A Taylor basis for kinematic nonlinear real-time simulations. Part II: The Taylor basis

Real-time simulations are used to a significant extent in many engineering fields. However, if nonlinearities are included, the real-time requirement significantly limits the size and complexity of numerical models. The present work constitutes the second of two papers where a general basis method to simulate kinematic nonlinear structures more efficiently is introduced. The advantage of the basis formulation is that it enables the number of basis vectors to be increased without increasing the number of unknown basis co-ordinates. This allows for larger numerical kinematically nonlinear models to run in real time. The basis is organized from a Taylor series that includes the system mode shapes and their complete first-order modal derivatives derived in Part I. The Taylor series predicts fixed linear relations between the modal co-ordinates of the system mode shapes and the modal derivatives, respectively. Thus, the full solution is known solely by determining the modal co-ordinates of the mode shapes, which significantly minimizes the computational costs. Furthermore, it is illustrated that the stability of the Taylor basis formulation is dependent on the mode shape frequencies only, allowing the applied time steps to be significantly larger than in standard nonlinear basis analysis. An example illustrates a case where the computational time can be decreased by one order of magnitude using a Taylor basis formulation compared with a standard basis formulation including identical basis vectors.