• Steel and Composite Structures
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• 제27권1호
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• pp.109-122
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• 2018

In This work an analysis of the propagation of waves of functionally graduated plates is presented by using a high order hyperbolic (HSDT) shear deformation theory. This theory has only four variables, which is less than the theory of first order shear deformation (FSDT). Therefore, a shear correction coefficient is not required. Unlike other conventional shear deformation theories, the present work includes a new field of displacement which introduces indeterminate integral variables. The properties of materials are supposed classified in the direction of the thickness according to two simple distributions of a power law in terms of volume fractions of constituents. The governing equations of the wave propagation in the functionally graded plate are derived by employing the Hamilton's principle. The analytical dispersion relation of the functionally graded plate is obtained by solving an eigenvalue problem. The convergence and the validation of the proposed theoretical numerical model are performed to demonstrate the efficacy of the model.

• International Journal of Aeronautical and Space Sciences
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• 제18권2호
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• pp.255-269
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• 2017

Free vibration analysis is presented for a simply-supported, functionally graded piezoelectric (FGP) nanobeam embedded on elastic foundation in the framework of third order parabolic shear deformation beam theory. Effective electro-mechanical properties of FGP nanobeam are supposed to be variable throughout the thickness based on power-law model. To incorporate the small size effects into the local model, Eringen's nonlocal elasticity theory is adopted. Analytical solution is implemented to solve the size-dependent buckling analysis of FGP nanobeams based upon a higher order shear deformation beam theory where coupled equations obtained using Hamilton's principle exist for such beams. Some numerical results for natural frequencies of the FGP nanobeams are prepared, which include the influences of elastic coefficients of foundation, electric voltage, material and geometrical parameters and mode number. This study is motivated by the absence of articles in the technical literature and provides beneficial results for accurate FGP structures design.

• Wind and Structures
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• 제29권6호
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• pp.371-387
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• 2019

In the present paper, a simple refined nth-higher-order shear deformation theory is applied for the free vibration analysis of laminated composite plates. The proposed displacement field is based on a novel kinematic in which include the undetermined integral terms and contains only four unknowns, as against five or more in case of other higher-order theories. The present theory accounts for adequate distribution of the transverse shear strains through the plate thickness and satisfies the shear stress-free boundary conditions on the top and bottom surfaces of the plate, therefore, it does not require problem dependent shear correction factor. The governing equations of motion are derived from Hamilton's principle and solved via Navier-type to obtain closed form solutions. The numerical results of non-dimensional natural frequencies obtained by using the present theory are presented and compared with those of other theories available in the literature to verify the validity of present solutions. It can be concluded that the present refined theory is accurate and efficient in predicting the natural frequencies of isotropic, orthotropic and laminated composite plates.

• Steel and Composite Structures
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• 제28권1호
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• pp.13-24
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• 2018

A size-dependent novel hyperbolic shear deformation theory of simply supported functionally graded beams is presented in the frame work of the non-local strain gradient theory, in which the stress accounts for only the nonlocal strain gradients stress field. The thickness stretching effect (${\varepsilon}_z{\neq}0$) is also considered here. Elastic coefficients and length scale parameter are assumed to vary in the thickness direction of functionally graded beams according to power-law form. The governing equations are derived using the Hamilton principle. The closed-form solutions for exact critical buckling loads of nonlocal strain gradient functionally graded beams are obtained using Navier's method. The derived results are compared with those of strain gradient theory.

• Structural Engineering and Mechanics
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• 제58권3호
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• pp.397-422
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• 2016

In the present work, a simple first-order shear deformation theory is developed and validated for a variety of numerical examples of the thermal buckling response of functionally graded sandwich plates with various boundary conditions. Contrary to the conventional first-order shear deformation theory, the present first-order shear deformation theory involves only four unknowns and has strong similarities with the classical plate theory in many aspects such as governing equations of motion, and stress resultant expressions. Material properties and thermal expansion coefficient of the sandwich plate faces are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The core layer is still homogeneous and made of an isotropic material. The thermal loads are considered as uniform, linear and non-linear temperature rises within the thickness direction. The results reveal that the volume fraction index, loading type and functionally graded layers thickness have significant influence on the thermal buckling of functionally graded sandwich plates. Moreover, numerical results prove that the present simple first-order shear deformation theory can achieve the same accuracy of the existing conventional first-order shear deformation theory which has more number of unknowns.

