• 한국군사과학기술학회지
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• 제12권6호
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• pp.785-795
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• 2009

In this paper, new type of finite element models for the analysis of nonlinear beam bending are developed by using unconventional residual minimizing method to increase accuracy of finite element solutions and overcome some of computational drawbacks. Developing procedures of the new models are presented along with the comparison of the numerical results of existing beam bending models.

• 대한기계학회논문집
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• 제1권3호
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• pp.141-145
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• 1977

In this paper, approximate solutions of the von Karman equations for the free flexural vibration of a transversely isotropic thin rectangular plate with two simply supported edges and two clamped edges are obtained. Applying one term Ritz-Galerkin procedure, the spatial dependent part of the equation is separated and time dependent function is found to be the Duffing's equation. Then the relation between nonlinear period and amplitude of the vibration is obtained by using averaging method which is a method of the perturbation procedure. It can be seen that averaging method is easy and agrees well with prior results.

• 소음진동
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• 제9권4호
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• pp.806-812
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• 1999

Dynamic behaviors are analyzed for a flexble spinning disk with angular acceleration, considering geometric nonlinearity. Based upon the Kirchhoff plate theory and the von Karman strain theory, the nonlinear governing equations are derived which are coupled equations with the in-plane and out-of-planedisplacements. The governing equations are discretized by using the Galerkin approximation. With the discretized nonlinear equations, the time responses are computed by using the generalized-$\alpha$ method and the Newton-Raphson method. The analysis shows that the existence of angular acceleration increases the displacements of the spinning disk and makes the disk unstable.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2001년도 춘계학술대회논문집
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• pp.897-903
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• 2001

The supersonic flutter analysis of cylindrical composite panels subject to thermal stresses has been performed using layerwise nonlinear finite elements. The geometric nonlinear finite elements of cylindrical shells are formulated using hamilton's principle with von Karman strain-displacement relationship. Hans Krumhaar's modified supersonic piston theory is appled to calculate aerodynamic loads for the panel flutter analysis. The present results show that the critical dynamic pressure of cylindrical panels under compressive thermal stresses can be dramatically reduced. The margin of aerothermoelastic stability considering thermal and aerodynamic coupling should be verified in the structural design of launch vehicles and high speed aircrafts.

• Steel and Composite Structures
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• 제26권6호
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• pp.733-743
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• 2018

This paper presents post-buckling responses of a simply supported laminated composite beam subjected to a non-follower axially compression loads. In the nonlinear kinematic model of the laminated beam, total Lagrangian approach is used in conjunction with the Timoshenko beam theory. In the solution of the nonlinear problem, incremental displacement-based finite element method is used with Newton-Raphson iteration method. There is no restriction on the magnitudes of deflections and rotations in contradistinction to von-Karman strain displacement relations of the beam. The distinctive feature of this study is post-buckling analysis of Timoshenko Laminated beams full geometric non-linearity and by using finite element method. The effects of the fibber orientation angles and the stacking sequence of laminates on the post-buckling deflections, configurations and stresses of the composite laminated beam are illustrated and discussed in the numerical results. Numerical results show that the above-mentioned effects play a very important role on the post-buckling responses of the laminated composite beams.

• Structural Engineering and Mechanics
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• 제19권5호
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• pp.535-550
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• 2005

The non-linear static and dynamic response of doubly curved thin isotropic shells has been studied for the step and sinusoidal loadings. Dynamic analogues Von Karman-Donnel type shell equations are used. Clamped immovable and simply supported immovable boundary conditions are considered. The governing nonlinear partial differential equations of the shell are discretized in space and time domains using the harmonic differential quadrature (HDQ) and finite differences (FD) methods, respectively. The accuracy of the proposed HDQ-FD coupled methodology is demonstrated by the numerical examples. Numerical examples demonstrate the satisfactory accuracy, efficiency and versatility of the presented approach.

• Advances in nano research
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• 제17권1호
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• pp.1-8
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• 2024

In this paper, stability analysis of sandwich toroidal shell segments (TSSs) with carbon nanotube (CNT)-reinforced face sheets featuring various types of auxetic cores, surrounded by elastic foundations under radial pressure is presented. Two distinct types of auxetic structures are considered for the core, including re-entrant auxetic structure and graphene origami (GOri)-enabled auxetic structure. The nonlinear stability equilibrium equations of the longitudinally shallow shells are formulated using the von Karman shell theory, in conjunction with Stein and McElman approximation while considering Winkler-Pasternak's elastic foundation to simulate the interaction between the shell and elastic foundation. The Galerkin method is employed to derive the nonlinear stability responses of the shells. The numerical investigations show the influences of various types of auxetic-core layers, CNT-reinforced face sheets, as well as elastic foundation on the stability of sandwich shells.

