• Journal of Korean Association for Spatial Structures
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• v.10 no.1
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• pp.119-126
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• 2010

The some papers which deal with the dynamic instability for shell-like structures under the dynamic excitation have been published, but there are few papers which treat the essential phenomenon of the dynamic buckling using the phase plane for investigating occurrence of chaos. In nonlinear dynamic, examining the characteristics of attractor on the phase plane and investigating the dynamic buckling process are very important thing for understanding why unstable phenomena are sensitively originated by various initial conditions. In this study, the direct and indirect snapping of shallow EP shell considering geometrical nonlinearity are investigated by Galerkin method numerically. This finding out the characteristic of the dynamic instability through the phases curves and running response spectrum.

• Journal of Korean Association for Spatial Structures
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• v.11 no.1
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• pp.121-130
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• 2011

Space frame structures have the advantage of constructing a large space structures without column and it may be considered as a shell structure. Nevertheless, with the characteristics of thin and long term of spacing, the unstable problem of space structure could not be set up clearly, and there is a huge difference between theory and experiment. Therefore, in this work, the tangential stiffness matrix of space frame structures is studied to solve the instability problem, and the nonlinear incremental analysis of the structures considering rise-span ratio(${\mu}$) and the ratio of load($R_L$) is performed for searching unstable points. Basing on the results of the example, global buckling can be happened by low rise-span ratio(${\mu}$), nodal buckling can be occurred by high rise-span ratio(${\mu}$). And in case of multi node space structure applying the ratio of load($R_L$), the nodal buckling phenomenon occur at low the ratio of load($R_L$), the global buckling occur a1 high the ratio of load($R_L$). In case of the global buckling, the load of bifurcation is about from 50% to 70% of perfect one's snap-through load.

• Journal of the Society of Naval Architects of Korea
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• v.32 no.1
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• pp.141-146
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• 1995

In this study the plastic buckling analysis of a simply supported plate under biaxial compression/tension loading is carried out considering the plastic compressibility. Plastic buckling of a biaxially loaded rectangular plate is governed by two kinds of mechanism, the tension strengthening and plastic weakening under which the optimal combination of tension and compression is obtained for the buckling strength. To consider the plastic compressibility, the Drucker-Prayer plastic potential is employed. General eigenvalue equations are derived for a rectangular plate within the framework of small strain plasticity and isotropic hardening.

• Proceedings of the Korean Society of Disaster Information Conference
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• 2016.11a
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• pp.188-189
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• 2016

본 논문은 초기하중을 하중을 받는 역대칭 angle-ply 와 cross-ply 적층판의 좌굴 및 진동특성을 무재하시의 고유진동수를 이용하여 산정하는 간편법을 제시하였다. 마주보는 두변이 단순 지지된 역대칭 적층판의 운동방정식은 전단변형과 회전강성효과를 고려한 YSN 이론으로 유도하였으며 이를 선점법을 이용하여 해석하였다. 초기응력을 받는 적층판의 무차원화 고유진동수, 임계좌굴계수 및 동적 주 불안정영역 문제들을 무재하시의 무차원화 고유진동수로서 각각의 특성을 정립시켰다. 본 연구에서 제안한 진동특성에 관한 간편산정식의 정당성과 사용성을 입증하기 위하여 수치예들로서 검토하였다.

• Journal of Korean Society of Steel Construction
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• v.24 no.3
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• pp.289-299
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• 2012

