Stability and Accuracy for Nonlinear Systems

Stability and accuracy of the Newmark method for solving nonlinear systems are analytically evaluated. It is proved that an unconditionally stable method for linear elastic systems is also unconditionally stable for nonlinear systems and a conditionally stable method for linear elastic systems remains conditionally stable for nonlinear systems except that the upper stability limit might vary with the step degree of nonlinearity and step degree of convergence. It is also found that numerical accuracy in the solution of nonlinear systems is highly related to the step degree of nonlinearity and the step degree of convergence although its general properties are similar to those of linear elastic systems. Analytical results are confirmed with numerical examples.