• 대한기계학회논문집A
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• 제40권4호
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• pp.381-387
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• 2016

본 논문에서는 생브낭의 원리가 근본적으로 구조물의 거동 예측에 잠재적으로 적용되어 있다는 점에 착안하여, 응력해석에 국한되어 있던 방법론을 자유진동 및 좌굴 문제 등에 적용하여 고전 보 이론의 정확도를 고차이론 수준으로 개선한다. 먼저 생브낭의 원리를 소개하고, 고전 보 이론에 의한 자유진동 그리고 좌굴해석 정식화를 진행하였다. 고전 보 이론의 변위장에 워핑함수와 섭동항을 추가하고, 합응력 등가(즉, 생브낭의 원리)를 적용하여 섭동항을 찾는다. 여기서 워핑함수들은 응력 평형방정식을 통하여 계산하였으며, 이 워핑함수들은 추가된 섭동항에 의하여 보의 응력 평형을 만족하게 된다. 제안된 방법론을 외팔보와 단순지지 보 문제에 적용하여 주파수 및 좌굴하중을 개선하였으며, 전단수정계수의 도입 없이 예측을 개선할 수 있음을 보였다.

• Structural Engineering and Mechanics
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• 제48권4호
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• pp.547-567
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• 2013

Nonlinear behavior of functionally graded material (FGM) plates under thermal loads is investigated here using an efficient sinusoidal shear deformation theory. The displacement field is chosen based on assumptions that the in-plane and transverse displacements consist of bending and shear components, and the shear components of in-plane displacements give rise to the sinusoidal distribution of transverse shear stress through the thickness in such a way that shear stresses vanish on the plate surfaces. Therefore, there is no need to use shear correction factor. Unlike the conventional sinusoidal shear deformation theory, the proposed efficient sinusoidal shear deformation theory contains only four unknowns. The material is graded in the thickness direction and a simple power law based on the rule of mixture is used to estimate the effective material properties. The neutral surface position for such FGM plates is determined and the sinusoidal shear deformation theory based on exact neutral surface position is employed here. There is no stretching-bending coupling effect in the neutral surface-based formulation, and consequently, the governing equations and boundary conditions of functionally graded plates based on neutral surface have the simple forms as those of isotropic plates. The non-linear strain-displacement relations are also taken into consideration. The thermal loads are assumed as uniform, linear and non-linear temperature rises across the thickness direction. Closed-form solutions are presented to calculate the critical buckling temperature, which are useful for engineers in design. Numerical results are presented for the present efficient sinusoidal shear deformation theory, demonstrating its importance and accuracy in comparison to other theories.

• Geomechanics and Engineering
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• 제22권2호
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• pp.119-132
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• 2020

In this study a new innovative three unknowns trigonometric shear deformation theory is proposed for the buckling and vibration responses of exponentially graded sandwich plates resting on elastic mediums under various boundary conditions. The key feature of this theoretical formulation is that, in addition to considering shear deformation effect, it has only three unknowns in the displacement field as in the case of the classical plate theory (CPT), contrary to five as in the first shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). Material characteristics of the sandwich plate faces are considered to vary within the thickness direction via an exponential law distribution as a function of the volume fractions of the constituents. Equations of motion are obtained by employing Hamilton's principle. Numerical results for buckling and free vibration analysis of exponentially graded sandwich plates under various boundary conditions are obtained and discussed. Verification studies confirmed that the present three -unknown shear deformation theory is comparable with higher-order shear deformation theories which contain a greater number of unknowns.

• Structural Engineering and Mechanics
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• 제68권4호
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• pp.409-421
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• 2018

In the present paper, functionally graded (FG) materials are presented to investigate the bending analysis of simply supported plates. It is assumed that the material properties of the plate vary through their length according to the power-law form. The displacement field of the present model is selected based on quasi-3D hyperbolic shear deformation theory. By splitting the deflection into bending, shear and stretching parts, the number of unknowns and equations of motion of the present formulation is reduced and hence makes them simple to use. Governing equations are derived from the principle of virtual displacements. Numerical results for deflections and stresses of powerly graded plates under simply supported boundary conditions are presented. The accuracy of the present formulation is demonstrated by comparing the computed results with those available in the literature. As conclusion, this theory is as accurate as other shear deformation theories and so it becomes more attractive due to smaller number of unknowns. Some numerical results are provided to examine the effects of the material gradation, shear deformation on the static behavior of FG plates with variation of material stiffness through their length.

• Steel and Composite Structures
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• 제21권3호
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• pp.537-551
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• 2016

A new type of composite beam which consists of a wide flange steel shape beam and an innovative type of composite slab was introduced. The composite slab is composed of concrete slab and normal flat steel plates, which are connected by perfobond shear connectors (PBL shear connectors). This paper describes experiments of two large-scale specimens of that composite beam. Both specimens were loaded at two symmetric points for 4-point loading status, and mechanical behaviors under hogging and sagging bending moments were investigated respectively. During the experiments, the crack patterns, failure modes, failure mechanism and ultimate bending capacity of composite beam specimens were investigated, and the strains of concrete and flat steel plate as well as steel shapes were measured and recorded. As shown from the experimental results, composite actions were fully developed between the steel shape and the composite slab, this new type of composite beams was found to have good mechanical performance both under hogging and sagging bending moment with high bending capacity, substantial flexure rigidity and good ductility. It was further shown that the plane-section assumption was verified. Moreover, a design procedure including calculation methods of bending capacity of this new type of composite beam was studied and proposed based on the experimental results, and the calculation methods based on the plane-section assumption and plastic theories were also verified by comparisons of the calculated results and experimental results, which were agreed with each other.

