates. By dividing the transverse displacement into bending, shear and thickness stretching parts, the number of unknowns and governing equations for the present theory is reduced, significantly facilitating engineering analysis. Indeed, the number of unknown functions involved in the present theory is only five, as opposed to six or even greater numbers in the case of other shear and normal deformation theories. The present theory accounts for both shear deformation and thickness stretching effects by a hyperbolic variation of ail displacements across the thickness and satisfies the stress-free boundary conditions on the upper and lower surfaces of the plate without requiring any shear correction factor. Equations of motion are derived from Hamilton's principle. Analytical solutions for the bending and free vibration analysis are obtained for simply supported plates. The obtained results are compared with three-dimensional and quasi- three-dimensional solutions and those predicted by other plate theories. It can be concluded that the present theory is not only accurate but also simple in predicting the bending and free vibration responses of functionally graded plates.

• Journal of Welding and Joining
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• 제13권2호
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• pp.96-105
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• 1995

본 연구에서는 종래의 미소피로균열 성장속도 해석방법에 대한 수정안을 제시하고 수정 후의 방 법에 의해서 계산한 값들과 S4SC 탄소강에 대한 Nisitani와 Goto의 실험결과를 비교하여 계산한 값과 실험데이터 사이에 양호한 일치가 있음을 보였다. 이미 제시된 피로균열성장속도 식에는 하한계수준과 피로한도를 연관시키는 재료상수와 탄소성 거동에 대한 수정 및 균열닫힘효과를 나타내는 방법이 포함되어 있다. 본 연구에서 행한 수정중의 하나는 기하학적인 상수대신에 퍼만(Forman)의 탄성응력 강도계수 범위식을 이용하는 것이고, 다른 하나는 균열이 성장함에 따라 편심형단면으로 되면서 모멘트에 기인해 발생되는 굽힘효과를 고려하는 것이다. 이 방 법을 수명예측에 사용하면 용접구조물은 물론 기계구조물의 보다 정확한 수명예측이 가능할 것 이다.

• 센서학회지
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• 제5권6호
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• pp.15-24
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• 1996

본 연구에서는 광섬유센서를 지능형 복합재 구조물에 적용하기 위한 기초적 연구의 일부로서, 구조물내에서의 광섬유센서의 건전성 평가와 주조물에 유발된 변현 및 손상에 대한 광섬유센서의 신호검출 거동을 연구 검토하였다. 첫째로, 최약체결파손이론에 거한 광섬유센서의 누적파손분포를 비교하고 수정계수를 도입함으로써, 굽힘시험이 인장시험을 대신할 수 있음을 보였다. 실험에 의해 Weibull 파라미터를 얻고, 굽힘시험에서 유도된 누적파손분포에 적용될 수정계수를 구했다. 열처리한 강섬유센서와 열처리하지 않은 광섬유센서의 인장강도 평균값을 비교함으로써 복합재료 적층관의 경화 사이클 동안 열처리에 의해 야기되는 광섬유센서의 건전성을 평가하였다. 둘째로, 직교적층판과 일방향적층판의 인장시험에서 측정된 시편의 응력-변형률과 삽입된 광섬유센서를 통과한 레이저신호 세기와의 관계를 검토하고, 광섬유센서를 이용한 효과적 손상검출 가능성을 연구 검토하였다.

• Structural Engineering and Mechanics
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• 제67권5호
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• pp.527-544
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• 2018

In this paper, the effect of homogenization models on stress analysis is presented for functionally graded plates (FGMs). The derivation of the effective elastic proprieties of the FGMs, which are a combination of both ceramic and metallic phase materials, is of most of importance. The majority of studies in the last decade, the Voigt homogenization model explored to derive the effective elastic proprieties of FGMs at macroscopic-scale in order to study their mechanical responses. In this work, various homogenization models were used to derive the effective elastic proprieties of FGMs. The effect of these models on the stress analysis have also been presented and discussed through a comparative study. So as to show this effect, a refined plate theory is formulated and evaluated, the number of unknowns and governing equations were reduced by dividing the transverse displacement into both bending and shear parts. Based on sinusoidal variation of displacement field trough the thickness, the shear stresses on top and bottom surfaces of plate were vanished and the shear correction factor was avoided. Governing equations of equilibrium were derived from the principle of virtual displacements. Analytical solutions of the stress analysis were obtained for simply supported FGM plates. The obtained results of the displacements and stresses were compared with those predicted by other plate theories available in the literature. This study demonstrates the sensitivity of the obtained results to different homogenization models and that the results generated may vary considerably from one theory to another. Finally, this study offers benchmark results for the multi-scale analysis of functionally graded plates.