• Computers and Concrete
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• 제32권1호
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• pp.61-74
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• 2023

This article investigates the wave propagation analysis of the imperfect functionally graded (FG) sandwich plates based on a novel simple four-variable integral quasi-3D higher-order shear deformation theory (HSDT). The thickness stretching effect is considered in the transverse displacement component. The presented formulation ensures a parabolic variation of the transverse shear stresses with zero-stresses at the top and the bottom surfaces without requiring any shear correction factors. The studied sandwich plates can be used in several sectors as areas of aircraft, construction, naval/marine, aerospace and wind energy systems, the sandwich structure is composed from three layers (two FG face sheets and isotropic core). The material properties in the FG faces sheet are computed according to a modified power law function with considering the porosity which may appear during the manufacturing process in the form of micro-voids in the layer body. The Hamilton principle is utilized to determine the four governing differential equations for wave propagation in FG plates which is reduced in terms of computation time and cost compared to the other conventional quasi-3D models. An eigenvalue equation is formulated for the analytical solution using a generalized displacements' solution form for wave propagation. The effects of porosity, temperature, moisture concentration, core thickness, and the material exponent on the plates' dispersion relations are examined by considering the thickness stretching influence.

• 항공우주시스템공학회지
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• 제18권4호
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• pp.10-17
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• 2024

국내외로 연구가 활발한 태양광 무인항공기는 일반적으로 고세장비 특징을 갖는다. 고세장비 날개는 날개 무게가 증가함에 따라 경량 설계되어 플러터에 취약하다. 따라서 초기 설계부터 플러터 해석이 필요하다. 대체로 플러터 해석은 날개 단면을 활용하거나 3D 모델을 이용하여 보다 정확하게 플러터 해석을 수행한다. 그러나 3D 모델은 해석에 시간이 많이 소모되기 때문에 본 연구에서는 2D 전기체 모델을 이용하고자 한다. 2D 전기체 모델은 3D 모델에 비해 계산이 빠르며 직관적으로 플러터 경계를 확보할 수 있다. 따라서 본 연구에서는 2D 전기체의 구조/공기력 모델을 수립하고 3D 반-모델과 해석결과를 비교하였다. 결과적으로 2D 전기체 모델과 3D 반-모델의 플러터 해석 결과, 오차는 약 3% 이내로 유사하고, 제시된 2D 전기체 모델의 타당성을 검증하였다.

• Geomechanics and Engineering
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• 제18권1호
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• pp.85-96
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• 2019

A free vibration analysis and wave propagation of triclinic and orthotropic plate has been presented in this work using an efficient quasi 3D shear deformation theory. The novelty of this paper is to introducing this theory to minimize the number of unknowns which is three; instead four in other researches, to studying bulk waves in anisotropic plates, other than it can model plates with great thickness ratio, also. Another advantage of this theory is to permits us to show the effect of both bending and shear components and this is carried out by dividing the transverse displacement into the bending and shear parts. Hamilton's equations are a very potent formulation of the equations of analytic mechanics; it is used for the development of wave propagation equations in the anisotropic plates. The analytical dispersion relationship of this type of plate is obtained by solving an eigenvalue problem. The accuracy of the present model is verified by confronting our results with those available in open literature for anisotropic plates. Moreover Numerical examples are given to show the effects of wave number and thickness on free vibration and wave propagation in anisotropic plates.

• 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.

• Structural Engineering and Mechanics
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• 제69권6호
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• pp.637-649
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• 2019

In the current research paper, a quasi-3D beam theory is developed for free vibration analysis of functionally graded microbeams. The volume fractions of metal and ceramic are assumed to be distributed through a beam thickness by three functions, power function, symmetric power function and sigmoid law distribution. The modified coupled stress theory is used to incorporate size dependency of micobeam. The equation of motion is derived by using Hamilton's principle, however, Navier type solution method is used to obtain frequencies. Numerical results show the effects of the function distribution, power index and material scale parameter on fundamental frequencies of microbeams. This model provides designers with guidance to select the proper distributions and functions.

