Large Deflection Of Spatial Beam Static And Dynamic Modeling, Analysis And Calculation

Based on the strain energy equation for the three-dimensional continuum, the finite element formulation for large deflection of three-dimensional beam is developed. The geometric non-linearity and the coupling action of bending and torsion are comprised in the static formulation, which can describe the large deflection of the three-dimensional beams. Focused on a cantilever beam, the Total Lagrange formulations and the Updated Lagrange formulations are founded; the validity of the present method is confirmed by comparing the calculation results with the theoretic results. The mass matrix and the coupling matrix of bending and torsion vary with the time concern to the deflections of the system when the nonlinear inertial term and the geometric non-linearity term are comprised in the dynamic formulation. The calculation results show that the solution is very close to the solution of linear system when the nonlinear term is weak. As the influence of the nonlinearity is obvious, the conclusion drawn from the present method is the same to the conclusion of the other correlative literatures.