Implicit numerical integration in hybrid simulation with iteration strategy for experimental substructures

A fully implicit iterative integration procedure is presented for hybrid simulation of the seismic response of structural systems. The advantage of this approach is that experimental elements can be introduced into a simulation using fully implicit integration algorithms designed for pure numerical simulations. The procedure utilizes the tangent stiffness matrices for both numerical and experimental substructures. The tangent stiffness matrix for experimental substructures is estimated using readily available experimental measurements and by classical diagonalization that reduces the number of unknowns in the matrix. In order to avoid physical application of the iterative displacements to experimental substructures, the restoring force of each actuator is estimated using polynomial interpolation and extrapolation of experimental measurements. Numerical and hybrid simulation are used to demonstrate that the proposed algorithm provides an efficient method for full implementation of implicit numerical integration in hybrid simulations of complex nonlinear structures.