• 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.

• Proceedings of the KSME Conference
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• 2007.05a
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• pp.596-601
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• 2007

A simplified finite element analysis method is proposed to calculate elasto-plastic responses of general hardening materials. The method provides an effective tool to calculate structural elasto-plastic responses. Numerical examples have demonstrated that its computational efficiency is very much higher than that of the incremental elasto-plastic finite element analysis, and computational results are accurate enough to meet the need of engineering practice. Compared with the general elasto-plastic incremental finite element analysis, the proposed method can avoid the incremental iteration of nodal displacements and the constitutive equation integration at each Gauss integral point, and computational results are accurate enough to meet the need of engineering practice.

• Transactions of the Korean Society of Automotive Engineers
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• v.3 no.1
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• pp.97-107
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• 1995

Global postbuckling analysis is accomplished for one-dimensional and two-dimensional delaminations. A new finite element model, which can be used to model the global postbuckling analysis of one-dimensional and two-dimensional delaminations, is presented. In order to calculate the strain energy release rate, geometrically nonlinear analysis is accomplished, and the incremental crack closure technique is introduced. To check the effectiveness of the finite element models and the incremental crack closure technique, the simplified closed-form sloution for a through-the-width delamination with plane strain condition is derived and compared with the finite element result. The finite element results show good agreement with the closed-foul1 solutions. The present method was extended to calculate the strain energy release rate for two-dimensional delamination. For a symmetric circular delamination, the strain energy release rate shows great variation along the delamination front. and the delamination growth appears to occur perpendicular to the loading direction.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2007.05a
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• pp.340-343
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• 2007

This paper introduces a new approach to consider the bending history in finite element inverse analysis of the cylindrical cup drawing. A modified membrane element is adopted to add the bending-unbending energy to the total plastic energy on the bending-unbending region predicted from the geometry of the final shape and tools. The algorithm suggested was applied to a cylindrical cup deep drawing process. The blank shape and the distribution of the thickness strain are compared with those obtained from incremental finite element analysis. The comparison demonstrates the algorithm proposed reduces the difference between the results from inverse analysis and those from incremental analysis when the bending history is considered.

• Transactions of Materials Processing
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• v.16 no.8
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• pp.590-595
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• 2007

This paper introduces a new approach to take account of bending history in finite element inverse analysis during sheet metal forming process. A modified membrane element was adopted for finite element inverse analysis so that bending-unbending energy was additionally imposed in the total plastic energy, predicting bending-unbending regions using the geometry of the final shape and tools. An algorithm was applied to a cylindrical cup deep drawing process. The blank shape and the distribution of the thickness strain were compared with those obtained from the incremental finite element analysis in order to evaluate the effect of the bending history. The algorithm reduced the difference between the results of the inverse analysis from those of the incremental analysis due to bending history. The analysis was also carried out with the variation of the thickness of the initial blank to investigate the effect of bending deformation. The results showed that the difference was remarkably reduced as the thickness of the initial blank increased. This indicates that the finite element inverse analysis cooperated with the suggested scheme is useful to obtain more accurate results, especially when bending effects are significant.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.32 no.4
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• pp.18-23
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• 2004

In this paper, material non-linear behavior of PZT wafer(3203HD, CTS) under high electric field and stress is experimentally investigated and the non-linearity of the PZT wafer is numerically simulated. Empirical functions that can represent the non-linear behavior of the PZT wafer have been extracted based on the measured piezo-strain under stress. The functions are implemented in an incremental finite element formulation for material non-linear analysis. New definition of the piezoelectric constant and the incremental strain are incorporated into the finite element formulation for a better reproduction of the non-linear behavior. With the new definition of the in incremental piero-strain the measured non-linear behavior of the PZT wafer has been accurately reproduced even for high electric field. For validation of the measured non-linear characteristics and the proposed approach, a PZT bimorph beam actuator has been numerically and experimentally tested. The predicted actuation displacement, based on the material nonlinear finite element analysis, showed a good agreement with the measured one.

• Journal of Korean Association for Spatial Structures
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• v.3 no.4 s.10
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• pp.85-92
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• 2003

In this work, a finite element model is presented for geometrically non-linear analysis of shell structures. Finite element by using a three-node flat triangular shell element is formulated. The non-linear incremental equilibrium equations are formulated by using an updated Lagrangian formulation and the solutions are obtained with the incremental/iterative Newton-Raphson method and arc length method. Some of results are presented for shell structures. The obtained results are in good agreement with the results available in existing literature.

• Computational Structural Engineering
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• v.10 no.1
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• pp.201-211
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• 1997

A clearly consistent finite element formulation for geometrically non-linear analysis of space frames is presented by applying incremental equilibrium equations based on the updated Lagrangian formulation and introducing Vlasov's assumption. The improved displacement field for symmetric cross sections is introduced based on inclusion of second order terms of finite rotations, and the potential energy corresponding to the semitangential rotations and moments is consistently derived. For finite element analysis, elastic and geometric stiffness matrices of the space frame element are derived by using the Hermitian polynomials as shape functions. A co-rotational formulation in order to evaluate the unbalanced loads is presented by separating the rigid body rotations and pure deformations from incremental displacements and evaluating the updated direction cosines of the frame element due to rigid body rotations and incremental member forces from pure deformaions. Finite element solutions for the spatial buckling and post-buckling analysis of space frames are compared with available solutions and other researcher's results.

• Structural Engineering and Mechanics
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• v.6 no.7
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• pp.817-826
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• 1998

A finite element model based on the incremental endochronic theory for flexible pavement materials was developed in this study. Three grid systems with eight-node cubic isoparametric elements, and different loading steps were used to perform the calculations for a specimen of circular cylinder. The uniaxial stress experimental results on an asphalt mixture at $60^{\circ}C$ in SHRP conducted by University of California at Berkeley were used to check the ability of the derived numerical model. Then, the numerical results showed isotropic response and deviatoric response on the specimen in a three dimensional manner, which provided a better understanding for a deformed flexible material under the specified loading conditions.

• Structural Engineering and Mechanics
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• v.12 no.3
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• pp.283-295
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• 2001

The postbuckling behaviour of thin plates is an important phenomenon in the design of thin plated structures. In reality plates possess small imperfections and the behaviour of such imperfect plates is of great interest. To numerically study the postbuckling behaviour of imperfect plates explicit incremental or secant matrices have been presented in this paper. These matrices can be used in combination with any thin plate element. The secant matrices are shown to be very accurate in tracing the postbuckling behaviour of thin plates.