Hybrid Simulation with Improved Operator-Splitting Integration Using Experimental Tangent Stiffness Matrix Estimation

Abstract

Improved numerical integration procedures are essential for the extension of hybrid numerical and experimental simulation to large and complex structural systems. While implicit integration algorithms are widely used in pure numerical simulations for their superior stability and accuracy, their direct application to hybrid simulation has been partially limited by difficulties in estimating the tangent stiffness matrix of multi-degree-of-freedom experimental substructures. Current applications of hybrid simulation using integrators with improved stability have mostly resorted to methods that are noniterative or utilize the initial stiffness matrix for iterative corrections. To improve the accuracy of integration procedures for hybrid simulation, a new method for online estimation of experimental tangent stiffness is proposed. The stiffness estimation procedure is tailored for fast online applications by transforming the measurements into a coordinate system, which reduces the number of unknown stiffness coefficients that need to be updated during the simulation. The updated experimental stiffness matrix is used in a modified operator-splitting integration scheme to improve the accuracy of hybrid simulations with highly nonlinear experimental substructures. The application and effectiveness of the proposed approach is demonstrated through hybrid simulations with multi-degree-of-freedom experimental substructures.