New method for concurrent dynamic analysis and fatigue damage prognosis of bridges

A new methodology for concurrent dynamic analysis and structural fatigue prognosis is proposed in this paper. The proposed methodology is on the basis of a novel small time scale formulation of material fatigue crack growth that calculates the incremental crack growth at any arbitrary time within a loading cycle. It defines the fatigue crack kinetics on the basis of the geometric relationship between the crack tip opening displacement and the instantaneous crack growth rate. The proposed crack growth model can be expressed as a set of first-order differential equations. The structural dynamics analysis and fatigue crack growth model can be expressed as a coupled hierarchical state-space model. The dynamic response (structural level) and the fatigue crack growth (material level) can be solved simultaneously. Several numerical problems with single degree-of-freedom and multiple degree-of-freedom cases are used to show the proposed methodology. Model predictions are validated using coupon testing data from open literature. Following this, the methodology is demonstrated using a steel-girder bridge. The proposed methodology shows that the concurrent structural dynamics and material fatigue crack growth analysis can be achieved. The cycle-counting method in the conventional fatigue analysis can be avoided. Comparison with experimental data for structural steels and aluminum alloy shows a satisfactory accuracy using the proposed coupled state-space model.