Formulation of the 2-Dimensional Beam Defined by the Absolute Nodal Coordinates with the Algebraic Constraints (The 2nd Report, Implementation of Numerical Simulation and Effect of Non-Linearity of Strain)

Abstract

This paper shows the implementation of the numerical simulation for the two-dimensional beam in the assumption of Euler-Bernoulli beam formulated by the absolute nodal coordinate formulation (ANCF). The proposed formulation is based on the canonical theory in the constraint system. The artificial algebraic constraints are introduced to simplify the derivation procedure of elastic forces with the nonlinear strain models. In this formulation, the Green-Lagrange strain model can be introduced to derive the elastic forces without the symbolic computer algebra program. This formulation gives two equations of motions, one has the expanded degrees of freedom caused by introducing the intentional algebraic constraints, the other has the reduced form, which can be identified as the equation in the previous researches. The accuracy and efficiency of these equations are examined in the numerical examples. Moreover, this study demonstrates the numerical examples focused on the effect of the strain models on the longitudinal and bending deflections. A linear strain model and two nonlinear strain models are introduced in order to discuss the effect. As the result, it is shown the significant difference between the linear and the nonlinear strain models in the large longitudinal and bending deflection problem.