• Steel and Composite Structures
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• 제48권3호
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• pp.335-351
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• 2023

This research studies the primary resonance and nonlinear vibratory responses of multilayer functionally graded shallow (MFGS) shells under external excitations. The shells considered with functionally graded porous (FGP) core and resting on two types of nonlinear viscoelastic foundations (NVEF) governed by either a linear model with two parameters of Winkler and Pasternak foundations or a nonlinear model of hardening/softening cubic stiffness augmented by a Kelvin-Voigt viscoelastic model. The shells considered have three layers, sandwiched by functionally graded (FG), FGP, and FG materials. To investigate the influence of various porosity distributions, two types of FGP middle layer cores are considered. With the first-order shear deformation theory (FSDT), Hooke's law, and von-Kármán equation, the stress-strain relations for the MFGS shells with FGP core are developed. The governing equations of the shells are consequently derived. For the sake of higher accuracy and reliability, the P-T method is implemented in numerically analyzing the vibration, and the method of multiple scales (MMS) as one of the perturbation methods is used to investigate the primary resonance. The results of the present research are verified with the results available in the literature. The analytical results are compared with the P-T method. The influences of material, geometry, and nonlinear viscoelastic foundation parameters on the responses of the shells are illustrated.

• Structural Engineering and Mechanics
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• 제86권4호
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• pp.519-533
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• 2023

This work focuses on the dynamic analysis of thermal barrier coated straight and curved turbine blades modelled as functionally graded sandwich panel under thermal environment. The pre- twisted straight/curved blade model is considered to be fixed to the hub and, the complete assembly of the hub and blade are assumed to be rotating. The functionally graded sandwich composite blade is comprised of functionally graded face-sheet material and metal alloy core. The constituents' material properties are assumed to be temperature-dependent, however, the overall properties are evaluated using Voigt's micromechanical scheme in conjunction with the modified power-law functions. The blade model kinematics is based on the equivalent single-layer shear deformation theory. The equations of motion are derived using the extended Hamilton's principle by including the effect of centrifugal forces, and further solved via 2D- isoparametric finite element approximations. The mesh refinement and validation tests are performed to illustrate the stability and accurateness of the present model. In addition, frequency characteristics of the pre-twisted rotating sandwich blades are computed under thermal environment at various sets of parametric conditions such as twist angles, thickness ratios, aspect ratios, layer thickness ratios, volume fractions, rotational velocity and blade curvatures which can be further useful for designing the blade type structures under turbine operating conditions.

• Steel and Composite Structures
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• 제44권5호
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• pp.633-649
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• 2022

This paper is first implemented with the bending behavior of three-dimensional functionally graded (3DFG) plates in the framework of level set-based topology optimization (LS-based TO). Besides, due to the suitable properties of the current design domain, the thin-plate spline (TPS) is recognized as a RBF to construct the LS function. The overall mechanical properties of the 3DFG plate are assessed using a power-law distribution scheme via Mori-Tanaka micromechanical material model. The bending response is obtained using the first-order shear deformation theory (FSDT). The mixed interpolation of four elements of tensorial components (MITC4) is also implemented to overcome a well-known shear locking problem when the thickness becomes thinner. The Hamilton-Jacobi method is utilized in each iteration to enforce the necessary boundary conditions. The mathematical formulas are expressed in great detail for the LS-based TO using 3DFG materials. Several numerical examples are exhibited to verify the efficiency and reliability of the current methodology with the previously reported literature. Finally, the influences of FG materials in the optimized design are explained in detail to illustrate the behaviors of optimized structures.

