Variational spectral approach for a problem of impact of a nonlinear elastic rod

This paper presents a numerical analysis of a nonlinear elastic impacted rod. The geometrical relations, mechanical equilibrium equations are linear, while the constitutive relations are nonlinear. Computations are based on spectral methods generalized to include nonlinear cases. A recurrent variational spectral method is introduced in which a discretization of the space and time variables of a function is treated in the same way. The iterative weak solutions are defined. The domain of a function is divided along a wave front to account for a boundary condition for stresses given by the Heaviside function and to include a jump of stresses on the wave front. Moduli of D54S aluminum alloy are used in the computations. The results indicate that nonlinear displacements and stresses are greater than corresponding linear ones.