• Structural Engineering and Mechanics
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• v.51 no.4
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• pp.601-625
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• 2014

Based on continuum mechanics and the principle of virtual displacements, incremental total Lagrangian formulation (T.L.) and incremental updated Lagrangian formulation (U.L.) were presented. Both T.L. and U.L. considered the large displacement stiffness matrix, which was modified to be symmetrical matrix. According to the incremental updated Lagrangian formulation, small strain, large displacement, finite rotation of three dimensional Timoshenko fiber beam element tangent stiffness matrix was developed. Considering large displacement and finite rotation, a new type of tangent stiffness matrix of the beam element was developed. According to the basic assumption of plane section, the displacement field of an arbitrary fiber was presented in terms of nodal displacement of centroid of cross-area. In addition, shear deformation effect was taken account. Furthermore, a nonlinear finite element method program has been developed and several examples were tested to demonstrate the accuracy and generality of the three dimensional beam element.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.25 no.3
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• pp.195-202
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• 2012

Two nonlinear frame elements taking into account geometric nonlinearity is presented and compared based on the Lagrangian co-rotational formulation. The first frame element is believed to be geometrically-exact because not only tangent stiffness matrices is exactly evaluated including stiffness matrices due to initial deformation but also total member forces are directly determined from total deformations in the deformed state. Particularly two exact tangent stiffness matrices based on total Lagrangian and updated Lagrangian formulation, respectively, are verified to be identical. In the second frame element, the deformed curved shape is regarded as the polygon and current flexural deformations in iteration process are neglected in evaluating tangent stiffness matrices and total member forces. Two numerical examples are given to demonstrate the accuracy and the good performance of the first frame element compared with the second element. Furthermore it is shown that the first frame element can be used in tracing nonlinear behaviors of cable members.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.10 no.3
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• pp.29-38
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• 1990

A totally, new approach of Lagrangian formulation named 'Pseudo Lagrangian Formulation(PLF)' for large deformation analysis of continue and structures by the finite of element method has been presented, and the efficiency and accuracy of nonlinear analysis beam element formulated by PLF has been discussed by solving several numerical examples. In PLF, the deformation of a body is maeasured by assigning a nonphysical 'Pseudo' configuration as reference. The Lagrangian deformation and the finite element mapping of the traditonal Lagrangian approaches are then carried out directly at the same time, The result of numerical tests shows superior performance of PLF to the traditional Lagrangian methods, Applications of PLF to small and finite deformation problems indicate that PLF not only serves as an alternative but has certain implementational advantages over total or updated Lagrangian formulations.

• Journal of Ocean Engineering and Technology
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• v.11 no.4
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• pp.7-22
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• 1997

A finite element analysis is performed for lateral buckling problems on the basis of a geometrically nonlinear formulation for a beam with small elastic strain but with possibly large rotations. The total Lagrangian formulation for a general large deformation, which involves finite rotations, is chosen and the exponential map is used to treat finite rotations from the Eulerian point of view. For lateral buckling, the point of vanishing determinant of the resulting unsymmetric tangent stiffness is traced to examine its relationship to bifurcation points. It is found that the points of vanishing determinant is not corresponding to bifurcation points for large deformations in general, which suggests that the present unsymmetric tangent stiffness is not an exact first derivative of internal forces with respect to displacement. This is illustrated through several numerical examples and followed by appropriate discussion.

• Proceedings of the KSME Conference
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• 2001.06a
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• pp.674-679
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• 2001

For a large deformation nonlinear dynamic analysis of two-dimensional frictional contact, the linear complementarity formulation combined with a linearization is used. The solution procedure is based on the total Lagrangian formulation with a predictor and corrector scheme. For contact searching, a hierarchical scheme with a circular territory is used. A second-order approximation of displacements is used to detect impact time and position. The formulation is illustrated by means of numerical examples.

• Journal of the Earthquake Engineering Society of Korea
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• v.12 no.4
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• pp.45-54
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• 2008

The purpose of this study was to investigate the performance of precast segmental PSC bridge columns with regard to P-delta effects. A model of precast segmental PSC bridge columns was tested under a constant axial load and a cyclically reversed horizontal load. A computer program, RCAHEST(Reinforced Concrete Analysis in Higher Evaluation System Technology), was used for the analysis of reinforced concrete structures. In addition to the material nonlinear properties, an algorithm for the problem of large displacement that may result in additional deformation has been formulated using total Lagrangian formulation. This study documents the testing of precast segmental PSC bridge columns under cyclic loading, and presents conclusions based on the experimental and analytical findings.

• Steel and Composite Structures
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• v.28 no.3
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• pp.389-401
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• 2018

An isoparametric six-node triangular element is utilized for geometrically nonlinear analysis of functionally graded (FG) shells. To overcome the shear and membrane locking, the element is improved by using strain interpolation functions. The Total Lagrangian formulation is employed to include the large displacements and rotations. Finding the nonlinear behavior of FG shells via laminated modeling is also the goal. A power function is employed to formulate the variation of elastic modulus through the thickness of shells. The results are presented in two ways, including the general FGM formulation and the laminated modeling. The equilibrium path is obtained by using the Generalized Displacement Control Method. Some popular benchmarks, including hyperbolical shell structures are solved to declare the correctness and accuracy of proposed formulations.

• Journal of the Earthquake Engineering Society of Korea
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• v.3 no.1
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• pp.55-66
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• 1999

This paper presents an analytical prediction of the hysteresis behavior of reinforced concrete long column with rectangular section under the cyclic loading state. The mechanical characteristic of cracked concrete and reinforcing bar in concrete has been modeled, considering the bond effect between reinforcing bar and concrete, the effect of aggregate interlocking at crack surface and the stiffness degradation after the crack has taken place. The strength increase of concrete due to the lateral confining reinforcement has been also taken into account to model the confined concrete. The formulation of these models for concrete and reinforcing bar has been based on the smeared crack concept that the stress-strain relationship of reinforced concrete element would be defined using the average values. In addition to the material nonlinear properties, the algorithm for large displacement problem that may give an additional deformation has been formulated using total Lagrangian formulation. The analytically predicted behavior was compared with test result and they showed good agreement in overall behavior.

• Proceedings of the KSME Conference
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• 2004.11a
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• pp.474-479
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• 2004

According to our previous study, it is confirmed that the Petrov-Galerkin natural element method (PGNEM) completely resolves the numerical integration inaccuracy in the conventional Bubnov-Galerkin natural element method (BG-NEM). This paper is an extension of PG-NEM to two-dimensional nonlinear dynamic problem. For the analysis, a constant average acceleration method and a linearized total Lagrangian formulation is introduced with the PG-NEM. At every time step, the grid points are updated and the shape functions are reproduced from the relocated nodal distribution. This process enables the PG-NEM to provide more accurate and robust approximations. The representative numerical experiments performed by the test Fortran program, and the numerical results confirmed that the PG-NEM effectively and accurately approximates the nonlinear dynamic problem.

• Journal of the Earthquake Engineering Society of Korea
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• v.5 no.3
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• pp.57-64
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• 2001

For the dynamic nonlinear analysis of stiffened plate and shell structures, total Lagrangian formulation is presented based upon the degenerated shell element considering finite rotation effects. Assumed strain concept is adopted in order to overcome shear locking phenomena and to eliminate spurious zero energy mode. In the elasto-plastic analysis, the return mapping algorithm based on the consistent elasto-plastic tangent modulus is applied to collapse analysis of shell structures. Newmark integration method is used for dynamic nonlinear analysis of shell structures under dynamic forces.