• Geomechanics and Engineering
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• 제35권4호
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• pp.367-383
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• 2023

The present paper examines the natural frequency responses of the bi-directional (n_x-n_y, n_y-n_z and n_z-n_x) and multidirectional (n_x-n_y-n_z) functionally graded (FG) plate and curved structures with and without porosity. The even and uneven kind of porosity pattern are considered to observe the influence of porosity type and porosity index. The numerical findings have been obtained using a higher order shear deformation theory (HSDT) based isometric finite element (FE) approach generated in a MATLAB platform. According to the convergence and validation investigation, the proposed HSDT based FE model is adequate to predict free vibrational responses of multidirectional porous FG plates and curved structures. Further a parametric analysis is carried out by taking various design parameters into account. The free vibrational behavior of bidirectional (2D) and multidirectional (3D) perfect-imperfect FGM structure is examined against various power law index, support conditions, aspect, and thickness ratio, and for the curvature of curved structures. The results indicate that the maximum non-dimensional fundamental frequency (NFF) value is observed in perfect FGM plates and curved structures compared to porous FGM plates and curved structures and it is maximum for FGM plates and curved structures with uneven kind of porosity than even porosity.

• Structural Engineering and Mechanics
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• 제90권1호
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• pp.1-18
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• 2024

The present study conducts a thorough analysis of thermal vibrations in functionally graded porous nanocomposite beams within a thermal setting. Investigating the temperature-dependent material properties of these beams, which continuously vary across their thickness in accordance with a power-law function, a finite element approach is developed. This approach utilizes a nonlocal strain gradient theory and accounts for a linear temperature rise. The analysis employs four different patterns of porosity distribution to characterize the functionally graded porous materials. A novel two-variable shear deformation beam nonlocal strain gradient theory, based on trigonometric functions, is introduced to examine the combined effects of nonlocal stress and strain gradient on these beams. The derived governing equations are solved through a 3-nodes beam element. A comprehensive parametric study delves into the influence of structural parameters, such as thicknessratio, beam length, nonlocal scale parameter, and strain gradient parameter. Furthermore, the study explores the impact of thermal effects, porosity distribution forms, and material distribution profiles on the free vibration of temperature-dependent FG nanobeams. The results reveal the substantial influence of these effects on the vibration behavior of functionally graded nanobeams under thermal conditions. This research presents a finite element approach to examine the thermo-mechanical behavior of nonlocal temperature-dependent FG nanobeams, filling the gap where analytical results are unavailable.

• Steel and Composite Structures
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• 제50권2호
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• pp.149-158
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• 2024

Considering that different boundary conditions can have an important impact on structural vibration characteristics. In this paper, the nonlinear forced vibration behavior of functionally graded material (FGM) doubly curved shells with initial geometric imperfections under different boundary conditions is studied. Considering initial geometric imperfections and von Karman geometric nonlinearity, the nonlinear governing equations of FGM doubly curved shells are derived using Reissner's first order shear deformation (FOSD) theory. Three different boundary conditions of four edges simply supported (SSSS), four edges clamped (CCCC), clamped-clamped-simply-simply (CCSS) were studied, and a system of nonlinear ordinary differential equations was obtained with the help of Galerkin principle. The nonlinear forced vibration response of the FGM doubly curved shell is obtained by using the modified Lindstedt Poincare (MLP) method. The accuracy of this method was verified by comparing it with published literature. Finally, the effects of curvature ratio, power law index, void coefficient, prestress, and initial geometric imperfections on the resonance of FGM doubly curved shells under different boundary conditions are fully discussed. The relevant research results can provide certain guidance for the design and application of doubly curved shell.

• Computers and Concrete
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• 제33권3호
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• pp.275-284
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• 2024

This work presents a comprehensive investigation of buckling behavior of bidirectional functionally graded imperfect beams exposed to several thermal loading with general boundary conditions. The nonlinear governing equations are derived based on 2D shear deformation theory together with Von Karman strain-displacement relation. The beams are composed of two different materials. Its properties are porosity-dependent and are continuously distributed over the length and thickness of the beams following a defined law. The resulting equations are solved analytically in order to determine the thermal buckling characteristics of BDFG porous beams. The precision of the current solution and its accuracy have been proven by comparison with works previously published. Numerical examples are presented to explore the effects of the thermal loading, the elastic foundation parameters, the porosity distribution, the grading indexes and others factors on the nonlinear thermal buckling of bidirectional FG beam rested on elastic foundation.

