Abstract Summary
Nonlinearities significantly limit the size and complexity of numerical models. The present work presents a general method to simulate kinematic nonlinear structures more efficiently. An efficient basis formulation that increases the number of basis vectors without increasing the number of unknown basis coordinates is used. The basis is organized from a Taylor series that includes the system mode shapes and their complete first-order modal derivatives. The Taylor series predicts fixed linear relations between the modal coordinates of the system mode shapes and the modal derivatives, respectively. Thus, the complete solution is known solely by determining the modal coordinates of the mode shapes. The fixed coordinate relation significantly minimizes the computational costs. Furthermore, it is illustrated that the stability of the Taylor basis is dependent on the mode shape frequencies only, allowing the applied time steps to be significantly larger than in standard nonlinear basis analysis. It is illustrated that the computational time can be decreased by one order of magnitude using a Taylor basis formulation compared to a standard basis formulation, including identical basis vectors.
