• International Journal of Naval Architecture and Ocean Engineering
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• v.4 no.3
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• pp.313-321
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• 2012

Vibration analysis of a thin-walled structure can be performed with a consistent mass matrix determined by the shape functions of all degrees of freedom (d.o.f.) used for construction of conventional stiffness matrix, or with a lumped mass matrix. In similar way stability of a structure can be analysed with consistent geometric stiffness matrix or geometric stiffness matrix with lumped buckling load, related only to the rotational d.o.f. Recently, the simplified mass matrix is constructed employing shape functions of in-plane displacements for plate deflection. In this paper the same approach is used for construction of simplified geometric stiffness matrix. Beam element, and triangular and rectangular plate element are considered. Application of the new geometric stiffness is illustrated in the case of simply supported beam and square plate. The same problems are solved with consistent and lumped geometric stiffness matrix, and the obtained results are compared with the analytical solution. Also, a combination of simplified and lumped geometric stiffness matrix is analysed in order to increase accuracy of stability analysis.

• Structural Engineering and Mechanics
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• v.7 no.2
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• pp.203-216
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• 1999

A previously proposed finite element formulation method is refined and modified to generate a new type of elements. The method is based on selecting a set of general solution modes for element formulation. The constant strain modes and higher order modes are selected and the formulation method is designed to ensure that the element will pass the basic single element test, which in turn ensures the passage of the basic patch test. If the element is to pass the higher order patch test also, the element stiffness matrix is in general asymmetric. The element stiffness matrix depends only on a nodal displacement matrix and a nodal force matrix. A symmetric stiffness matrix can be obtained by either modifying the nodal displacement matrix or the nodal force matrix. It is shown that both modifications lead to the same new element, which is demonstrated through numerical examples to be more robust than an assumed stress hybrid element in plane stress application. The method of formulation can also be used to arrive at the conforming displacement and hybrid stress formulations. The convergence of the latter two is explained from the point of view of the proposed method.

• Structural Engineering and Mechanics
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• v.42 no.1
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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.

• Computational Structural Engineering
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• v.10 no.1
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• pp.193-200
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• 1997

Even though there are many analysis methods of circular tanks on elastic foundation, the finite element method is widely used for that purpose. But the finite element method requires a number of memory spaces, computation time to solve large stiffness equations. In this study many the simplified methods(Analogy of Beam on Elastic Foundation, Foundation Stiffness Matrix, Finite Element Method and Transfer Matrix Method) are applied to analyze a circular tank on elastic foundation. By the given analysis methods, BEF analogy and foundation matrix method, the circular tank was transformed into the skeletonized frame structure. The frame structure was divided into several finite elements. The stiffness matrix of a finite element is related with the transfer matrix of the element. Thus, the transfer matrix of each finite element utilized the transfer matrix method to simplify the analysis of the tank. There were no significant difference in the results of two methods, the finite element method and the transfer matrix method. The transfer method applied to a circular tank on elastic foundation resulted in four simultaneous equations to solve completely.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.22 no.11
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• pp.1144-1151
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• 2012

A damage in structure alters its dynamic characteristics. The change is characterized by changes in the modal parameter, i.e., modal frequencies, modal damping value and mode shape associated with each modal frequency. Changes also occur in some of the structural parameters; namely, the mass, damping, stiffness matrices of the structure. In this paper, evaluation of changes in stiffness matrix of a structure is presented as a method not only for identifying the presence of the damage but also locating the damage. It is shown that changed stiffness matrix can be accurately estimated a sensitivity coefficient matrix derived from modifying mode shapes, First, with 4 story shear structure models, the effect of presence of damage in a structure on its stiffness matrix is studied. By using these analytical model, the effectiveness of using change of stiffness matrix in detecting and locating damages is demonstrated. To validate the predicted changing stiffness and its location, the obtained results are compared to the reanalysis result which shows good agreement.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1995.10a
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• pp.528-533
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• 1995

An analyical method is proposed to construct a clamp jointed structure as an equivalent stiffness matrix element in the finite element modal analysis of a complex beam structure. Static structural analysis was first made for the detail finite element model of the clamp joint. Utilizing the results of this analysis, the equivalent stiffness matrix element was buildup by using the flexibility influence coefficient method and Guyan condensation. The proposed method was applied to finite element modal analysis of a clamp jointed cantilever beam. And the finite element analysis results were compared to those experimental modal analysis. Comparison shows doog agreement each other Furthermore the effects of normal contact(or clamping) load on the equivalent stiffness matrix was also examined. The equivalent stiffness matrix showed little change in spite of the remakable increase in the contact load on the clamp joint.

• Structural Engineering and Mechanics
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• v.7 no.3
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• pp.259-276
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• 1999

An analytical solution for the shape functions of a beam segment supported on a generalized two-parameter elastic foundation is derived. The solution is general, and is not restricted to a particular range of magnitudes of the foundation parameters. The exact shape functions can be utilized to derive exact analytic expressions for the coefficients of the element stiffness matrix, work equivalent nodal forces for arbitrary transverse loads and coefficients of the consistent mass and geometrical stiffness matrices. As illustration, each distinct coefficient of the element stiffness matrix is compared with its conventional counterpart for a beam segment supported by no foundation at all for the entire range of foundation parameters.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.19 no.10
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• pp.1021-1027
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• 2009

Finite element models of dynamic systems can be updated in two stages. In the first stage, mass and stiffness matrices are updated neglecting damping. In the second stage, a damping matrix is estimated with the mass and stiffness matrices fixed. Methods to estimate a damping matrix for this purpose are proposed in this paper. For a system with proportional damping, a damping matrix is estimated using the modal parameters extracted from the measured responses and the modal matrix calculated from the mass and stiffness matrices from the first stage. For a system with non-proportional damping, a damping matrix is estimated from the impedance matrix which is the inverse of the FRF matrix. Only one low or one column of the FRF matrix is measured, and the remaining FRFs are synthesized to obtain a full FRF matrix. This procedure to obtain a full FRF matrix saves time and effort to measure FRFs.

• Composites Research
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• v.17 no.5
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• pp.25-38
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• 2004

In this study, the stiffness of spatially reinforced composites (SRC) are predicted by using superposition of a rod and matrix stiffnesses in an arbitrary direction. To confirm the predicted values, the material properties of SRC are measured. The predicted values from the volume average of stiffness matrix are consistent with the tested values in a rod direction, but are inconsistent in an off-rod direction while reverse is true fur the volume average of compliance matrix. Therefore, the harmony function from superposition of stiffness and compliance matrix is introduced. The predicted values from the harmony function are consistent with the tested values in both the rod and the off-rod directions.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.12 no.6
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• pp.50-55
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• 2003

This study proposed the analysis of damage detection due to the change of the stiffness of structure by using the original and modified dynamic characteristics. The present approach allows the use of composite data which consist of eigenvalues and eigenvectors. The suggested method is applied to examples of a cantilever and 3 degree of freedom system by modifying the stiffness. The predicted damage detections are in good agreement with these from the structural reanalysis using the modified stiffness.