Numerical dissipation for pseudodynamic testing of nonlinear systems

It is well known that for linear elastic systems favorable numerical dissipation can suppress the spurious growth of high frequency modes while low frequency modes are almost unaffected. Thus, it is interesting to analytically explore the performance of numerical dissipation in the solution of a nonlinear system. In this paper, a novel technique is introduced to evaluate the numerical and error propagation properties of the γ-function explicit method for nonlinear systems. It is analytically and numerically verified that this method has favorable numerical dissipation not only for linear elastic but also nonlinear systems. In fact, the suppression of high frequency modes for nonlinear systems is analytically proved. The importance of the spectral radius for a nonlinear system is also addressed. The rate of suppression of the spurious growth of high frequency responses will be accelerated due to stiffness hardening while it is decelerated due to stiffness softening.