• Structural Engineering and Mechanics
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• 제13권4호
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• pp.437-453
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• 2002

In this paper, dynamic stiffness and flexibility for circular membranes are analytically derived using an efficient mixed-part dual boundary element method (BEM). We employ three approaches, the complex-valued BEM, the real-part and imaginary-part BEM, to determine the dynamic stiffness and flexibility. In the analytical formulation, the continuous system for a circular membrane is transformed into a discrete system with a circulant matrix. Based on the properties of the circulant, the analytical solutions for the dynamic stiffness and flexibility are derived. In deriving the stiffness and flexibility, the spurious resonance is cancelled out. Numerical aspects are discussed and emphasized. The problem of numerical instability due to division by zero is avoided by choosing additional constraints from the information of real and imaginary parts in the dual formulation. For the overdetermined system, the least squares method is considered to determine the dynamic stiffness and flexibility. A general purpose program has been developed to test several examples including circular and square cases.

• 한국구조물진단유지관리공학회 논문집
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• 제15권2호
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• pp.125-135
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• 2011

유연도법 기반의 공식화에서는 변위영역의 형상함수를 라그랑지언(Lagrangian)보간법에 의한 곡률로부터 횡방향 변위를 유도한다. 곡률변위보간법으로 유도한 매트릭스를 사용한 기하학적 비선형 해석방법과 강성도법을 기반으로 한 비선형 기존의 유한요소 해석 프로그램의 결과를 비교하여 적용이 가능함을 확인하였고, Spacone의 이론을 확장시켜 기하학적 비선형 거동을 예측할 수 있는 유연도법의 알고리즘을 제안하였다. 예제를 통하여 실제 문제에 대한 기하학적 비선형 해석을 수행하였다.

• Structural Engineering and Mechanics
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• 제8권3호
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• pp.257-272
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• 1999

In this paper a simple finite element is proposed for analyzing out of plane vibration of thin walled curved beams, with both open and closed sections, considering shear flexibility. The present element is obtained from a variational formulation governing the dynamics of a three-dimensional elastic body in which the stress tensor as well as the displacements are variationally independent. The element has two nodes with four degrees of freedom in each. Numerical examples for the first six frequencies are performed in order to assess the accuracy of the finite element formulation and to show the influence of the shear flexibility on the dynamics of the member.

• Computers and Concrete
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• 제6권5호
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• pp.377-390
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• 2009

In this paper an improved one-dimensional frame element for modelling of reinforced concrete beams and columns subjected to impact is presented. The model is developed in the framework of a flexibility fibre element formulation that ignores the shear effect at material level. However, a simple shear cap is introduced at section level to take account of possible shear failure. The effect of strain rate at the fibre level is taken into account by using the dynamic increase factor (DIF) concept for steel and concrete. The capability of the formulation for estimating the element response history is demonstrated by some numerical examples and it is shown that the developed 1D element has the potential to be used for dynamic analysis of large framed structures subjected to impact of air blast and rigid objects.

• Structural Engineering and Mechanics
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• 제56권2호
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• pp.169-188
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• 2015

There are two types of nonlinear analysis methods for building frameworks depending on the method of modeling the plastification of members including lumped plasticity and distributed plasticity. The lumped plasticity method assumes that plasticity is concentrated at a zero-length plastic hinge section at the ends of the elements. The distributed plasticity method discretizes the structural members into many line segments, and further subdivides the cross-section of each segment into a number of finite elements. When a reinforced concrete member experiences inelastic deformations, cracks tend to spread form the joint interface resulting in a curvature distribution. The program IDARC includes a spread plasticity formulation to capture the variation of the section flexibility, and combine them to determine the element stiffness matrix. In this formulation, the flexibility distribution in the structural elements is assumed to be the linear. The main objective of this study is to evaluate the accuracy of linear flexibility distribution assumed in the spread inelasticity model. For this purpose, nonlinear analysis of two reinforced concrete frames is carried out and the linear flexibility models used in the elements are compared with the real ones. It is shown that the linear flexibility distribution is incorrect assumption in cases of significant gravity load effects and can be lead to incorrect nonlinear responses in some situations.

