Integration Methods for Improved Stability and Accuracy of Hybrid Simulations

Abstract eng:
Two novel implementation methods of implicit integration procedures for hybrid simulation are presented. The first solves the equation of motion using a fully implicit iterative formulation. The experimental restoring force for each iterative displacement is estimated from curve-fitting of recent force-displacement measurements, avoiding physical iterations on the experimental substructures. For steps that do not converge, the procedure defaults to an explicit formulation. The second integration procedure is a modified operator-splitting integration scheme with two enhancements: a new formulation for the prediction phase with improved accuracy, and the use of an estimated tangent stiffness matrix of the experimental substructure to improve the accuracy of the correction step. A procedure for estimating the experimental tangent stiffness matrix is presented; it is updated only in the steps with significant displacement increments, and remains unchanged otherwise to ensure that the quality of measured data is reliable. Both integration procedures have been successfully implemented experimentally and shown to improve the stability and accuracy of hybrid simulations. Numerical and experimental simulations demonstrate the effectiveness of these integration schemes, especially in utilization of longer time steps, prevention of excitation of higher modes, and testing of stiff and highly nonlinear systems. Improvements in accuracy are demonstrated by measuring the energy balance in the equation of motion.

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