• Title, Summary, Keyword: matrix stiffness method

### Stiffness Analysis of Planar Parallel Manipulators with Serially Connected Legs (직렬체인 다리를 갖는 평면 병렬형 기구의 강성해석)

• Kim, Han Sung
• Journal of The Korean Society of Manufacturing Technology Engineers
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• v.23 no.2
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• pp.164-172
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• 2014
• This paper presents a method for analyzing the stiffness of full and low DOF (degree of freedom) planar parallel manipulators with serially connected legs. The individual stiffness of each leg is obtained by applying reciprocal screws to the leg twist using passive joints and elastic elements consisting of actuators and links. Because the legs are connected in parallel, the manipulator stiffness is determined by summing the individual leg stiffness values. This method does not require the assumption that springs should be located along reciprocal screws and is applicable to a planar parallel manipulator with a generic or singular configuration. The stiffness values of three planar parallel manipulators with different DOFs are analyzed. The numerical results are confirmed using ADAMS S/W.

### Dynamic Stability Analysis of Non-conservative Systems under Pasternak Elastic Foundations (Pasternak 탄성지지 하에서 비보존력계의 동적 안정성해석)

• 이준석;김남일;김문영
• Proceedings of the Computational Structural Engineering Institute Conference
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• pp.73-80
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• 2004
• Mass matrix, elastic stiffness matrix, load correction stiffness matrix by circulatory non-conservative force, and Winkler and Pasternak foundation matrix of framed structure in 2-D are calculated for stability analysis of divergence or flutter system. Then, a matrix equation of the motion for the non-conservative system is formulated and numerical results are presented to demonstrate the effect of some parameters with using Newmark method.

### Application of Stiffness Matrix Element for Finite Element Analysis of Spine (척추의 유한 요소 해석을 위한 강성 행렬 요소의 적용)

• 정일섭;안면환
• Journal of the Korean Society for Precision Engineering
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• v.20 no.10
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• pp.226-232
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• 2003
• Difficulties in the finite element modeling of human spine are evaded by using a stiffness matrix element whose properties can be characterized from experimentally measured stiffness of functional spinal units. Relative easiness is in that inter-vertebral discs, ligaments, and soft tissues connecting vertebrae do not need to be modeled as they are. The remarkable coupling effect between distinct degrees of freedom induced by the geometric complexity can be accommodated without much effort. An idealized block model with simple geometry for vertebra is employed to assess the feasibility of this method. Analyses are performed in both levels of motion segment and spinal column, and the result is compared with that from detail model. As far as the global behavior of spine is concerned, the simplification is found not to aggravate inaccuracy only if sufficient experimental data is provided and interpreted properly.

### A Study for Structural Damage Identification Method Using Genetic Algorithm (유전자 알고리즘을 이용한 구조물 손상 탐색기법에 관한 연구)

• Woo, Ho-Kil;Choi, Byoung-Min
• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.17 no.1
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• pp.80-87
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• 2007
• In this paper, a method for identifying the location and extent of a damage in a structure using residual forces was presented. Element stiffness matrix reduction parameters in a finite element model were used to describe the damaged structure mathematically. The element stiffness matrix reduction parameters were determined by minimizing a global error derived from dynamic residual vectors, which were obtained by introducing a simulated experimental data into the eigenvalue problem. Genetic algorithm was used to get the solution set of element stiffness reduction parameters. The proposed scheme was verified using Euler-Bernoulli beam. The results were presented in the form of tables and charts.

### Influence of Pile Cap's Boundary Conditions in Piled Pier Structures (교량 말뚝기초의 단부 지점조건의 영향분석)

• Jeong, Sang-Seom;Won, Jin-Oh
• Proceedings of the Korean Geotechical Society Conference
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• pp.25-32
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• 2005
• Modeling techniques of piled pier were reviewed and the influences of pile cap's boundary conditions were analyzed in this study. Among various modeling techniques, equivalent cantilever method seems relatively simple for modeling pile groups and it has some problems to determine the virtual fixed points. Through the analyses, it was found that the method of nonlinear p-y model with soil springs was more appropriate than equivalent cantilever method. The method modeling a pile group using stiffness matrix seems useful for practical design, which can represent the nonlinear three-dimensional behavior of a piled pier. In this study, the stiffness matrix of a pile group could be estimated efficiently and precisely using three-dimensional nonlinear analysis programs of pile groups (FBPier 3.0, YSGroup).

