Study of a Mixed Finite Element Model for the Analysis of a Geometrically Nonlinear Plate

기하학적 비선형 판재 해석을 위한 혼합형 FE Model 연구

  • Kim, Woo-Ram (Dept. of Mechanical Engineering, Korea Army Academy at Yeong Cheon) ;
  • Choi, Youn-Dae (Dept. of Mechanical Engineering, Korea Army Academy at Yeong Cheon)
  • Received : 2010.07.05
  • Accepted : 2010.07.20
  • Published : 2010.10.01


A mixed finite element model was developed using the classical plate theory to analyze the nonlinear bending of a plate. The appropriate weight functions for the constraints integrated over the domain were determined by the Lagrange multiplier method by using the principle of minimum virtual energy; which provides the constitutive relations between force-like variables and strains. All of detail terms of element wise coefficient matrices and associate tangent matrices to be used in the Newton iterative method are presented. Then, the linear solutions of the current model and those of the traditional displacement model under the SS (simple support) boundary conditions were compared with the existing analytical solution. The post-processed images of the nonlinear results of the force-like variables are presented to show the continuity of the solutions at the joint of the element boundaries. Finally, the converged nonlinear finite element solutions of the current model are compared with those of existing traditional displacement model.


von K$\acute{a}$rm$\acute{a}$n Nonlinearity;Geometric Nonlinearity;Mixed Finite Element Model;Classical Plate Theory;Galerkin Method;Lagrange Multiplier Method


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