Reduced stiffness method for nonlinear analysis of structural frames

This paper addresses a numerical algorithm for nonlinear analysis of frames, using the unitdisplacement method, in generating a reduced stiffness matrix of the structure. this algorithm canproperly be used in nonlinear static analysis or in the incremental response spectral method. here, theinstantaneous reduced stiffness matrix of the structure is calculated, considering its linear behavior atthe latest state, by performing a set of numerical tests on the whole structure. each numerical testconsists of imposing prescribed displacement fields on the lateral displacement of stories and calculatingthe reactions of the structure. the solution procedure of each test is based on the division of degreesof freedom into three parts: (1) predefined lateral displacement of joints, (2) vertical displacement ofjoints, considered as linear degrees of freedom, and (3) rotation of joints, regarded as nonlinear degreesof freedom. the stiffness matrices are generated distinctly for all mentioned parts. therefore, the linearstiffness matrix is inverted once at the beginning of the analysis. the suggested method is not limitedto any special case or physical assumptions. this model has good accuracy in representing structuralresponses and modal properties, confirmed by different numerical examples. regarding computationalcost, the proposed algorithm is more efficient in comparison with the conventional method.