• Structural Engineering and Mechanics
• /
• 제35권6호
• /
• pp.677-697
• /
• 2010

This paper focuses on geometrically non-linear static analysis of a simply supported beam made of hyperelastic material subjected to a non-follower transversal uniformly distributed load. As it is known, the line of action of follower forces is affected by the deformation of the elastic system on which they act and therefore such forces are non-conservative. The material of the beam is assumed as isotropic and hyperelastic. Two types of simply supported beams are considered which have the following boundary conditions: 1) There is a pin at left end and a roller at right end of the beam (pinned-rolled beam). 2) Both ends of the beam are supported by pins (pinned-pinned beam). In this study, finite element model of the beam is constructed by using total Lagrangian finite element model of two dimensional continuum for a twelve-node quadratic element. The considered highly non-linear problem is solved by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. In order to use the solution procedures of Newton-Raphson type, there is need to linearized equilibrium equations, which can be achieved through the linearization of the principle of virtual work in its continuum form. In the study, the effect of the large deflections and rotations on the displacements and the normal stress and the shear stress distributions through the thickness of the beam is investigated in detail. It is known that in the failure analysis, the most important quantities are the principal normal stresses and the maximum shear stress. Therefore these stresses are investigated in detail. The convergence studies are performed for various numbers of finite elements. The effects of the geometric non-linearity and pinned-pinned and pinned-rolled support conditions on the displacements and on the stresses are investigated. By using a twelve-node quadratic element, the free boundary conditions are satisfied and very good stress diagrams are obtained. Also, some of the results of the total Lagrangian finite element model of two dimensional continuum for a twelve-node quadratic element are compared with the results of SAP2000 packet program. Numerical results show that geometrical nonlinearity plays very important role in the static responses of the beam.

• 한국정밀공학회지
• /
• 제25권3호
• /
• pp.44-49
• /
• 2008

• Smart Structures and Systems
• /
• 제25권5호
• /
• pp.619-630
• /
• 2020

This paper studies nonlinear free vibration characteristics of nonlocal magneto-electro-elastic (MEE) nanobeams resting on nonlinear elastic substrate having geometrical imperfection by considering piezoelectric reinforcement scheme. The piezoelectric reinforcement can cause an enhanced vibration behavior of smart nanobeams under magnetic field. All of previously reported studies on MEE nanobeams ignore the influences of geometric imperfections which are very substantial due to the reason that a nanobeam cannot be always perfect. Nonlinear governing equations of a smart nanobeam are derived based on classical beam theory and an analytical trend is provided to obtained nonlinear vibration frequency. This research shows that changing the volume fraction of piezoelectric constituent in the material has a great influence on vibration behavior of smart nanobeam under electric and magnetic fields. Also, it can be seen that nonlinear vibration behaviors of smart nanobeam are dependent on the magnitude of exerted electric voltage, magnetic potential, hardening elastic foundation and geometrical imperfection.

• Coupled systems mechanics
• /
• 제4권2호
• /
• pp.191-209
• /
• 2015

Hybrid girders can be constructed in different geometrical forms and from different materials. Selection of beam's effective constellation represents a complex process considering the variations of geometrical parameters, changes of built in material characteristics and their mutual relations, which has important effect on the behavior of the girder. This paper presents the theoretical and experimental research on behavior of the timber-steel hybrid girders' different geometrical constellation with external prestressing and in different conditions of timber moisture. These researches are based on linear elastic analysis, and further refine by using the plasticity and damage models.

• 대한토목학회논문집
• /
• 제29권1A호
• /
• pp.53-60
• /
• 2009

이 논문은 양단회전 후좌굴 변단면 기둥의 기하 비선형 해석에 관한 연구이다. 기둥의 변단면은 변화폭, 변화깊이, 정방형 변단면으로 채택하였다. Bernoulli-Euler 보 이론을 이용하여 후좌굴 기둥의 정확탄성곡선을 지배하는 미분방정식을 유도하였다. 이 미분방정식은 두 개의 미지수를 가지며 이러한 미분방정식을 풀 수 있는 수치해석 방법을 개발하였다. 후좌굴 기둥의 수치해석 결과로 평형경로, 정확탄성곡선 및 합응력을 산정하였다. 실험을 통하여 후좌굴 거동의 이론을 검증하였다.

