Modeling errors due to Timoshenko approximation in damage identification

Summary The use of accurate computational models for damage identification problems may lead to prohibitive costs. Damage identification problems are often characterized as inverse ill‐posed problems. Thus, the use of approximate models such as simplified physical and/or reduced‐order models typically yields misleading results. In this paper, we carry out a preliminary study on a particular simplified physical model, the Timoshenko beam model in the context of damage identification. The actual beam is a two‐dimensional relatively high aspect ratio (thickness/length) beam with a distributed damage that is modeled as a spatially varying Young modulus. We state the problem in the Bayesian framework for inverse problems and carry out approximative marginalization over the related modeling errors. The numerical experiments suggest that the proposed approach yields more stable results than using the Timoshenko beam model as an accurate model. Due to the severity of the Timoshenko approximation, however, the posterior error estimates of the proposed approach are not always feasible in the probabilistic sense.