• 한국광학회지
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• 제5권3호
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• pp.349-355
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• 1994

Rayleigh의 분해능 한계 $\epsilon_R$보다 작은 선폭 $\epsilon_0$을 분해할 수 있는 광결상계사 이론적으로 취급되었고, 이어서 초분해능을 지니는 광학계가 제시되었다. 먼저 초분해능을 역변환 문제로 취급하여 초분해능 회절상의 진폭 임펄스 함수를 주는 적분방정식을 도입하고 매개변수 $\beta$(양정수)에 따라서 진폭 임펄스 함수의 반치폭이 조사되었다. 이 초분해능 광학계의 구경함수의 진폭 분포가 변조되었고 또 구경에서 나가는 Huygens 파동의 위상도 Holography로 변조되었다. 이들의 변조를 위하여 이용된 광변조 소자가 제시되었다. 초미세 광리소그라피에 유용한 결론을 얻었다.

• Structural Engineering and Mechanics
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• 제53권6호
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• pp.1215-1240
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• 2015

In this work, a novel simple first-order shear deformation plate theory based on neutral surface position is developed for bending and free vibration analysis of functionally graded plates and supported by either Winkler or Pasternak elastic foundations. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations of the present theory is reduced, and hence, makes it simple to use. The governing equations are derived by employing the Hamilton's principle and the physical neutral surface concept. There is no stretching-bending coupling effect in the neutral surface-based formulation, and consequently, the governing equations and boundary conditions of functionally graded plates based on neutral surface have the simple forms as those of isotropic plates. Numerical results of present theory are compared with results of the traditional first-order and the other higher-order theories reported in the literature. It can be concluded that the proposed theory is accurate and simple in solving the static bending and free vibration behaviors of functionally graded plates.

• Wind and Structures
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• 제25권3호
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• pp.283-299
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• 2017

Two types of aerodynamic admittance function (AAF) that have been adopted in bridge aerodynamics are addressed. The first type is based on a group of supposed relations between flutter derivatives and AAFs. In so doing, the aero-elastic properties of a section could be used to determine AAFs. It is found that the supposed relations hold only for cases when the gust frequencies are within a very low range. Predominant frequencies of long-span bridges are, however, far away from this range. In this sense, the AAFs determined this way are of little practical significance. Another type of AAFs is based on the relation between the Theodorsen circulation function and the Sears function, which holds for thin airfoil theories. It is found, however, that an obvious illogicality exists in this methodology either. In this article, a viewpoint is put forward that AAFs of bluff bridge deck sections are inherently dependent on oncoming turbulent properties. This kind of dependence is investigated with a thin plate and a double-girder bluff section via computational fluid dynamics method. Two types of wind fluctuations are used for identification of AAFs. One is turbulent wind flow while the other is harmonic. The numerical results indicate that AAFs of the thin plate agree well with the Sears AAF, and show no obvious dependence on the oncoming wind fields. In contrast, for the case of bluff double-girder section, AAFs identified from the turbulent and harmonic flows of different amplitudes differ among each other, exhibiting obvious dependence on the oncoming wind field properties.

• Steel and Composite Structures
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• 제25권6호
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• pp.717-726
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• 2017

In this paper, a new simple shear deformation theory for bending analysis of functionally graded plates is developed. The present theory involves only three unknown and three governing equation as in the classical plate theory, but it is capable of accurately capturing shear deformation effects, instead of five as in the well-known first shear deformation theory and higher-order shear deformation theory. A shear correction factor is, therefore, not required. The material properties of the functionally graded plates are assumed to vary continuously through the thickness, according to a simple power law distribution of the volume fraction of the constituents. Equations of motion are obtained by utilizing the principle of virtual displacements and solved via Navier's procedure. The elastic foundation is modeled as two parameter elastic foundation. The results are verified with the known results in the literature. The influences played by transversal shear deformation, plate aspect ratio, side-to-thickness ratio, elastic foundation, and volume fraction distributions are studied. Verification studies show that the proposed theory is not only accurate and simple in solving the bending behaviour of functionally graded plates, but also comparable with the other higher-order shear deformation theories which contain more number of unknowns.

• Steel and Composite Structures
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• 제41권5호
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• pp.697-711
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• 2021

In this work, a simple quasi 3-D parabolic shear deformation theory is developed to examine the bending response of antisymmetric cross-ply laminated composite plates under different types of mechanical loading. The main feature of this theory is that, in addition to including the transverse shear deformation and thickness stretching effects, it has only five-unknown variables in the displacement field modeling like Mindlin's theory (FSDT), yet satisfies the zero shear stress conditions on the top and bottom surfaces of the plate without requiring a shear correction factor. The static version of principle of virtual work was employed to derive the governing equations, while the bending problem for simply supported antisymmetric cross-ply laminated plates was solved by a Navier-type closed-form solution procedure. The adequacy of the proposed model is handled by considering the impact of side-to-thickness ratio on bending response of plate through several illustrative examples. Comparison of the obtained numerical results with the other shear deformation theories leads to the conclusion that the present model is more accurate and efficient in predicting the displacements and stresses of laminated composite plates.