• Geomechanics and Engineering
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• 제13권3호
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• pp.385-410
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• 2017

This work presents a simple and refined nth-order shear deformation theory for mechanical and thermal buckling behaviors of functionally graded (FG) plates resting on elastic foundation. The proposed refined nth-order shear deformation theory has a new displacement field which includes undetermined integral terms and contains only four unknowns. Governing equations are obtained from the principle of minimum total potential energy. A Navier type analytical solution methodology is also presented for simply supported FG plates resting on elastic foundation which predicts accurate solution. The accuracy of the present model is checked by comparing the computed results with those obtained by classical plate theory (CPT), first-order shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). Moreover, results demonstrate that the proposed theory can achieve the same accuracy of the existing HSDTs which have more number of variables.

• 대한간호학회지
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• 제42권5호
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• pp.659-670
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• 2012

Purpose: The purpose of this study was to verify effects of the Active Parenting Today (APT) program based on King's Goal Attainment Theory on parenting stress, parenting behavior, and parenting satisfaction in mothers of school-age children. Methods: This was a quasi-experimental study with a non-equivalent control group pre-post test design. Participants were 39 mothers of school-age children (19 in the experiment group and 20 in the control group) who were registered at two community children centers in G city. The experimental group received the APT program (2 hours/session/week) and telephone counseling (2 times/week) for 8 weeks. Data were analyzed using ${\chi}^2$-test, t-test, Fisher exact probability test, and ANCOVA with the SPSS/Win15.0 program. Results: Parenting stress was significantly lower in the experimental group than in the control group. Positive parenting behavior and parenting satisfaction were significantly higher in the experimental group than in the control group. However, negative parenting behavior was not significantly different between the two groups. Conclusion: The results of this study indicate that the APT program based on King's Goal Attainment Theory is useful in reducing parenting stress, creating positive parenting behavior change, and promoting parenting satisfaction in mothers of school-age children.

• Geomechanics and Engineering
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• 제37권5호
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• pp.453-465
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• 2024

This paper presents a logarithmic shear deformation theory to study the thermal buckling response of power-law FG one-dimensional structures in thermal conditions with different boundary conditions. It is assumed that the functionally graded material and thermal properties are supposed to vary smoothly according to a contentious function across the vertical direction of the beams. A P-FG type function is employed to describe the volume fraction of material and thermal properties of the graded (1D) beam. The Ritz model is employed to solve the thermal buckling problems in immovable boundary conditions. The outcomes of the stability analysis of FG beams with temperature-dependent and independent properties are presented. The effects of the thermal loading are considered with three forms of rising: nonlinear, linear and uniform. Numerical results are obtained employing the present logarithmic theory and are verified by comparisons with the other models to check the accuracy of the developed theory. A parametric study was conducted to investigate the effects of various parameters on the critical thermal stability of P-FG beams. These parameters included support type, temperature fields, material distributions, side-to-thickness ratios, and temperature dependency.

• 동양고전연구
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• 제59호
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• pp.297-324
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• 2015

