• Structural Engineering and Mechanics
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• 제90권1호
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• pp.83-96
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• 2024

This paper suggests an analytical approach to investigate the free vibration and stability of functionally graded (FG) beams with both perfect and imperfect characteristics using a quasi-3D higher-order shear deformation theory (HSDT) with stretching effect. The study specifically focuses on FG beams resting on variable elastic foundations. In contrast to other shear deformation theories, this particular theory employs only four unknown functions instead of five. Moreover, this theory satisfies the boundary conditions of zero tension on the beam surfaces and facilitates hyperbolic distributions of transverse shear stresses without the necessity of shear correction factors. The elastic medium in consideration assumes the presence of two parameters, specifically Winkler-Pasternak foundations. The Winkler parameter exhibits variable variations in the longitudinal direction, including linear, parabolic, sinusoidal, cosine, exponential, and uniform, while the Pasternak parameter remains constant. The effective material characteristics of the functionally graded (FG) beam are assumed to follow a straightforward power-law distribution along the thickness direction. Additionally, the investigation of porosity includes the consideration of four different types of porosity distribution patterns, allowing for a comprehensive examination of its influence on the behavior of the beam. Using the virtual work principle, equations of motion are derived and solved analytically using Navier's method for simply supported FG beams. The accuracy is verified through comparisons with literature results. Parametric studies explore the impact of different parameters on free vibration and buckling behavior, demonstrating the theory's correctness and simplicity.

• Steel and Composite Structures
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• 제36권3호
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• pp.261-272
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• 2020

A novel precast concrete-encased steel composite beam, which can be abbreviated as PCES beam, is introduced in this paper. In order to investigate the shear behavior of this PCES beam, a test of eight full-scale PCES beam specimens was carried out, in which the specimens were subjected to positive bending moment or negative bending moment, respectively. The factors which affected the shear behavior, such as the shear span-to-depth aspect ratio and the existence of concrete flange, were taken into account. During the test, the load-deflection curves of the test specimens were recorded, while the crack propagation patterns together with the failure patterns were observed as well. From the test results, it could be concluded that the tested PCES beams could all exhibit ductile shear behavior, and the innovative shear connectors between the precast concrete and cast-in-place concrete, namely the precast concrete transverse diaphragms, were verified to be effective. Then, based on the shear deformation compatibility, a theoretical model for predicting the shear capacity of the proposed PCES beams was put forward and verified to be valid with the good agreement of the shear capacities calculated using the proposed method and those from the experiments. Finally, in order to facilitate the preliminary design in practical applications, a simplified calculation method for predicting the shear capacity of the proposed PCES beams was also put forward and validated using available test results.

• 한국강구조학회 논문집
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• 제12권6호
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• pp.749-758
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• 2000

본 연구는 지그재그모델에 근거하여 두꺼운 금속, 폴리머 복합재료 면재의 전단변형 효과를 고려해서 샌드위치평판의 휨해석 지배방정식을 유도하였으며, 판의 네 변은 단순지지 되어 있다고 가정하였다. 역대칭 적층면재의 화이버 각도와 면재의 적층수를 변화시켜가며 휨해석의 결과를 나타내었다. 해석방법의 정확성을 위해 일반 적층판이론의 값과 비교를 하여 검증을 하였다. 그 결과 적층판이론으로 구한 값보다 처짐에 있어서 더 큰 값을 나타냄을 알 수 있었는데, 그 이유로는 본 해석방법이 면재, 심재 모두 휨강성과 전단변형을 고려하였기 때문이라 사료된다. 강재, 폴리머 복합면재를 갖는 샌드위치평판을 설계할 때 제시된 정보를 유용하게 이용될 수 있을 것이다.

• 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.

• 한국강구조학회 논문집
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• 제18권3호
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• pp.289-299
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• 2006

강바닥판 교량은 비교적 얇은 강판을 서로 용접에 의해 연결한 구조물로서 많은 양의 용접을 피할 수 없다. 강바닥판의 횡리브복부판에서는 전단력과 비틀림 모멘트가 작용하는 동시에 종리브의 비틀림으로 인한 면내 면외 변형이 작용하기 때문에 종리브-횡리브 복부판-데크플레이트 교차부 및 횡리브복부판 컷아웃(슬릿)부에서 응력집중 현상이 두드러지게 발생하게 된다. 본 논문에서는 교차부 및 컷아웃(슬릿)부에서의 응력집중 현상 완화 및 피로성능 개선에 유리한 구조상세를 도출하고자 교차부에 스캘럽 유무 및 횡리브 복부판면과 일치되도록 종리브 내부에 설치하는 다이아프램의 설치 유무를 매개변수로 구조해석을 수행하였다. 다이아프램을 설치하는 동시에 교차부에 스캘럽을 두지 않을 경우 교차부 및 컷아웃(슬릿)부에서 최대응력 감소효과가 있음을 알 수 있었다. 따라서 교차부 및 컷아웃부에서의 응력집중 현상을 완화시켜 피로성능 개선에 기대효과가 있음을 알 수 있었다.

