A Nonlinear Finite Element Formulation for Very Large Deformation based on Updated Material Reference Frame

변화되는 재료의 기준 물성치에 근거한 매우 큰 변화에 대한 비선형 유한요소의 정식화

  • 윤영묵 (미국 퍼듀대학교 토목공학과) ;
  • 박문호 (경북대학교 공과대학 토목공학과)
  • Received : 1992.05.22
  • Published : 1992.09.30


A nonlinear finite element formulation which has the capability of handling very large geometrical changes is presented. The formulation is based on an updated material reference frame and hence true stress-strain test can be directly applied to properly characterize properties of materials which are subjected to very large deformation. For the large deformation, a consistent formulation based on the continuum mechanics approach is derived. The kinematics is referred to an updated material frame. Body equilibrium is also established in an updated geometry and the second Piola-Kirchhoff stress and the updated Lagrangian strain tensor are used in the formulation. Numerical examples for very large deformation of framed structures and plane solids are analyzed for verification purposes. The numerical solutions are obtained by an incremental numerical procedure. The importance of handing material properties properly is also demonstrated.