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

摘要

Numerous civil engineering structures exhibit nonlinearities. Even though the nonlinear-ities constitute only a small part of the structure, the entire structure behaves nonlin-early, and the analysis of the whole structure is consequently computationally expensive. This paper develops Kron?s substructuring method for fast computation of structural re-sponses 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 combi-nation 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 pro-posed method are verified by a nonlinear spring-mass system and a relatively large-scale nonlinear frame. ? 2021 Elsevier Ltd. All rights reserved.