Dynamic condensation approach to calculation of structural responses and response sensitivities

Structural responses and response sensitivities are widely used in the finite element model updating, damage identification and optimization design. Calculation of the responses and response sensitivities of a large-scale structure consumes considerable computation storage and is usually time-consuming. This paper proposes an improved dynamic condensation approach to calculate the structural responses and response sensitivities. The condensed vibration equation is achieved by a simplified iterative scheme. By selecting the DOFs associated with the concerned element to be master DOFs, the response sensitivity is rapidly calculated from the derivatives of the master stiffness and mass matrices. Since the condensed vibration equation has a much smaller size than the original vibration equation, the proposed method is quite efficient in calculating the structural responses and response sensitivities. Finally, applications of the proposed method to an eight-storey frame and a cantilever plate demonstrate its accuracy and efficiency in the calculation of structural responses and response sensitivities.