• 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.

• 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.

• 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.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.589-596
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• 2006

An improved numerical method to obtain the exact element stiffness matrix is newly proposed to perform the spatially coupled elastic and stability analyses of non-symmetric thin-walled beam-columns with two-types of elastic foundation. This method overcomes drawbacks of the previous method to evaluate the exact stiffness matrix for the spatially coupled stability analysis of thin-walled beam-column. This numerical technique is firstly accomplished via a generalized eigenproblem associated with 14 displacement parameters by transforming equilibrium equations to a set of first order simultaneous ordinary differential equations. Then exact displacement functions are constructed by combining eigensolutions and polynomial solutions corresponding to non-zero and zero eigenvalues, respectively. Consequently an exact stiffness matrix is evaluated by applying the member force-deformation relationships to these displacement functions.

• 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.

• Interaction and multiscale mechanics
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• v.5 no.4
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• pp.385-397
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• 2012

In this paper the dynamic stiffness matrix method was used for the free vibration analysis of axially moving micro beam with constant velocity. The extended Hamilton's principle was employed to derive the governing differential equation of the problem using the modified couple stress theory. The dynamic stiffness matrix of the moving micro beam was evaluated using appropriate expressions of the shear force and bending moment according to the Euler-Bernoulli beam theory. The effects of the beam size and axial velocity on the dynamic characteristic of the moving beam were investigated. The natural frequencies and critical velocity of the axially moving micro beam were also computed for two different end conditions.

• Structural Engineering and Mechanics
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• v.11 no.4
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• pp.423-442
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• 2001

This paper presents a method of elastic-plastic analysis for planar steel frames that provides the accuracy of distributed plasticity methods with the computational efficiency that is greater than that of distributed plasticity methods but less than that of plastic-hinge based methods. This method accounts for the effect of spread of plasticity accurately without discretization through the cross-section of a beam-column element, which is achieved by the following procedures. First, nonlinear equations describing the relationships between generalized stresses and strains of the cross-section are derived analytically. Next, nonlinear force-deformation relationships for the beam-column element are obtained through lengthwise integration of the generalized strains. Elastic-plastic flexibility coefficients are then calculated by differentiating the above element force-deformation relationships. Finally, an elastic-plastic stiffness matrix is obtained by making use of the flexibility-stiffness transformation. Adding the conventional geometric stiffness matrix to the elastic-plastic stiffness matrix results in the tangent stiffness matrix, which can readily be used to evaluate the load carrying capacity of steel frames following standard nonlinear analysis procedures. The accuracy of the proposed method is verified by several examples that are sensitive to the effect of spread of plasticity.

• 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.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2003.06a
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• pp.760-763
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• 2003

This study proposed the analysis of damage defection due to the change of the stiffness of structure by using the original and modified dynamic characteristics. The method is applied to examples of a cantilever and 3 degree of freedom by modifying the stiffness. The predicted damage detections are in good agreement with these from the structural reanalysis using the modified stiffness.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.1933-1938
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• 2000

The partial differential equations for a coil spring derived from Timoshenko beam theory and Frenet formulae. Dynamic stiffness matrix of a coil spring composed of a circular wire is assembled by using dispersion relationship, waves and natural frequencies. Natural frequencies are obtained from maxima in the determinant of inverse of a dynamic stiffness matrix with appropriate boundary conditions. The results of the dynamic stiffness method are compared with those of transfer matrix method, finite element method and test.