A scaled boundary finite element method and Woodbury formula-based algorithm to solve an inverse heat conduction problem with crack identification

Purpose The presented work focuses on the crack identification under the Fourier heat conduction framework so as to provide an efficient numerical algorithm to predict potential failure risks induced by cracks. Design/methodology/approach The identification is conducted by solving a geometric inverse heat conduction problem (IHCP). The forward problem is formulated by SBFEM, which is convenient and efficient to tackle with the crack-induced heat flux singularity. By leveraging SBFEM, a crack can geometrically be represented in a super SBFEM element, and its position can be characterized by sets of coordinates which need to be identified. Findings The proposed approach is verified via numerical examples, in which cracks either on the boundary or inside the domain can be effectively identified and impacts of noisy data, identification resolution, layout of measurement points, etc. are taken into account. Originality/value An SBFEM-based geometric representation is presented to characterize edge and internal cracks with sets of representative coordinates. Due to the locality of the crack, a partitioned heat conduction matrix is derived for which only its small part needs to be updated. A Woodbury formula-based algorithm is developed to reduce the solution scale of the inverse heat conduction matrix. Highlights