• 한국광학회지
• /
• 제24권5호
• /
• pp.224-230
• /
• 2013

레이저 리프트 오프(Laser Lift-Off: LLO)는 수직형 LED 제조를 위하여 GaN 또는 AlN 박막을 사파이어 웨어퍼로부터 레이저를 이용하여 제거하는 공정으로 광원, 레이저의 출력 파워를 조절해주는 감쇠기, 빔의 형태를 잡아주는 빔 성형 광학계, 원하는 빔 사이즈를 만들어 주고 빔을 균일하게 섞어주는 빔 균일 광학계, 기판에 투사 이전에 빔을 한번 잘라주는 조리개 부분과 마스크 단에서 잘린 빔을 기판에 투사해주는 투사렌즈 부분으로 구성되어 있다. 본 논문에서는 LLO 시스템을 구성하고 있는 광학계 중 감쇠기와 투사렌즈 부분의 설계 및 분석을 진행하였다. 투사렌즈의 $7{\times}7mm^2$ 빔 사이즈 구현을 위하여 광학 설계 프로그램인 지맥스를 통해 설계 및 초점심도를 분석하였으며, 조명 설계 프로그램인 라이트 툴을 사용하여 빔 사이즈 및 균일도를 분석하였다. 성능 분석 결과 사각형 빔의 크기 $6.97{\times}6.96mm^2$, 균일도 91.8%, 초점심도 ${\pm}30{\mu}m$를 확인하였다. 또한 고출력의 엑시머레이저의 빔 강도를 감쇠시키기 위한 장치인 감쇠기의 투과율을 높이기 위하여 에센설 맥클라우드 코팅 프로그램을 사용하여 유전체 코팅을 실시한 결과 총 23층의 박막과 s 편광의 입사각도 $45{\sim}60^{\circ}$에서 10-95%의 투과율을 확인 할 수 있었다.

• 한국전산구조공학회:학술대회논문집
• /
• 한국전산구조공학회 2004년도 봄 학술발표회 논문집
• /
• pp.17-24
• /
• 2004

This paper established the dynamic model of a flexible Timoshenko beam with geometrical nonlinearities subject to large overall motions by using the finite element method. The equations of motion are derived by using Hamilton principle based on expressing the kinetic and potential energies of the flexible beam in terms of generalized coordinates. The nonlinear constraint equations are adjoined to the system equations of motion by using Lagrange multipliers.

• Structural Engineering and Mechanics
• /
• 제19권2호
• /
• pp.141-151
• /
• 2005

There are several ways of decreasing the vibration energy of structures. One of which is special damping layers made of various viscoelastic materials are widely applied in structures subjected to dynamic loading. In this study, a cantilever beam, partially covered by damping a constraining layers, is investigated by using Finite Element method (FEM). The frequency and system loss factor are evaluated. The effects of different physical and geometrical parameters on the natural frequency and system loss factors are discussed.

• Advances in nano research
• /
• 제13권2호
• /
• pp.113-120
• /
• 2022

In this paper, a finite element (FE) simulation has been developed in order to examine the nonlinear stability of reinforced sandwich beams with graphene oxide powders (GOPs). In this regard, the nonlinear stability curves have been obtained asuming that the beam is under compressive loads leading to its buckling. The beam is considered to be a three-layered sandwich beam with metal core and GOP reinforced face sheets and it is rested on elastic substrate. Moreover, a higher-order refined beam theory has been considered to formulate the sandwich beam by employing the geometrically perfect and imperfect beam configurations. In the solving procedure, the utalized finite element simulation contains a novel beam element in which shear deformation has been included. The calculated stability curves of GOP-reinforced sandwich beams are shown to be dependent on different parameters such as GOP amount, face sheet thickness, geometrical imperfection and also center deflection.

• Geomechanics and Engineering
• /
• 제17권2호
• /
• pp.175-180
• /
• 2019

This research is concerned with post-buckling investigation of nano-scaled beams constructed from porous functionally graded (FG) materials taking into account geometrical imperfection shape. Hence, two types of nanobeams which are perfect and imperfect have been studied. Porous FG materials are classified based on even or uneven porosity distributions. A higher order nonlinear refined beam theory is used in the present research. Both perfect and imperfect nanobeams are formulated based on this refined theory. A detailed study is provided to understand the effects of geometric imperfection, pore distribution, material distribution and small scale effects on buckling of FG nanobeams.