An efficient simulation method for large-scale systems with local nonlinearities

Abstract

In practice, most mechanical systems show nonlinear characteristics within the operational envelope. However, the nonlinearities are often caused by local phenomena and many mechanical systems can be well represented by a linear model enriched with local nonlinearities. Conventional nonlinear response simulations are often computationally intensive; the problem which becomes more severe when large-scale nonlinear systems are concerned. Thus, there is a need to further develop efficient simulation techniques. In this work, an efficient simulation method for large-scale systems with local nonlinearities is proposed. The method is formulated in a state-space form and the simulations are done in the Matlab environment. The nonlinear system is divided into a linearized system and a nonlinear part represented as external nonlinear forces acting on the linear system; thus taking advantage in the computationally superiority in the locally nonlinear system description compared to a generally nonlinear counterpart. The triangular-order hold exponential integrator is used to obtain a discrete state-space form. To shorten the simulation time additionally, auxiliary matrices, similarity transformation and compiled C-codes (mex) to be used for the time integration are studied. Comparisons of the efficiency and accuracy of the proposed method in relation to simulations using the ODE45 solver in Matlab and MSC Nastran are demonstrated on numerical examples of different model sizes.