### On triply coupled vibration of eccentrically loaded thin-walled beam using dynamic stiffness matrix method

• Ghandi, Elham;Shiri, Babak
• Structural Engineering and Mechanics
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• v.62 no.6
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• pp.759-769
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• 2017
• The effect of central axial load on natural frequencies of various thin-walled beams, are investigated by some researchers using different methods such as finite element, transfer matrix and dynamic stiffness matrix methods. However, there are situations that the load will be off centre. This type of loading is called eccentric load. The effect of the eccentricity of axial load on the natural frequencies of asymmetric thin-walled beams is a subject that has not been investigated so far. In this paper, the mentioned effect is studied using exact dynamic stiffness matrix method. Flexure and torsion of the aforesaid thin-walled beam is based on the Bernoulli-Euler and Vlasov theories, respectively. Therefore, the intended thin-walled beam has flexural rigidity, saint-venant torsional rigidity and warping rigidity. In this paper, the Hamilton‟s principle is used for deriving governing partial differential equations of motion and force boundary conditions. Throughout the process, the uniform distribution of mass in the member is accounted for exactly and thus necessitates the solution of a transcendental eigenvalue problem. This is accomplished using the Wittrick-Williams algorithm. Finally, in order to verify the accuracy of the presented theory, the numerical solutions are given and compared with the results that are available in the literature and finite element solutions using ABAQUS software.

### Inelastic Buckling Analysis of Frames with Semi-Rigid Joints (부분강절 뼈대구조의 비탄성 좌굴해석)

• Min, Byoung Cheol
• Journal of Korean Society of Steel Construction
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• v.26 no.3
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• pp.143-154
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• 2014
• An improved method for evaluating effective buckling length of semi-rigid frame with inelastic behavior is newly proposed. Also, generalized exact tangential stiffness matrix with rotationally semi-rigid connections is adopted in previous studies. Therefore, the system buckling load of structure with inelastic behaviors can be exactly obtained by only one element per one straight member for inelastic problems. And the linearized elastic stiffness matrix and the geometric stiffness matrix of semi-rigid frame are utilized by taking into account 4th terms of taylor series from the exact tangent stiffness matrix. On the other hands, two inelastic analysis programs(M1, M2) are newly formulated. Where, M1 based on exact tangent stiffness matrix is programmed by iterative determinant search method and M2 is using linear algorithm with elastic and geometric matrices. Finally, in order to verify this present theory, various numerical examples are introduced and the effective buckling length of semi-rigid frames with inelastic materials are investigated.

### Dynamic analysis of trusses including the effect of local modes

• Structural Engineering and Mechanics
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• v.7 no.1
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• pp.81-94
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• 1999
• The dynamic analysis of trusses using the finite element method tends to overlook the effect of local member dynamic behavior on the overall response of the complete structure. This is due to the fact that the lateral inertias of the members are omitted from the global inertia terms in the structure mass matrix. In this paper a condensed dynamic stiffness matrix is formulated and used to calculate the exact dynamic properties of trusses without the need to increase the model size. In the examples the limitations of current solutions are presented together with the exact results obtained from the proposed method.

### An Analysis of Continuous Beam by Material Non-linear Transfer Matrix Method (재료비선형 전달행렬법에 의한 연속보의 해석)

• Seo, Hyun Su;Kim, Jin Sup;Kwon, Min Ho
• Journal of the Korea institute for structural maintenance and inspection
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• v.15 no.1
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• pp.77-84
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• 2011
• This study is to develop nonlinear analysis algorithm for transfer matrix method, which can be applied to continuous beam analysis. Gauss-Lobatto integral rule is adopted and the transfer matrix is derived from stiffness matrix. In the transfer matrix method, the system equation has a constant number of unknowns regardless of number of D.O.F. Therefore, the transfer matrix method has computational efficiencies not only in linear elastic analysis but also in nonlinear analysis. To verify the developed method, the analysis results of several examples are compared with commercial code in moment-curvature, moment-displacement and load-displacement relation.