• Composites Research
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• 제13권5호
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• pp.50-59
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• 2000

본 논문에서는 복합재료 패널 플러터를 억제할 수 있는 두 가지 방법에 대해서 연구하였다. 첫번째, 능동제어 방법에서는 선형 제어 이론을 바탕으로 제어기를 설계하였으며 제어입력이 작동기에 가해진다. 여기서 작동기로는 PZT를 사용하였다. 두 번째, 인덕터와 저항으로 구성되어진 션트회로를 사용하여 시스템의 감쇠를 증가시킴으로써 패널 플러터를 억제할 수 있는 새로운 방법인 수동감쇠기법에 대한 연구가 수행되었다. 이 수동감쇠기법은 능동적 제어보다 강건(robust)하며 커다란 전원 공급이 필요하지 않고 제어기나 감지 시스템과 같이 복잡한 주변 기기가 필요 없이도 실제 패널 플러터 억제에 쉽게 응용할 수 있는 장점을 가지고 있다. 최대의 작동력/감쇠 효과를 얻기 위해서 유전자 알고리듬을 사용하여 압전 세라믹의 형상과 위치를 결정하였다. 해밀턴 원리를 사용해서 지배 방정식을 유도하였으며, 기하학적 대변형을 고려하기 위해 von-Karman의 비선형 변형률-변위 관계식을 사용하였으며 공기력 이론으로는 준 정상 피스톤 1차 이론을 사용하였다. 4절점 4각형 평판 요소를 이용하여 이산화된 유한 요소 방정식을 유도하였다. 효율적인 플러터 억제를 위해 패널 플러터에 중요한 영향을 미치는 플러터 모드를 이용한 모드축약기법을 사용하였으며, 이를 통해 비선형 연계 모달 방정식이 얻어지게 된다. 능동적 제어 방법과 수동 감쇠 기법에 의해 수행되어진 플러터 억제 결과들을 Newmark 비선형 시분할 적분법을 통해 시간 영역에서 살펴 보았다.

• Smart Structures and Systems
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• 제9권2호
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• pp.127-143
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• 2012

The present paper deals with the nonlinear analysis of the functionally graded piezoelectric (FGP) annular plate with two smart layers as sensor and actuator. The normal pressure is applied on the plate. The geometric nonlinearity is considered in the strain-displacement equations based on Von-Karman assumption. The problem is symmetric due to symmetric loading, boundary conditions and material properties. The radial and transverse displacements are supposed as two dominant components of displacement. The constitutive equations are derived for two sections of the plate, individually. Total energy of the system is evaluated for elastic solid and piezoelectric sections in terms of two components of displacement and electric potential. The response of the system can be obtained using minimization of the energy of system with respect to amplitude of displacements and electric potential. The distribution of all material properties is considered as power function along the thickness direction. Displacement-load and electric potential-load curves verify the nonlinearity nature of the problem. The response of the linear analysis is investigated and compared with those results obtained using the nonlinear analysis. This comparison justifies the necessity of a nonlinear analysis. The distribution of the displacements and electric potential in terms of non homogenous index indicates that these curves converge for small value of piezoelectric thickness with respect to elastic solid thickness.

• Advances in aircraft and spacecraft science
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• 제6권5호
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• pp.409-426
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• 2019

The aim of the present work is to study the nonlinear behavior of the laminated composite plates under transverse sinusoidal loading using a new inverse trigonometric shear deformation theory, where geometric nonlinearity in the Von-Karman sense is taken into account. In the present theory, in-plane displacements use an inverse trigonometric shape function to account the effect of transverse shear deformation. The theory satisfies the traction free boundary conditions and violates the need of shear correction factor. The governing equations of equilibrium and boundary conditions associated with present theory are obtained by using the principle of minimum potential energy. These governing equations are solved by eight nodded serendipity element having five degree of freedom per node. A square laminated composite plate is considered for the geometrically linear and nonlinear formulation. The numerical results are obtained for central deflections, in-plane stresses and transverse shear stresses. Finite element Codes are developed using MATLAB. The present results are compared with previously published results. It is concluded that the geometrically linear and nonlinear response of laminated composite plates predicted by using the present inverse trigonometric shape function is in excellent agreement with previously published results.