이 논문은 한국의 대표적인 경학자인 다산(茶山) 정약용(丁若鏞)(1762-1836)의 "서경" 인식을 고찰, 제시하는 것을 목표로 한다. 다산의 과제는 요순(堯舜)-주공(周公)-공자지도(孔子之道)라고 하는 본원유학의 원형과 정신을 복명(復命)하고, 그를 통해 질곡된 현실을 극복하는 데에 있었고, 그의 "서경"에 대한 관심과 해석 역시 여기에서 유래한다고 할 수 있다. 육서오경에 대한 방대한 식견과 청나라의 고증학적 경향, 심지어 일본의 유학연구에도 정통했던 다산은 "서경"에 대한 단순한 의문제기를 넘어, 체계 전반을 문제로 삼았다. 그래서 그는 후대 위작으로 간주된 고문(古文)의 유출경위를 증명하고, 방대한 자료를 검토하여 원 자료의 수집과 채록을 통해 "서경"의 본모습을 회복하려고 시도했다. 이 글은 다산의 이러한 시도에서 드러난 "서경"에 대한 인식과 그 특징을 제시하려고 했다. 이를 위해 우선 "서경"이란 어떤 책이며, 왜 다른 어떤 경전보다 유독 판본과 진위 문제가 항상 발생하였는지에 대해 살펴보고자 한다. 그런 다음 다산의 "서경" 연구과정을 서술하고, 거기서 나타난 다산의 관점과 특징을 대표작인 "매씨서평" 및 그 뒤의 저술들을 중심으로 고찰하고자 한다. 다산은 "서경"을 정치의 표준이 제시되어 있는 옛 성인의 정사를 알려주는 역사책으로 이해하였다. 그리고 이러한 표준을 제대로 알아 소통하기만 하면 곧바로 현실에 응용하여, 적용할 수 있다고 판단했다. 그런데 그는 "서경"을 알기 위해서는 당연히 자구에 대한 훈고(訓?)가 우선되어야 한다고 생각했다. 그런데 자구에 대한 훈고를 이루려 하면 우선 경문(經文)이 정립되어 있어야 하는데, "서경"은 잔결(殘缺)이 가장 많은 경전이라 할 수 있다. 그래서 그는 당시 통행되고 있던 "상서" 중에서 후대에 위조된 부분을 변별한 다음, 그 본 모습을 회복하려고 시도한다. 다산이 회복하려고 했던 원형 "상서"란 공자가 직접 산정하고 서(序)를 썼다고 말한 100편("우서(虞書)" 20편, "하서(夏書)" 40편, "주서(周書)" 40편)이었다. 그러나 그는 공자가 편집했던 "상서" 100편의 원형회복이란 진본이 망실되었기 때문에 사실상 불가능하다고 판단했다. 그래서 그는 우선 방대한 문헌적 지식을 원용하여 한대 이전의 경전 가운데 신뢰할 수 있는 것을 채록 배열한 다음 여러 학설을 모으고("상서고훈수략(尙書古訓蒐略)"), 수집된 고훈들의 동이(同異)를 대비하면서 자신의 의견을 덧붙여("상서지원록(尙書知遠錄)") 합본한다("상서고훈(尙書古訓)") 다산은 이런 시도의 목표는 "상서"를 해석하기 보다는 옛 원형을 보존하여(존고(存古)), "상서"의 본래 모습 혹은 대체(大體)을 알게 해 주는 단서를 제시하려는 것이었다.

• Steel and Composite Structures
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• 제35권5호
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• pp.671-685
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• 2020

This manuscript presents impacts of gradation of material functions and axial load functions on critical buckling loads and mode shapes of functionally graded (FG) thin and thick beams by using higher order shear deformation theory, for the first time. Volume fractions of metal and ceramic materials are assumed to be distributed through a beam thickness by both sigmoid law and symmetric power functions. Ceramic-metal-ceramic (CMC) and metal-ceramic-metal (MCM) symmetric distributions are proposed relative to mid-plane of the beam structure. The axial compressive load is depicted by constant, linear, and parabolic continuous functions through the axial direction. The equilibrium governing equations are derived by using Hamilton's principles. Numerical differential quadrature method (DQM) is developed to discretize the spatial domain and covert the governing variable coefficients differential equations and boundary conditions to system of algebraic equations. Algebraic equations are formed as a generalized matrix eigenvalue problem, that will be solved to get eigenvalues (buckling loads) and eigenvectors (mode shapes). The proposed model is verified with respectable published work. Numerical results depict influences of gradation function, gradation parameter, axial load function, slenderness ratio and boundary conditions on critical buckling loads and mode-shapes of FG beam structure. It is found that gradation types have different effects on the critical buckling. The proposed model can be effective in analysis and design of structure beam element subject to distributed axial compressive load, such as, spacecraft, nuclear structure, and naval structure.