A Modal Derivatives Enhanced Kron’s Substructuring Method to Calculate Structural Responses and Response Sensitivities of Geometrically Nonlinear Systems

Abstract

This paper develops a modal derivative enhanced Kron’s substructuring method to calculate the structural responses and response sensitivities of geometrically nonlinear systems. The proposed method divides the global structure into substructures, which are then assembled in a dual form. The substructural displacements are approximated around the initial linear equilibrium position by using a quadratic modal manifold governed by a few master modes only. A time-variant reduction basis augmented by the master modal derivatives is derived from the quadratic modal manifold, enabling the geometric nonlinearities to be accurately captured. With the reduction basis, the global system is transformed into a reduced one containing the master modes only. Subsequently, the master modal responses and response sensitivities are solved efficiently from the reduced system. The global structural responses and response sensitivities are finally recovered from the master modal solutions based on the quadratic modal manifold. The effectiveness of the proposed method is demonstrated through its application to a thin plate structure. The reduced system enjoys the merit of Kron’s substructuring method that does not contain the interface degrees of freedom. Besides, the proposed reduced system is formed from the quadratic modal manifold directly. Its size is equal to the number of master modes of the substructures and smaller than that of the conventional method, where its size grows quadratically with the number of master modes.