Fracture analysis of bridges by spline finite strip method - Song, Zhaobin (University of Ottawa (Canada), 2004)
The primary objective of this thesis is to develop crack strip method and verify the convergency of the method, finally to perform fracture analysis of bridge structures using spline finite strip method. In this thesis, combining the shape function of spline finite strip with the eigenfunction expansions at a crack tip, three types of crack strips, namely anti-plane shear crack strip, plane crack strip and bending crack strip, have been developed, in which cracks are perpendicular to the longitudinal axis of strips and the stress intensity factors can be computed directly. Based on plane crack strips and bending crack strips, the flat shell crack strip is developed for the fracture analysis of box girder bridges. Several case studies have demonstrated the satisfactory convergence of the proposed method. The fracture analysis of different types of bridges have been successfully conducted using these crack strips. In Chapter 3, the basic model of the crack strip is farmed. Substructure technique and extra knots are employed to enhance the efficiency and the convergence of this model. Two Gaussian quadratures for improper integrals are introduced to calculate the singular integral in the crack strip. The efficiencies of these two methods are compared through case studies. On the basis of anti-plane eigenfunction expansion derived by Tilley (1978), plane eigenfunction expansion by Williams (1957) and bending eigenfunction expansion by Williams (1961) in the area around the crack tip, anti-plane shear crack strip, plane crack strip and bending crack strip are developed in Chapter 4 to 6, respectively. The convergence of the proposed models is generally good as shown by case studies. In Chapter 7, these crack strip models are applied to the fracture analysis of bridge structures. Based on the plane crack strip and the bending crack strip, flat shell crack strip is formed for the fracture analysis of box girder bridges. The fracture analysis of different types of bridges, such as slab bridge, continuous slab bridge, single - cell box girder bridge and continuous bridge with top-open box girder, are successfully conducted using these crack strips. The leading diagonal terms are replaced by large numbers to deal with those restraints in the continuous bridges. The present method, i.e., combining the spline finite strip method with the analytical solution for the area around crack tip, provides a new and efficient approach for fracture analysis of structures, especially for the fracture analysis of bridge structures.
Keywords: Engineering, Civil.