Identification of multiple cracks using a dynamic mesh-refinement method

A dynamic mesh-refinement method (DMRM) of multiple cracks identification is presented, which is based on the relationship of natural frequency change ratios with crack parameters in a beam. The beam is first divided into a coare mesh and the crack is represented by a rotational spring, and expressions relating changes in natural frequencies and the damage index matrix are formulated via an influence matrix. The damage index matrix can be solved by the resulting system of linear algebraic equations. The elements corresponding to the damage indexes with positive values are predicted to contain the crack. Then, these damage elements are refined with the successive subdivision method. The influence matrix is reconstructed through integrating a new subdomain of the damage elements. The new damage index matrix for the refinement meh can focus the crack on the refinement element. In this way, elements are gradually refined until the desired element size is found. The final refinement result indicates the crack location. In each tiny damage element, the spring crack model can be used to quantify the size of the descrete crack. Numerical examples are proposed to demonstrate the effectiveness of the presented method.