A spectral finite element for wave propagation and structural diagnostic analysis of composite beam with transverse crack

Abstract

A spectral finite element with embedded transverse crack is developed and implemented to simulate the diagnostic wave scattering in composite beams with various forms of transverse crack, such as surface-breaking cracks, matrix cracking and fiber fracture. The cracked region is discretized into few internal elements, which are modeled as one-dimensional (1D) waveguides. First-order shear deformable kinematics in each of these waveguides is assumed. Appropriate displacement continuity at the element-internal waveguides are enforced. The equilibrium equations are represented using compact matrix notations. After assembly of the element-internal system of waveguides, the internal nodes are condensed out and finally a two-node finite element in frequency domain is obtained. Using this element, namely a single transverse crack is modeled through only three input parameters, the span-wise crack location and the thickness-wise locations of the crack-tips. Although, the proposed element is not suited for dynamic fracture analysis at the local level, it is best suited for narrow-band as well as broad-band wave-based diagnostic simulations for structural health monitoring applications. Numerical simulations and comparison with detail 2D finite element prediction show highly efficient performance of the proposed element to predict the crack location and overall trends due to various crack configurations. Important conclusions are drawn on the advantages of the proposed approach, limitations of the element and further scope of improved diagnostic analysis of cracked beam.