• Journal of the Earthquake Engineering Society of Korea
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• v.2 no.2
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• pp.57-68
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• 1998

For free vibration of monosymmetric thin-walled circular arches including restrained warping effect, the elastic strain and kinetic energy is derived by introducing displacement fields of circular arches in which all displacement parameters are defined at the centroid axis. The cubic Hermitian polynomials are utilized as shape functions for development of the curved thin-walled beam element having eight degrees of freedom. Analytical solution for free vibration behaviors of simply supported thin-walled curved beam element is presented by evaluating elastic stiffness and mass matrices. In order to illustrate the accuracy and practical usefulness of this study, analytical and numerical solutions for free vibration of circular arches are presented and compared with solutions analyzed by the FEM using straight beam element.

• Structural Engineering and Mechanics
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• v.33 no.3
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• pp.307-323
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• 2009

This article presents the differential system that governs the mechanical behaviour of a curved-beam element, with varying cross-section area, subjected to generalized load. This system is solved by an exact procedure or by the application of a new numerical recurrence scheme relating the internal forces and displacements at the two end-points of an increase in its centroid-line. This solution has a transfer matrix structure. Both the stiffness matrix and the equivalent load vector are obtained arranging the transfer matrix. New structural matrices have been defined, which permit to determine directly the unknown values of internal forces and displacements at the two supported ends of the curved-beam element. Examples are included for verification.

• Journal of Korean Society of Steel Construction
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• v.10 no.1 s.34
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• pp.47-61
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• 1998

The behavior of horizontally curved I-girder bridges is complex because the flexural and torsional behavior of curved girders are coupled due to their initial curvature. Also, the behavior is affected by cross beams. To investigate the behavior of horizontally curved I-girder bridges, it is necessary to consider curved girders with cross beams. In order to perform free vibration analyses of horizontally curved I-girder bridges, a finite element formulation is presented here and a finite element analysis program is developed. The formulation that is presented here consists of curved and straight beam elements, including the warping degree of freedom. Based on the theory of thin-walled curved beams, the shape functions of the curved beam elements are derived from homogeneous solutions of the static equilibrium equations. Third-order hermits polynomials are used to form the shape functions of the straight beam elements. In the finite element analysis program, global stiffness and mass matrix are composed, based on the Cartesian coordinate system. The Gupta method is used to efficiently solve the eigenvalue problem. Comparing the results of several examples here with those of previous studies, the formulation presented is verified. The validity of the program developed is shown by comparing results with those analyzed by the shell element.

• Structural Engineering and Mechanics
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• v.52 no.2
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• pp.221-238
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• 2014

A four-noded curved shell finite element for the geometrically non-linear analysis of beams curved in plan is introduced. The structure is conceived as a sequence of macro-elements (ME) having the form of transversal segments of identical topology where each slice is formed using a number of the curved shell elements which have 7 degrees of freedom (DOF) per node. A curved box-girder beam example is modelled using various meshes and linear analysis results are compared to the solutions of a well-known computer program SAP2000. Linear and non-linear analyses of the beam under increasing uniformly distributed loads are also carried out. In addition to box-girder beams, the proposed element can also be used in modelling open-section beams with curved or straight axes and circular plates under radial compression. Buckling loads of a circular plate example are obtained for coarse and successively refined meshes and results are compared with each other. The advantage of this element is that curved systems can be realistically modelled and satisfactory results can be obtained even by using coarse meshes.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.8 no.1
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• pp.116-120
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• 2007

In this study, it is presented analytic results of bending problems in the anisotropic curved thick beam and the anisotropic curved thin beam. The anisotropy is that the material properties are different in each directions and it is difficult to solve the analytical solutions because the behavior is complex. In applying numerical method to solve differential equations of anisotropic curved beams, this study uses the finite element method. Both thin beam theory and thick beam theory are used as the basic governing equations of bending problems in the anisotropic beams. The analytic results are compared between the anisotropic curved thick beams and the anisotropic curved thin beams.

• Structural Engineering and Mechanics
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• v.5 no.1
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• pp.33-49
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• 1997

A method of analysis is proposed for curved multicell box girder grillages. The method can be used to analyze box girder grillages comprising straight and/or curved segments. Each segment can be modelled by a number of beam elements. Each element has three nodes and the nodal degrees of freedom (DOF) consist of the six DOF for a conventional beam plus DOF to account for torsional warping, distortion, distortional warping, and shear lag. This element is an extension of a straight element that was developed earlier. For a more realistic analysis of the intersection regions of non-colinear box girder segments, the concept of a rigid connector is introduced, and the compatibility requirements between adjoining elements in those regions are discussed. The results of the analysis showed good agreement with the shell finite element results, but the proposed method of analysis needs a fraction of the time and effort compared to the shell finite element analysis.