• Structural Engineering and Mechanics
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• 제5권5호
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• pp.523-528
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• 1997

Stiffness and flexibility equations are combined in the buckling analysis of a braced structure - stiffness for the original structure and flexibility for the bracing. Choosing a flexibility formulation for the bracing gives a very compact computational problem. It also gives theoretical insights into the behaviour of the braced structure.

• Structural Engineering and Mechanics
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• 제36권1호
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• pp.57-78
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• 2010

A novel flexibility-based 1D element that captures the material nonlinearity and second order P-$\Delta$ effects within a reinforced concrete frame member is developed. The formulation is developed for 2D planar frames in the modified fiber element framework but can readily be extended to 3D cases. The nonlinear behavior of concrete including cracking and crushing is taken into account through a modified hypo-elastic model. A parabolic and a constant shear stress distribution are used at section level to couple the normal and tangential tractions at material level. The lack of objectivity due to softening of concrete is addressed and objectivity of the response at the material level is attained by using a technique derived from the crack band approach. Finally the efficiency and accuracy of the formulation is compared with experimental results and is demonstrated by some numerical examples.

• Structural Engineering and Mechanics
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• 제42권1호
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• pp.39-53
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• 2012

This paper presents an alternative way to derive the exact element stiffness matrix for a beam on Winkler foundation and the fixed-end force vector due to a linearly distributed load. The element flexibility matrix is derived first and forms the core of the exact element stiffness matrix. The governing differential compatibility of the problem is derived using the virtual force principle and solved to obtain the exact moment interpolation functions. The matrix virtual force equation is employed to obtain the exact element flexibility matrix using the exact moment interpolation functions. The so-called "natural" element stiffness matrix is obtained by inverting the exact element flexibility matrix. Two numerical examples are used to verify the accuracy and the efficiency of the natural beam element on Winkler foundation.

• Geomechanics and Engineering
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• 제24권4호
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• pp.371-388
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• 2021

A novel flexibility-based beam-foundation model for inelastic analyses of beams resting on foundation is presented in this paper. To model the deformability of supporting foundation media, the Winkler-Pasternak foundation model is adopted. Following the derivation of basic equations of the problem (strong form), the flexibility-based finite beam-foundation element (weak form) is formulated within the framework of the matrix virtual force principle. Through equilibrated force shape functions, the internal force fields are related to the element force degrees of freedom. Tonti's diagrams are adopted to present both strong and weak forms of the problem. Three numerical simulations are employed to assess validity and to show effectiveness of the proposed flexibility-based beam-foundation model. The first two simulations focus on elastic beam-foundation systems while the last simulation emphasizes on an inelastic beam-foundation system. The influences of the adopted foundation model to represent the underlying foundation medium are also discussed.

• 한국산업정보학회논문지
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• 제26권3호
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• pp.9-22
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• 2021

본 연구에서는 조립산업의 공급망(Supply chain)에서의 발생할 수 있는 공급붕괴(Supply disruption)를 고려한 공급망 네트워크(Supply chain network: SCN) 모델이 제안된다. 공급붕괴를 위해 공급자 붕괴(Supplier disruption)와 경로 붕괴(Route disruption)가 함께 SCN 모델에서 고려되며, 이러한 두 가지의 붕괴 현상을 함께 고려한 SCN 모델은 유연성(Flexibility)과 효율성(Efficiency)을 성취할 수 있게 된다. SCN 모델은 수리모형으로 표현되며, 혼합유전알고리즘(Proposed hybrid genetic algorithm: pro-HGA) 접근법을 이용해 이행된다. 수치실험에서는 몇몇 상이한 규모를 가진 SCN 모델을 이용해 제안된 pro-HGA 접근법의 수행도와 기존 접근법의 수행도를 비교분석하였으며, 공급자 수와 백업경로(Backup route) 수의 변화를 통한 민감도 분석을 실시하였다. 실험 결과, 제안된 pro-HGA 접근법의 효율성을 입증하였고, SCN 모델의 유연성과 효용성을 검증하였다. 마지막으로 본 연구 수행의 의의 및 향후 개선방향에 대해 논하였다.