• Steel and Composite Structures
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• 제12권6호
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• pp.505-522
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• 2012

An artificial bee colony (ABC) algorithm is developed for the optimum design of geometrically non-linear steel frames. The ABC is a new swarm intelligence method which simulates the intelligent foraging behaviour of honeybee swarm for solving the optimization problems. Minimum weight design of steel frames is aimed under the strength, displacement and size constraints. The geometric non-linearity of the frame members is taken into account in the optimum design algorithm. The performance of the ABC algorithm is tested on three steel frames taken from literature. The results obtained from the design examples demonstrate that the ABC algorithm could find better designs than other meta-heuristic optimization algorithms in shorter time.

• Structural Engineering and Mechanics
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• 제66권1호
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• pp.27-36
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• 2018

The objective of this work is to analyze geometrically nonlinear static analysis a simply supported laminated composite beam subjected to a non-follower transversal point load at the midpoint of the beam. In the nonlinear model of the laminated beam, total Lagrangian finite element model of is used in conjunction with the Timoshenko beam theory. The considered non-linear problem is solved considering full geometric non-linearity by using incremental displacement-based finite element method in conjunction 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. In the numerical results, the effects of the fiber orientation angles and the stacking sequence of laminates on the nonlinear deflections and stresses of the composite laminated beam are examined and discussed. Convergence study is performed. Also, the difference between the geometrically linear and nonlinear analysis of laminated beam is investigated in detail.

• 한국복합재료학회:학술대회논문집
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• 한국복합재료학회 2004년도 춘계학술발표대회 논문집
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• pp.87-90
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• 2004

In this paper, geometrically non-linear finite element analyses were performed to study the mechanical behavior of the material system of the envelope of stratospheric airships. The microstructure of the load­bearing plain weave layer was identified and modeled. The Updated Lagrangian formulation was employed to consider the geometric non-linearity as well as the induced structural non-linearity for the fiber tows. The stress-strain behavior was predicted and the effective elastic modulus was calculated by numerical experiments. It was found the non-linear stress-strain curves were largely different from those by linear analysis with much higher non-linear elastic moduli. The difference was more distinguishable when the tow waviness was smaller.

• Steel and Composite Structures
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• 제9권6호
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• pp.535-555
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• 2009

The harmony search method based optimum design algorithm is presented for geometrically non-linear semi-rigid steel frames. Harmony search method is recently developed metaheuristic algorithm which simulates the process of producing a musical performance. The optimum design algorithm aims at obtaining minimum weight steel frames by selecting from standard set of steel sections such as European wide flange beams (HE sections). Strength constraints of Turkish Building Code for Steel Structures (TS648) specification and displacement constraints were used in the optimum design formulation. The optimum design algorithm takes into account both the geometric non-linearity of the frame members and the semi-rigid behaviour of the beam-to-column connections. The Frye-Morris polynomial model is used to calculate the moment-rotation relation of beam-to-column connections. The robustness of harmony search algorithm, in comparison with genetic algorithms, is verified with two benchmark examples. The comparisons revealed that the harmony search algorithm yielded not only minimum weight steel frames but also required less computational effort for the presented examples.

• Structural Engineering and Mechanics
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• 제51권6호
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• pp.955-971
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• 2014

Large post-buckling behavior of Timoshenko beams subjected to non-follower axial compression loads are studied in this paper by using the total Lagrangian Timoshenko beam element approximation. Two types of support conditions for the beams are considered. In the case of beams subjected to compression loads, load rise causes compressible forces end therefore buckling and post-buckling phenomena occurs. It is known that post-buckling problems are geometrically nonlinear problems. The considered highly non-linear problem is solved considering full geometric non-linearity by using incremental displacement-based finite element method in conjunction 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 beams considered in numerical examples are made of lower-Carbon Steel. In the study, the relationships between deflections, rotational angles, critical buckling loads, post-buckling configuration, Cauchy stress of the beams and load rising are illustrated in detail in post-buckling case.

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

• 한국항공우주학회지
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• 제36권8호
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• pp.734-739
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• 2008

본 논문에서는 미시 및 중시 역학의 2-단계 해석 전략을 채택하여 유연직물 복합재료의 기계적 거동을 예측하였다. 미시역학에서는 섬유다발의 유효물성치를 계산하였고 그 결과를 이용해 중시역학에서 유연직물복합재료의 인장탄성계수를 예측하였다. 중시역학 해석 과정에서는 섬유다발의 회전 및 전단 대변형에 의한 기하학적 비선형성을 고려하기 위하여 사용자 정의 부프로그램을 개발하여 ABAQUS 내에 삽입하였다. 해석결과, 인장하중을 받는 유연직물복합재료의 응력-변형률은 비선형 거동을 보였고, 계산된 유효탄성계수는 시험값과 잘 일치하는 것으로 나타났다.

• Composites Research
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• 제18권2호
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• pp.30-37
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• 2005

본 논문에서는 평직구조를 갖는 성층권 비행선 기낭의 하중막재에 대한 비선형 유한요소 해석 결과를 기술하였다. 평직구조를 갖는 하중막재의 미세구조를 3차원적으로 구현하였고, Updated Lagrangian 방법을 사용하여 기하학적 비선형성을 고려하였다 계산결과, 큰 변형률에서 비선형해석으로부터 얻은 응력-변형률 곡선은 선형해석의 결과와 큰 차이를 보였다. 또한 응력-변형률 곡선으로부터 얻은 비선형 탄성계수 값은 선형 탄성계수보다 큰 값을 보였는데 그 차이는 섬유의 굴곡도가 작은 경우 더욱 두드러지게 나타났다

• Structural Engineering and Mechanics
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• 제54권3호
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• pp.433-451
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• 2015

This paper focuses on large deflection static behavior of edge cracked simple supported beams subjected to a non-follower transversal point load at the midpoint of the beam by using the total Lagrangian Timoshenko beam element approximation. The cross section of the beam is circular. The cracked beam is modeled as an assembly of two sub-beams connected through a massless elastic rotational spring. It is known that large deflection problems are geometrically nonlinear problems. The considered highly nonlinear problem is solved considering full geometric non-linearity by using incremental displacement-based finite element method in conjunction 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 beams considered in numerical examples are made of Aluminum. In the study, the effects of the location of crack and the depth of the crack on the non-linear static response of the beam are investigated in detail. The relationships between deflections, end rotational angles, end constraint forces, deflection configuration, Cauchy stresses of the edge-cracked beams and load rising are illustrated in detail in nonlinear case. Also, the difference between the geometrically linear and nonlinear analysis of edge-cracked beam is investigated in detail.

• 수산해양교육연구
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• 제24권5호
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• pp.699-711
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• 2012

An undergraduate course named computational structural analysis becomes more significant in recent years because of its important role in industries and the recent innovation in computer technology. Typically, the course consists of introduction to finite element method, utilization of general purpose finite element software, and examples focusing on static and linear analyses on various structural members such as a beam, truss, frame, arch, and cable. However, in addition to the static and linear analyses, current industries ask graduates to acquire basic knowledge on structural dynamics and nonlinear analysis, which are not listed in the conventional syllabus of the computational structural analysis. Therefore, this study develops geometrically nonlinear examples, which can help students to easily capture the fundamental nonlinear theory, software manipulation, and problem solving skills. For the purpose, five different examples are found, developed for the analyses of cables and cable nets, which naturally have strong geometrical non-linearity. In the paper, these examples are presented, discussed, and finally compared for a better subject development.