• Structural Engineering and Mechanics
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• v.33 no.4
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• pp.447-484
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• 2009

The spatially coupled buckling, in-plane, and lateral bucking analyses of thin-walled Timoshenko curved beam with non-symmetric, double-, and mono-symmetric cross-sections resting on elastic foundation are performed based on series solutions. The stiffness matrices are derived rigorously using the homogeneous form of the simultaneous ordinary differential equations. The present beam formulation includes the mechanical characteristics such as the non-symmetric cross-section, the thickness-curvature effect, the shear effects due to bending and restrained warping, the second-order terms of semitangential rotation, the Wagner effect, and the foundation effects. The equilibrium equations and force-deformation relationships are derived from the energy principle and expressions for displacement parameters are derived based on power series expansions of displacement components. Finally the element stiffness matrix is determined using force-deformation relationships. In order to verify the accuracy and validity of this study, the numerical solutions by the proposed method are presented and compared with the finite element solutions using the classical isoparametric curved beam elements and other researchers' analytical solutions.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.1 s.244
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• pp.18-25
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• 2006

The purpose of this research work is to demonstrate a successful application of hybrid-mixed formulation and nodeless degrees of freedom in developing a very accurate in-plane curved beam element for free vibration analysis. To resolve the numerical difficulties due to the spurious constraints, the present element, based on the Hellinger-Reissner variational principle and considering the effect of shear deformation, employed consistent stress parameters corresponding to cubic displacement polynomials with additional nodeless degrees. The stress parameters were eliminated by the stationary condition, and the nodeless degrees were condensed by Guyan Reduction. Several numerical examples indicated that the property of the mass matrix as well as that of the stiffness matrix have a great effect on the numerical performance. The element with consistent mass matrix produced best results on convergence and accuracy in the numerical analysis of Eigenvalue problems. Also, the higher-order mixed curved beam element showed a superior numerical behavior for the free vibration analyses.

• Structural Engineering and Mechanics
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• v.22 no.4
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• pp.483-510
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• 2006

The dynamic instability characteristics of laminated composite stiffened shell panels subjected to in-plane harmonic edge loading are investigated in this paper. The eight-noded isoparametric degenerated shell element and a compatible three-noded curved beam element are used to model the shell panels and the stiffeners respectively. As the usual formulation of degenerated beam element is found to overestimate the torsional rigidity, an attempt has been made to reformulate it in an efficient manner. Moreover the new formulation for the beam element requires five degrees of freedom per node as that of shell element. The method of Hill's infinite determinant is applied to analyze the dynamic instability regions. Numerical results are presented to demonstrate the effects of various parameters like shell geometry, lamination scheme, stiffening scheme, static and dynamic load factors and boundary conditions, on the dynamic instability behaviour of laminated composite stiffened panels subjected to in-plane harmonic loads along the boundaries. The results of free vibration and buckling of the laminated composite stiffened curved panels are also presented.

• Structural Engineering and Mechanics
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• v.88 no.1
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• pp.83-94
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• 2023

An accurate and highly efficient inverse element labelled iPCB is developed based on the inverse finite element method (iFEM) for real-time shape estimation of plane-curved structures (such as arch bridges) utilizing onboard strain data. This inverse problem, named shape sensing, is vital for the design of smart structures and structural health monitoring (SHM) procedures. The iPCB formulation is defined based on a least-squares variational principle that employs curved Timoshenko beam theory as its baseline. The accurate strain-displacement relationship considering tension-bending coupling is used to establish theoretical and measured section strains. The displacement fields of the isoparametric element iPCB are interpolated utilizing nonuniform rational B-spline (NURBS) basis functions, enabling exact geometric modelling even with a very coarse mesh density. The present formulation is completely free from membrane and shear locking. Numerical validation examples for different curved structures subjected to different loading conditions have been performed and have demonstrated the excellent prediction capability of iPCBs. The present formulation has also been shown to be practical and robust since relatively accurate predictions can be obtained even omitting the shear deformation contributions and considering polluted strain measures. The current element offers a promising tool for real-time shape estimation of plane-curved structures.