A scaled thickness conditioning for solid- and solid-shell discretizations of thin-walled structures |
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Authors: | Thomas Klöppel Michael W Gee Wolfgang A Wall |
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Affiliation: | 1. School of Engineering, Deakin University, Melbourne, Australia;2. School of Engineering, RMIT University, Melbourne, Australia;3. Software Engineer, ITW Construction, Asia Pacific, Melbourne, Australia;4. Australian Research Council Centre of Excellence for Geotechnical Science and Engineering, The University of Newcastle, Australia;1. Sahloul Hospital, Department of Urology, Route de la ceinture, Hammam Sousse, 4011, Sousse, Tunisia;2. Farhat Hached Hospital, Department of Histopathology, Ibn El Jazzar Road, Sousse Ezzouhour, 4031, Sousse, Tunisia;3. Research Lab: Transfer in Technology in Anatomic Pathology (LR12SP08), Tunisia;4. Sahloul Hospital, Department of Radiology, Route de la ceinture, Hammam Sousse, 4011, Sousse, Tunisia;5. Farhat Hached Hospital, Department of General Surgery, Ibn El Jazzar Road, Sousse Ezzouhour, 4031, Sousse, Tunisia;1. Shanghai Key Laboratory of Power Station Automation Technology, School of Mechatronical Engineering and Automation, Shanghai University, Shanghai 200072, China;2. School of Electronics, Electrical Engineering and Computer Science, Queen''s University Belfast, Belfast BT9 5 AH, UK |
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Abstract: | The numerical discretization of thin shell structures yields ill-conditioned stiffness matrices due to an inherent large eigenvalue spectrum. Finite element parametrization that depends on shell thickness, like relative displacement shells, solid shells and other solid finite elements even add to the ill-conditioning by introducing high eigenmodes.To overcome this numerical issue we present a scaled thickness conditioning (STC) approach, a mechanically motivated preconditioner for thin-walled structures discretized with continuum based element formulations. The proposed approach is motivated by the scaled director conditioning (SDC) method for relative displacement shell elements. In contrast to SDC, the novel STC approach yields a preconditioner for the effective linear system. It is applicable independently of element technology employed, coupling to other physical fields, boundary conditions applied and additional algebraic constraints and can be easily extended to multilayer shell formulations.The effect of the proposed preconditioner on the conditioning of the effective stiffness matrix and its eigenvalue spectrum is studied. It is shown that the condition number of the modified system becomes almost independent from the aspect ratio of the employed elements. The improved conditioning has a positive influence on the convergence behavior of iterative linear solvers. In particular, in combination with algebraic multigrid preconditioners the number of iterations could be decreased by more than 85% for some examples and the computation time could be reduced by about 60%. |
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