Kron's substructuring method to the calculation of structural responses and response sensitivities of nonlinear systems

Abstract

Numerous civil engineering structures exhibit nonlinearities. Even though the nonlinearities constitute only a small part of the structure, the entire structure behaves nonlinearly, and the analysis of the whole structure is consequently computationally expensive. This paper develops Kron's substructuring method for fast computation of structural responses and response sensitivities of nonlinear systems. The nonlinearity is detected and located using the ordinary coherence function. The global structure is then divided into linear and nonlinear substructures. The local nonlinearities are thus restricted in a few nonlinear substructures. The linear substructural responses are interpreted as the combination of a few master modal responses based on the mode superposition. The discarded slave modal responses of the linear substructures are compensated by the corresponding master modal responses, nonlinear substructural responses and external excitation on the linear substructures. A reduced vibration equation of a much smaller size is then derived with the transformation matrices. The structural responses and response sensitivities are calculated from the reduced vibration equation. The precision and efficiency of the proposed method are verified by a nonlinear spring-mass system and a relatively large-scale nonlinear frame.