Fast simulations for solving fracture mechanics inverse problems using POD-RBF XIGA and Jaya algorithm

An inverse algorithm based on Proper Orthogonal Decomposition (POD) and Radial Basis Functions (RBF) for single and multiple cracks identification in plate structures is presented. The inverse analyses combine experimental fracture mechanics tests with numerical models based on the eXtended IsoGeometric Analysis (XIGA) method. The proposed technique identifies the location of cracks in a plate using static strains as input data. Simple and powerful algorithms, namely Jaya and Cuckoo search algorithms are coupled with the proposed XIGA-POD-RBF technique. The objective function is expressed as the difference between the strains of the actual cracks and those of the estimated ones. It is found that the proposed methodology is able to accurately estimate the cracks locations with high accuracy and much faster than other techniques used in the literature. The stability of the identification algorithm based on Jaya is tested against measurement uncertainty by introducing a white Gaussian noise in the input data. The results show high stability for noise levels up to 4%.