A simple numerical model of a geometrically nonlinear Timoshenko beam

In the original problem for which this model was developed, onedimensional flexible objects interact through a non-linear contact model. Due to the non-linear nature of the contact model, a numerical time-domain approach was adopted. One of the goals was to see if the coupling between axial and transverse deformations had an influence on the results and so this capacity had to be included. In addition, large deformations should be allowed as well as non-prismatic, non-symmetrical cross-sections and inhomogeneous constitutive properties. To accommodate these requirements the linear model which was being used, was upgrade to meet these requirements. The model created with the procedure explain in this paper consist of discrete masses connected by a set of nonlinear springs. The expressions for the masses and springs are obtained by discretization of the continuum representation of a Timoshenko beam. The required number of springs is proportional to the desired order of geometrical nonlinearity the model should accurately capture. This paper explains the procedure to create a model which can accurately capture geometrically nonlinear effects up to a desired order.