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Stress evaluation in plane strain problems by elasto-plastic finite element analysis with reduced integration (저감적분 탄소성 유한요소해석에 의한 평면변형문제에서의 응력계산)
The sheet metal forming process is accompanied by the large amount of deformation and rotation which causes springback after unloading. To calculate the amount of springback, the proper evaluation of stress components should be achieved in finite element simulation. In an elasto-plastic finite element analysis, the stress components in each incremental step is evaluated and employed to construct the stiffness matrix of the next step. Therefore, accurate stress calculation in the finite element analysis is very important. In this study, an elasto-plastic finite element analysis is carried out using 4-node iso-parametric element and accuracy of stress calculation at each integration point in each incremental step is examined. When the directional reduced integration or the full integration scheme is adopted, the proper evaluation of stress components at each integration point cannot be achieved. To obtain accurate stress values at integration points, a reduced integration scheme is adopted with the treatment of the hourglass modes which arise due to reduced integration. The hourglass modes can be controlled by an assumed strain method. The finite element program developed using a reduced integration scheme is applied to a class of plane strain problems such as tension of a tapered specimen and bending of a simply supported beam. The numerical result demonstrates the deviation of stress values calculated by a DRI or FI scheme from that by a RI scheme. The application also studies the effect of the aspect ratio of an element and the number of layers in the thickness direction on the calculated solutions.