An efficient simulation method for structures with local nonlinearity

In general, simulating the nonlinear behavior of systems needs a lot of computational effort. Since researchers in different fields are increasingly targeting nonlinear systems, attempts toward fast nonlinear simulation have attracted much interest in recent years. Examples of such fields are system identification and system reliability. In addition to efficiency, the algorithmic stability and accuracy need to be addressed in the development of new simulation procedures. In this paper, we propose a method to treat localized nonlinearity in a structure in an efficient way. The system will be separated by a linearized part and a nonlinear part that is considered as external pseudo forces that act on the linearized system. The response of the system is obtained by iterations in which the pseudo forces are updated. Since the method is presented in linear state space model form, all manipulations that are made on these, like similarity transformations and model reduction, can easily be exploited. To do numerical integration, time-stepping schemes like the triangular hold interpolation can be used to the advantage. We demonstrate the efficiency, stability and accuracy of the method on numerical examples