The goal of this paper is to apply the multi-step Taylor method to a space truss, a non-linear discrete dynamic system, and analyze the non-linear dynamic response and unstable behavior of the structures. The accurate solution based on an analytical approach is needed to deal with the inverse problem, or the dynamic instability of a space truss, because the governing equation has geometrical non-linearity. Therefore, the governing motion equations of the space truss were formulated by considering non-linearity, where an accurate analytical solution could be obtained using the Taylor method. To verify the accuracy of the applied method, an SDOF model was adopted, and the analysis using the Taylor method was compared with the result of the 4th order Runge-Kutta method. Moreover, the dynamic instability and buckling characteristics of the adopted model under step excitation was investigated. The result of the comparison between the two methods of analysis was well matched, and the investigation shows that the dynamic response and the attractors in the phase space can also delineate dynamic snapping under step excitation, and damping affects the displacement of the truss. The analysis shows that dynamic buckling occurs at approximately 77% and 83% of the static buckling in the undamped and damped systems, respectively.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.15 no.3
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• pp.463-469
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• 2002

The governing equation and force-displacement rotations of a beam-column element on elastic foundation we derived based on variational approach of total potential energy. An exact static and dynamic 4×4 element stiffness matrix of the beam-column element is established via a generalized lineal-eigenvalue problem by introducing 4 displacement parameters and a system of linear algebraic equations with complex matrices. The structure stiffness matrix is established by the conventional direct stiffness method. In addition the F. E. procedure is presented by using Hermitian polynomials as shape function and evaluating the corresponding elastic and geometric stiffness and the mass matrix. In order to verify the efficiency and accuracy of the beam-column element using exact dynamic stiffness matrix, buckling loads and natural frequencies are calculated for the continuous beam structures and the results are compared with F E. solutions.

• Journal of Korean Society of Steel Construction
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• v.11 no.2 s.39
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• pp.153-165
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• 1999

In order to trace the lateral-torsional post-bucking behaviors of thin-walled space frames with non-symmetric cross sections, a geometrically non-linear finite element formulation is presented by applying incremental equilibrium equations based on the updated Lagrangian formulation and introducing Vlasov's assumption. The improved displacement field for non-symmetric thin-walled 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, tangent stiffness matrices of thin-walled space frame element are derived by using the Hermition 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 and incremental member forces.

• Computational Structural Engineering
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• v.10 no.4
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• pp.205-216
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• 1997

In order to trace the lateral post-buckling behaviors of thin-wafled space frames, a geometrically nonlinear finite element formulation is presented by applying incremental equilibrium equations based on the updated Lagrangian formulation and introducing Vlasov's assumption. The improved displacement field for symmetric thin-walled 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, tangent stiffness matrices of the thinwalled space frame element with 7 degrees of freedom including the restrained warping for each node are derived by using the Hermition 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 deformations. Finite element solutions for the spatial buckling and post-buckling analysis of thin-walled space frames are presented and compared with available solutions and other researcher's results.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.22 no.4
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• pp.594-600
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• 2021

Curved beam structures are generally used as components in structures such as railroad bridges and vehicles. The stability analysis of curved beams has been studied by a large number of researchers. Due to the complexities of structural components, it is difficult to obtain an analytical solution for any boundary conditions. In order to overcome these difficulties, the differential quadrature method (DQM) has been applied for a large number of cases. In this study, DQM was used to solve the complicated partial differential equations for buckling analysis of curved beams. The governing differential equation was deduced and solved for beams subjected to uniformly distributed radial loads. Critical loads were calculated with various opening angles, boundary conditions, and parameters. The results of the DQM were compared with exact solutions for available cases, and the DQM gave outstanding accuracy even when only a small number of grid points was used. Critical loads were also calculated for the in-plane inextensional buckling of the asymmetric curved beams, and two theories were compared. The study of a beam with extensibility of the arch axis shows that the effects on the critical loads are significant.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.10 no.3
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• pp.67-75
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• 1990

A geometrically nonlinear analysis procedure including the damping effects is presented for the investigation of the dynamic post-divergence and post-flutter behavior of a non-conservative system. The dynamic nonlinear analysis of plane frame structure subjected to conservative and non-conservative forces is carried out by solving the equations of motion using Newmark method. Numerical results are presented to demonstrate the effects of the internal and external damping forces in the conservative and non-conservative systems.