• Wind and Structures
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• 제26권6호
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• pp.355-367
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• 2018

This paper studies the aerodynamic stability of a tensioned, geometrically nonlinear orthotropic membrane structure with hyperbolic paraboloid in sag direction. Considering flow separation, the wind field around membrane structure is simulated as the superposition of a uniform flow and a continuous vortex layer. By the potential flow theory in fluid mechanics and the thin airfoil theory in aerodynamics, aerodynamic pressure acting on membrane surface can be determined. And based on the large amplitude theory of membrane and D'Alembert's principle, interaction governing equations of wind-structure are established. Then, under the circumstance of single-mode response, the Bubnov-Galerkin approximate method is applied to transform the complicated interaction governing equations into a system of second-order nonlinear differential equation with constant coefficients. Through judging the frequency characteristic of the system characteristic equation, the critical velocity of divergence instability is determined. Different parameter analysis shows that the orthotropy, geometrical nonlinearity and scantling of structure is significant for preventing destructive aerodynamic instability in membrane structures. Compared to the model without considering flow separation, it's basically consistent about the divergence instability regularities in the flow separation model.

• Smart Structures and Systems
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• 제22권1호
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• pp.105-120
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• 2018

In this paper, the nonlinear free and forced vibration responses of sandwich nano-beams with three various functionally graded (FG) patterns of reinforced carbon nanotubes (CNTs) face-sheets are investigated. The sandwich nano-beam is resting on nonlinear Visco-elastic foundation and is subjected to thermal and electrical loads. The nonlinear governing equations of motion are derived for an Euler-Bernoulli beam based on Hamilton principle and von Karman nonlinear relation. To analyze nonlinear vibration, Galerkin's decomposition technique is employed to convert the governing partial differential equation (PDE) to a nonlinear ordinary differential equation (ODE). Furthermore, the Multiple Times Scale (MTS) method is employed to find approximate solution for the nonlinear time, frequency and forced responses of the sandwich nano-beam. Comparison between results of this paper and previous published paper shows that our numerical results are in good agreement with literature. In addition, the nonlinear frequency, force response and nonlinear damping time response is carefully studied. The influences of important parameters such as nonlocal parameter, volume fraction of the CNTs, different patterns of CNTs, length scale parameter, Visco-Pasternak foundation parameter, applied voltage, longitudinal magnetic field and temperature change are investigated on the various responses. One can conclude that frequency of FG-AV pattern is greater than other used patterns.

• Structural Engineering and Mechanics
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• 제42권4호
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• pp.589-608
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• 2012

In this study, the effect of in-plane deformations on the dynamic behavior of laminated plates is investigated. For this purpose, the displacement-time and strain-time histories obtained from the large deflection analysis of laminated plates are compared for the cases with and without including in-plane deformations. For the first one, in-plane stiffness and inertia effects are considered when formulating the dynamic response of the laminated composite plate subjected to the blast loading. Then, the problem is solved without considering the in-plane deformations. The geometric nonlinearity effects are taken into account by using the von Karman large deflection theory of thin plates and transverse shear stresses are ignored for both cases. The equations of motion for the plate are derived by the use of the virtual work principle. Approximate solution functions are assumed for the space domain and substituted into the equations of motion. Then, the Galerkin method is used to obtain the nonlinear algebraic differential equations in the time domain. The effects of the magnitude of the blast load, the thickness of the plate and boundary conditions on the in-plane deformations are investigated.

• Smart Structures and Systems
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• 제5권6호
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• pp.613-632
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• 2009

The present paper is concerned with the design of a proper patch actuator network in order to track a desired displacement of the sidewalls of a one-storey frame structure; both, for the static and the dynamic case. Weights for each patch of the actuator network found in our previous work were based on beam theory; in the present paper a refinement of these weights by modeling the sidewalls of the frame structure as thin plates is presented. For the sake of calculating the refined weights approximate solutions of the plate equations are calculated by an extended Galerkin method. The solutions based on the analytical plate model are compared with three-dimensional Finite Element results computed in the commercially available code ANSYS. The patch actuator network is put into practice by means of four piezoelectric patches attached to each of the two sidewalls of the frame structures, to which electric voltages proportional to the analytically refined patch weights are applied. Analytical and numerical results coincide very well over a broad frequency range.

• Nuclear Engineering and Technology
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• 제26권2호
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• pp.212-224
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• 1994

원형도관내의 비점성유동장에 놓인 동심인 유연성 실린더의 안정성을 분석하기 위하여 수치해석적방법이 개발되었다. 진동하는 실린더에 작용하는 비정상·비점성 유체유발력을 스펙트럼 배치방법을 사용하여 지배방정식을 단순화시키지 않음으로서 더 정밀하게 예측하였다. 본 수치해석이론은 기존의 퍼텐샬이론과 비해 비교적 넓은 환의 경우와 짧은 실린더의 경우에도 적용할 수 있다. 비점성유동의 지배방정식은 라플라스방정식으로부터 구하였다. 유체유동과 결부된 실린더의 유동방정식은 갤러킨의 방법에 의하여 불연속방정식으로 표시되며 이로부터 계의 운동특성을 검토하였다. 계가 좌굴현상에 의하여 안정성을 잃는 임계유속에 대한 환의 간격과 실린더의 길이의 영향이 검토되었다. 수치해석방법을 입증하기 위하여 얇은 막 근사이론에 근거를 두고 호프슨이 제안한 퍼텐샬이론을 개선하였다. 계의 안정성과 동적특성을 수치해석방법에 의하여 예시하였고 기존의 이론과 본 연구에서 제안된 근사법으로 구한 결과와 비교하여 잘 일치함을 보였다. 무차원화된 임계유속은 환의 간격이 넓을수록 실린더의 길이 가 짧을수록 증가함을 보였다.

