저자명 이형욱 
년도 2003 
Most structural analyses are concerned with the behavior of shell structures that are the effective form of relatively thin and flexible structures. Deformation of the shell structures is generally calculated by the finite element analysis with shell elements. The demand of shell models is rapidly growing in a wide range of finite element analyses of the shell structures in order to perform large-scale computations in complicated three-dimensional problems of structural analyses and forming processes. Among various types of shell elements, the four-node bilinear degenerated shell element is widely used for numerical analysis Many recent efforts have been done to include the sixth degree of freedom of the drilling rotation compatible to the physical meaning.
  In this paper, a four-node degenerated shell element with the drilling DOF is developed to solve nonlinear problems with the implicit numerical scheme based on the Belytschko-Leviathan's shell element and the Zhu-Zacharia's bilinear quadrilateral shell element. The drilling DOF has been interpolated by a cubic polynomial function of the beam deflection mechanism and the assumed strain method for the purpose of eliminating the in-plane shear locking phenomenon induced by the third order polynomial interpolation. A suitable assumed strain method for the drilling DOF is obtained by the Rayleigh-Ritz method and is applied to portion of the drilling DOF among the in-plane strain components of a shell element. The transverse shear locking phenomenon is prevented by the Dvorkin and Bathe's assumed strain method. The one point integration rule is adopted for the computational efficiency. Since the reduced integration results in spurious energy modes so called hourglass modes, the physical stabilization method is applied in order to control these spurious modes. The shell element developed is extended to deal with the geometric and the material nonlinearities. The material nonlinearity is considered by applying the return mapping method for a plane stress problem by Simo and Taylor in order to deal with the elasto-plastic constitutive model.
  Several benchmark problems and example problems were solved to investigate the performance of the element developed. The eigenvalue analysis confirmed the validity of the developed shell element and the analysis of linear problems demonstrated the accuracy and convergence of the element developed. Results of linear problems demonstrated that the element developed was free from the in-plane shear locking phenomenon and had good convergence and accuracy under the in-plane deformation and the warped geometry even with the coarse mesh system. The result form the full hemispherical shell problem showed that the membrane locking phenomenon still occurred with the coarse mesh system since it was influenced by the term with ξη.
  Nonlinear problems including the geometrical and the material nonlinearities were chosen in order to confirm the versatility of the drilling degree of freedom and the robustness in the large rotational problem. The nonlinear problems of the bending, the torsion, the plate with a hole, collapse of a square box and collapse of a S-rail have been solved with the element developed and the results fully demonstrate the versatility and performance of the developed shell element. Results showed that the element developed was useful not only in linear problems but also in nonlinear problems including the geometrical and the material nonlinearities.

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14 Microscopic investigation of the strain rate hardening for auto-body steel sheet(차체강판 변형률속도 경화의 미시적 관찰) 윤종헌  2010.07.13 16891
13 Analysis of Elasto-Plastic Stress Waves by a Time Discontinuous Variational Integrator of Hamiltonian with a Second-Order Integration Scheme of the Constitutive Model (해밀토니안의 시간 불연속 변분적분기와 구성방정식의 2차 정확도 적분법을 이용한 탄소 조상순  2008.12.15 21647
12 A Study on the Dynamic Failure Model of a Spot Weld under Combined Loading Conditions for Auto-body Crash Analyses (차체용 부재의 충돌해석을 위한 복합하중조건에서 점용접부의 동적 파단모델 연구) [1] 송정한  2008.07.24 18512
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» Development of a Nonlinear Degenerated Shell Element with the Drilling Degree of Freedom by the Cubic Polynomial Interpolation and the Assumed Strain Method (드릴링 자유도의 삼차 근사법과 대체변형률법을 이용한 비선형 감절점 쉘 요소의 개발) 이형욱  2005.11.29 17665