A reduced-order model manifold technique for automated structural defects judging using the PGD with analytical validation

Abstract

Automation is conquering new fields on a daily basis. Aiming for faster and more reliable products, industrials as well as researchers are oriented into automation. Non-destructive testing as well as defect quantification is not an exception. In fact, decisions with minimum allowable error are sought in real-time when facing any potential defect. In this work, we suggest a comprehensive method based on model order reduction techniques to judge if a structure shall be salvaged. The real-time decision is based on multidimensional parametric simulation, performed offline, using the Proper Generalized Decomposition (PGD). The PGD is a model order reduction technique that allows circumventing the curse of dimensionality by using domain decomposition. Therefore, the 6D simulation illustrated in this paper is performed within a few minutes on a standard laptop. Later on, a stress concentration manifold is built and used online for decision-making. The manifold is validated on a few selected solutions solved analytically using an analytical procedure. The aforementioned procedure is developed, in this paper, to calculate the tangential stress around circular holes of different sizes, in an infinite isotropic plate containing any number of holes and subjected to in-plane pressure loading at the tip of the infinite plate. The procedure is based on determining two Muskhelishvili complex potentials in terms of complex Fourier series, and applying the Schwartz alternating method repeatedly until the boundary conditions on the contour of every hole are satisfied.