• Structural Engineering and Mechanics
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• 제90권6호
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• pp.551-568
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• 2024

The present study deals with static and dynamic behaviors including forced vibrations of an elastic rectangular nano plate on the two-parameter foundation. Firstly, the rectangular plate is assumed to be subjected to uniformly distributed and eccentrically applied concentrated loads. The governing equations of the problem are derived by considering the dynamic response of the plate, employing a series of the Chebyshev polynomials for the displacement function and applying the Galerkin method. Then, effects of the non-essential boundary conditions of the plate, i.e., the boundary conditions related to the shearing forces, the bending moments and the corner forces, are included in the governing equation of motion to compensate for the non-satisfied boundary conditions and increase the accuracy of the Galerkin method. The approximate numerical solution is accomplished using an iterative process due to the non-linearity of the unilateral property of the two-parameter foundation. The plate under static concentrated load is investigated in detail numerically by considering a wide range of parameters of the plate and the foundation stiffnesses. Numerical treatment of the problem in the time domain is carried out by assuming a stepwise variation of the concentrated load and the linear acceleration procedure is employed in the solution of the system of governing differential equations derived from the equation of motion. Time variations of the contact region and those of the displacements of the plate are presented in the figures for various numbers of the two-parameter of the foundation, as well as the classical and nano parameters of the plate particularly focusing on the non-linearity of the problem due to the plate lift-off from the unilateral foundation. The effects of classical and nonlocal parameters and loading are investigated in detail. Definition of the separation between the plate and the two-parameter foundation is presented and applied to the given problem. The effect of the lift-off on the static and dynamic behavior of the rectangular plate is studied in detail by considering various loading conditions. The numerical study shows that the effect of nonlocal parameters on the behavior of the plate becomes significant, when nonlinearity becomes more profound, due to the lift-off of the plate. It is seen that the size effects are significant in static and dynamic analysis of nano-scaled rectangular plates and need to be included in the mechanical analyses. Furthermore, the corner displacement of the plate is affected more significantly from the lift-off, whereas it is less marked in the time variation of the middle displacement of the plate. Several numerical examples are presented to examine the sensibility of various parameters associated with nonlocal parameters of the plate and foundation. Both stiffening and softening nonlocal parameters behavior of the plate are identified in the numerical solutions which show that increasing the foundation stiffness decreases the extent of the contact region, whereas the stiffness of the shear layer increases the contact region and reduces the foundation settlement considerably.

• 한국전산응용수학회:학술대회논문집
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• 한국전산응용수학회 2003년도 KSCAM 학술발표회 프로그램 및 초록집
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• pp.1-1
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• 2003

In this talk, a reduced-order modeling methodology based on centroidal Voronoi tessellations (CVT's)is introduced. CVT's are special Voronoi tessellations for which the generators of the Voronoi diagram are also the centers of mass (means) of the corresponding Voronoi cells. The discrete data sets, CVT's are closely related to the h-means clustering techniques. Even with the use of good mesh generators, discretization schemes, and solution algorithms, the computational simulation of complex, turbulent, or chaotic systems still remains a formidable endeavor. For example, typical finite element codes may require many thousands of degrees of freedom for the accurate simulation of fluid flows. The situation is even worse for optimization problems for which multiple solutions of the complex state system are usually required or in feedback control problems for which real-time solutions of the complex state system are needed. There hava been many studies devoted to the development, testing, and use of reduced-order models for complex systems such as unsteady fluid flows. The types of reduced-ordered models that we study are those attempt to determine accurate approximate solutions of a complex system using very few degrees of freedom. To do so, such models have to use basis functions that are in some way intimately connected to the problem being approximated. Once a very low-dimensional reduced basis has been determined, one can employ it to solve the complex system by applying, e.g., a Galerkin method. In general, reduced bases are globally supported so that the discrete systems are dense; however, if the reduced basis is of very low dimension, one does not care about the lack of sparsity in the discrete system. A discussion of reduced-ordering modeling for complex systems such as fluid flows is given to provide a context for the application of reduced-order bases. Then, detailed descriptions of CVT-based reduced-order bases and how they can be constructed of complex systems are given. Subsequently, some concrete incompressible flow examples are used to illustrate the construction and use of CVT-based reduced-order bases. The CVT-based reduced-order modeling methodology is shown to be effective for these examples and is also shown to be inexpensive to apply compared to other reduced-order methods.