T Tangent Stiffness Matrix

The propagation of axial waves in nonlinear elastic rods is studied using three different Galerkin Finite Element schemes. The nonlinearity is introduced using the Murnaghan strain energy function and the equations governing the dynamics of the rod are derived assuming linear kinematics. A nonlinear Semi-Discrete Galerkin Finite Element model with Newmark time integration and Newton-Raphson iteration in the Galerkin spatial ap-proximation, Taylor-Galerkin schemes derived using Pade ́ approximations and Generalized Galerkin Finite Element schemes with quadratic time interpolation are developed for the nonlinear wave equation. The propagation of axial waves in fixed-free rods generated by an impulsive external load at the free end is studied using these Finite Element models and their relative advantages and disadvantages are discussed