Application of the base forces concept in geometrically nonlinear finite element method on complementary energy

In this paper, a new explicit expression of thegeometrically nonlinear finite element method was developed on thecomplementary energy principle for the large displacement and large rotationproblem on the basis of the concept of base forces as fundamental variables.The complementary energy of an element under large deformation case isdivided into the deformation part and rotation part. The formulations of thecontrol equations for the base forces finite element method are obtainedusing the Lagrange multiplier method, and an explicit displacementformulation of nodes is given. The numerical results are compared with thoseof the theoretical solution and the assumed displacement finite elementmethod based on potential energy principle. It has been demonstrated thatthe new finite element formulations proposed in this paper is effective,accurate, and capable of simulating the large rotation case under one largeload step.