• Computers and Concrete
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• 제32권5호
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• pp.499-511
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• 2023

Anchor channels are commonly used for façade, tunnel, and structural connections. These connections encounter various types of loadings during their service life, including high rate or impact loading. For anchor channels that are placed close and parallel to an edge and loaded in shear perpendicular to and towards the edge, the failure is often governed by concrete edge breakout. This study investigates the transverse shear behavior of the anchor channels under quasi-static and high rate loadings using a numerical approach (3D finite element analysis) utilizing a rate-sensitive microplane model for concrete as constitutive law. Following the validation of the numerical model against a test performed under quasi-static loading, the rate-sensitive static, and rate-sensitive dynamic analyses are performed for various displacement loading rates varying from moderately high to impact. The increment in resistance due to the high loading rate is evaluated using the dynamic increase factor (DIF). Furthermore, it is shown that the failure mode of the anchor channel changes from global concrete edge failure to local concrete crushing due to the activation of structural inertia at high displacement loading rates. The research outcomes could be valuable for application in various types of connection systems where a high rate of loading is expected.

• Structural Engineering and Mechanics
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• 제85권4호
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• pp.433-443
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• 2023

The current paper discusses the dynamic and stability responses of cross-ply composite laminated plates by employing a refined quasi-3D trigonometric shear deformation theory. The proposed theory takes into consideration shear deformation and thickness stretching by a trigonometric variation of in-plane and transverse displacements through the plate thickness and assures the vanished shear stresses conditions on the upper and lower surfaces of the plate. The strong point of the new formulation is that the displacements field contains only 4 unknowns, which is less than the other shear deformation theories. In addition, the present model considers the thickness extension effects (ε_z≠0). The presence of the Winkler-Pasternak elastic base is included in the mathematical formulation. The Hamilton's principle is utilized in order to derive the four differentials' equations of motion, which are solved via Navier's technique of simply supported structures. The accuracy of the present 3-D theory is demonstrated by comparing fundamental frequencies and critical buckling loads numerical results with those provided using other models available in the open literature.

• 조명전기설비학회논문지
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• 제23권1호
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• pp.141-149
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• 2009

본 논문에서는 준정적 FDTD 기법을 FORTRAN 프로그래밍을 통해 직접 구현하고 이를 이용해 중간주파수 대역의 인체유도전류 분포를 해석하였다. 제작된 프로그램의 타당성을 검증하기 위하여 기존 FDTD 기법을 적용하기 어려운 테스트 모델에 대한 계산결과를 이론적 해와 비교하고, 타임스텝이 크게($5.68{\times}10^6$배) 단축되는 것을 확인하였다. 검증된 수치해석 기법을 이용하여 20[kHz] 자기장과 1[MHz] 전기장에 노출된 3차원 고해상도 인체모델에 유기되는 유도전류의 분포를 계산하고, 양 발의 접지조건이 유도전류의 분포와 크기에 미치는 영향을 분석하였다. 본 연구는 인체유도전류의 안전성 평가, 생체전기 응용 진단장치 개발 등을 포함한 다양한 분야에서 활용될 것으로 기대된다.

• Geomechanics and Engineering
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• 제16권2호
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• pp.141-150
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• 2018

In this current work a quasi 3D "trigonometric shear deformation theory" is proposed and discussed for the dynamic of thick orthotropic plates. Contrary to the classical "higher order shear deformation theories" (HSDT) and the "first shear deformation theory" (FSDT), the constructed theory utilizes a new displacement field which includes "undetermined integral terms" and presents only three "variables". In this model the axial displacement utilizes sinusoidal mathematical function in terms of z coordinate to introduce the shear strain impact. The cosine mathematical function in terms of z coordinate is employed in vertical displacement to introduce the impact of transverse "normal deformation". The motion equations of the model are found via the concept of virtual work. Numerical results found for frequency of "flexural mode", mode of shear and mode of thickness stretch impact of dynamic of simply supported "orthotropic" structures are compared and verified with those of other HSDTs and method of elasticity wherever considered.

• Structural Engineering and Mechanics
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• 제56권2호
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• pp.223-240
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• 2015

In this work, a nonlocal quasi-3D trigonometric plate theory for micro/nanoscale plates is proposed. In order to introduce the size influences, the Eringen's nonlocal elasticity theory is utilized. In addition, the theory considers both shear deformation and thickness stretching effects by a trigonometric variation of all displacements within the thickness, and respects the stress-free boundary conditions on the top and bottom surfaces of the plate without considering the shear correction factor. The advantage of this theory is that, in addition to considering the small scale and thickness stretching effects (${\varepsilon}_z{\neq}0$), the displacement field is modelled with only 5 unknowns as the first order shear deformation theory (FSDT). Analytical solutions for vibration of simply supported micro/nanoscale plates are illustrated, and the computed results are compared with the available solutions in the literature and finite element model using ABAQUS software package. The influences of the nonlocal parameter, shear deformation and thickness stretching on the vibration behaviors of the micro/nanoscale plates are examined.