• Nuclear Engineering and Technology
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• 제55권12호
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• pp.4561-4569
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• 2023

A correct understanding of vibration-based degradation is crucial from the standpoint of maintenance for Steam Generators (SG) as crucial mechanical equipment in nuclear power plants. This study has established a novel approach to developing a model for investigating tube bundle degradation according to crack growth caused by two-phase Flow-Induced Vibration (FIV). An important step in the approach is to calculate the two-phase flow field parameters between the SG tube bundles in various zones using the porous media model to determine the velocity and vapor volume fraction. Afterward, to determine the vibration properties of the tube bundles, the Fluid-Solid Interaction (FSI) analysis is performed in eighteen thermal-hydraulic zones. Tube bundle degradation based on crack growth using the sixteen most probable initial cracks and within each SG thermal-hydraulic zone is performed to calculate useful lifetime. Large Eddy Simulation (LES) model, Paris law, and Wiener process model are considered to model the turbulent crossflow around the tube bundles, simulation of elliptical crack growth due to the vibration characteristics, and estimation of SG tube bundles degradation, respectively. The analysis shows that the tube deforms most noticeably in the zone with the highest velocity. As a result, cracks propagate more quickly in the tube with a higher height. In all simulations based on different initial crack sizes, it was observed that zone 16 experiences the greatest deformation and, subsequently, the fastest degradation, with a velocity and vapor volume fraction of 0.5 m/s and 0.4, respectively.

• Advances in nano research
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• 제16권4호
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• pp.395-412
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• 2024

This article develops a nonclassical size dependent nanoplate model to study the dynamic response of functionally graded carbon nanotube (FGCNT) nanoplates under a moving load. Both nonlocal and microstructure effects are incorporated through the nonlocal strain gradient elasticity theory. To investigate the effect of reinforcement orientation of CNT, four different configurations are studied and analysed. The FGM gradation thorough the thickness direction is simulated using the power law. In the context of the first order shear deformation theory, the dynamic equations of motion and the associated boundary conditions are derived by Hamilton's principle. An analytical solution of the dynamic equations of motion is derived based on the Navier methodology. The proposed model is verified and compared with the available results in the literature and good agreement is found. The numerical results show that the dynamic performance of FGCNT nanoplates could be governed by the reinforcement pattern and volume fraction in addition to the non-classical parameters and the moving load dimensionless parameter. Obtained results are reassuring in design and analysis of nanoplates reinforced with CNTs.

• 대한토목학회논문집
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• 제7권1호
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• pp.141-150
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• 1987

1973년(年)에 완공(完工)된 소양강댐은 매설계기가 잘 설치되어 그 댐의 응력(應力)과 변형(變形)의 측정결과는 이미 발표된 바 있다. 그러나 이론적(理論的)인 해석은 지금까지 이루어지지 않았다. 본(本)연구(硏究)는 시공시(施工時) 재료의 자중을 받고 또 담수시 물 하중을 받게 되는 댐 본체의 응력(應力)과 변형(變形) 거동을 수치적(數値的)으로 해석하려는데 그 목적(目的)이 있다. 해석(解析)에 사용(使用)된 구성법칙(構成法則)은 Duncan 등(等)이 개발한 hyperbolic 모델이며, 시공단계(施工段階)를 모방한 비선형증가(非線型增加) 유한요소해석(有限要素解析)이 본(本) 연구(硏究)에 적용되었다. hyperbolic 파라미터들은 문헌에서 추정하여 사용(使用)하였다. 이론적(理論的) 해석(解析)으로부터 얻어진 결과는 댐의 임의의 단면에서의 변형특성과 응력벡타를 명확(明確)하게 나타내었다. 해석결과는 최대단면(最大斷面)에서의 변형측정치(變形測定値)와 잘 일치(一致)하였으나 수평변형(水平變形)과 심벽(心壁)에 생긴 응력에 있어서는 약간의 차이를 보였다. 수치해석과 측정치와의 비교(比較)로부터 얻은 본댐의 거동의 특징(特徵)은 심벽에서 비교적(比較的) 큰 시공침하(施工沈下)가 생겼고, 심벽의 토피하중(土被荷重)은 아아칭 효과에 의해 상당히 감소되었고, 또 양안부근(兩岸附近)에서는 수평변위(水平變位)가 커서 인장구역(引張區域)이 생길 수 있다는 것이다.