• Structural Engineering and Mechanics
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• 제41권2호
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• pp.205-229
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• 2012

This paper presents a new nine-node Lagrangian quadrilateral plate bending element (MQP9) using the Integrated Force Method (IFM) for the analysis of thin and moderately thick plate bending problems. Three degrees of freedom: transverse displacement w and two rotations ${\theta}_x$ and ${\theta}_y$ are considered at each node of the element. The Mindlin-Reissner theory has been employed in the formulation which accounts the effect of shear deformation. Many standard plate bending benchmark problems have been analyzed using the new element MQP9 for various grid sizes via Integrated Force Method to estimate defections and bending moments. These results of the new element MQP9 are compared with those of similar displacement-based plate bending elements available in the literature. The results are also compared with exact solutions. It is observed that the presented new element MQP9 is free from shear locking and produced, in general, excellent results in all plate bending benchmark problems considered.

• Advances in aircraft and spacecraft science
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• 제2권1호
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• pp.57-76
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• 2015

We investigated complex damped modes in beams in the presence of a viscoelastic layer sandwiched between two elastic layers. The problem was solved using two approaches, (1) Rayleigh beam theory and analyzed using the Ritz method, and (2) by using 2D plane stress elasticity based finite-element method. The damping in the layers was modeled using the complex modulus. Simply-supported, cantilever, and viscously supported boundary conditions were considered in this study. Simple trigonometric functions were used as admissible functions in the Ritz method. The key idea behind sandwich structure is to increase damping in a beam as affected by the presence of a highly-damped core layer vibrating mainly in shear. Different assumptions are utilized in the literature, to model shear deformation in the core layer. In this manuscript, we used FEM without any kinematic assumptions for the transverse shear in both the core and elastic layers. Moreover, numerical examples were studied, where the base and constraining layers were also damped. The loss factor was calculated by modal strain energy method, and by solving a complex eigenvalue problem. The efficiency of the modal strain energy method was tested for different loss factors in the core layer. Complex mode shapes of the beam were also examined in the study, and a comparison was made between viscoelastically and viscously damped structures. The numerical results were compared with those available in the literature, and the results were found to be satisfactory.

• Steel and Composite Structures
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• 제14권4호
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• pp.335-347
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• 2013

In this paper, the nonlinear cylindrical bending behavior of functionally graded nanocomposite plates reinforced by single-walled carbon nanotubes (SWCNTs) is studied using an efficient and simple refined theory. This theory is based on assumption that the in-plane and transverse displacements consist of bending and shear components in which the bending components do not contribute toward shear forces and, likewise, the shear components do not contribute toward bending moments. The material properties of SWCNTs are assumed to be temperature-dependent and are obtained from molecular dynamics simulations. The material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTCRs) are assumed to be graded in the thickness direction, and are estimated through a micromechanical model. The fundamental equations for functionally graded nanocomposite plates are obtained using the Von-Karman theory for large deflections and the solution is obtained by minimization of the total potential energy. The numerical illustrations concern the nonlinear bending response of FG-CNTRC plates under different sets of thermal environmental conditions, from which results for uniformly distributed CNTRC plates are obtained as comparators.

• Structural Engineering and Mechanics
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• 제18권6호
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• pp.807-829
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• 2004

The Element-Based Lagrangian Formulation of a 9-node resultant-stress shell element is presented for the isotropic and anisotropic composite material. The effect of the coupling term between the bending strain and displacement has been investigated in the warping problem. The strains, stresses and constitutive equations based on the natural co-ordinate have been used throughout the Element-Based Lagrangian Formulation of the present shell element which offers an advantage of easy implementation compared with the traditional Lagrangian Formulation. The element is free of both membrane and shear locking behavior by using the assumed natural strain method such that the element performs very well in thin shell problems. In composite plates and shells, the transverse shear stiffness is defined by an equilibrium approach instead of using the shear correction factor. The arc-length control method is used to trace complex equilibrium paths in thin shell applications. Several numerical analyses are presented and discussed in order to investigate the capabilities of the present shell element. The results showed very good agreement compared with well-established formulations in the literature.

• Steel and Composite Structures
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• 제24권5호
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• pp.603-613
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• 2017

In this research, the free vibration response of laminated composite plates is investigated using a novel and simple higher order shear deformation plate theory. The model considers a non-linear distribution of the transverse shear strains, and verifies the zero traction boundary conditions on the surfaces of the plate without introducing shear correction coefficient. The developed kinematic uses undetermined integral terms with only four unknowns. Equations of motion are obtained from the Hamilton's principle and the Navier method is used to determine the closed-form solutions of antisymmetric cross-ply and angle-ply laminates. Numerical examples studied using the present formulation is compared with three-dimensional elasticity solutions and those calculated using the first-order and the other higher-order theories. It can be concluded that the present model is not only accurate but also efficient and simple in studying the free vibration response of laminated composite plates.