Topology optimization considering stress, fatigue and load uncertainties

Abstract

Linköping, November 2015Cover: Optimized topology of an L-shaped beam, obtained by minimizing the mass subjected to stress constraints. The design domain and boundary conditions are given in Printed by: LiU-Tryck, Linköping, Sweden, 2015 ISBN 978-91-7685-883-7 ISSN 0345-7524 Distributed by: Linköping University Department of Management and Engineering SE-581 83, Linköping, Sweden c 2015 Erik Holmberg This document was prepared with L A T E X, November 25, 2015 No part of this publication may be reproduced, stored in a retrieval system, or be transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without prior permission of the author. PrefaceThe work presented in this dissertation has been carried out at Saab AB and at the Division of Solid Mechanics, Linköping University. The research has been supported by NFFP (nationella flygtekniska forskningsprogrammet) Grant No. 2013-01221, which is funded by the Swedish Armed Forces, the Swedish Defence Materiel Administration and the Swedish Governmental Agency for Innovation Systems.I am very grateful for the guiding from my supervisors, Anders Klarbring and Bo Torstenfelt, and I have very much appreciated all interesting and fruitful discussions, with them and Carl-Johan Thore, about structural optimization and finite element analysis. I would also like to thank colleagues at Saab AB and Linköping University for encouragement and interesting work-related, as well as off-topic, discussions. Finally, I would also like to express my gratitude for the daily support from my lovely wife Elina and our wonderful son Sixten. Erik HolmbergLinköping, November 2015iii Abstract This dissertation concerns structural topology optimization in conceptual design stages. The objective of the project has been to identify and solve problems that prevent structural topology optimization from being used in a broader sense in the avionic industry; therefore the main focus has been on stress and fatigue constraints and robustness with respect to load uncertainties.The thesis consists of two parts. The first part gives an introduction to topology optimization, describes the new contributions developed within this project and motivates why these are important. The second part includes five papers.The first paper deals with stress constraints and a clustered approach is presented where stress constraints are applied to stress clusters, instead of being defined for each point of the structure. Different approaches for how to create and update the clusters, such that sufficiently accurate representations of the local stresses are obtained at a reasonable computational cost, are developed and evaluated.High-cycle fatigue constraints are developed in the second paper, where loads described by a variable-amplitude load spectrum and material data from fatigue tests are used to determine a limit stress, for which below fatigue failure is not expected. A clustered approach is then used to constrain the tensile principal stresses below this limit.T...

Bulletin of the Polish Academy of Sciences: Technical Sciences

“…Research provided a method for effectively controlling maximum stress by avoiding stress concentrations in notches. In the article, Holmberg et al [14] and a Ph.D. dissertation [15], the author presents a method for stress-based optimization, also with fatigue constraints, for structural problems. They proposed a methodology for a shown methodology of designing optimal structures with fatigue and Bull.…”

On a Nash Game for Topology Optimization Under Load-Uncertainty – Finding the Worst Load

“…the load(s) which maximize (or minimize) f . The setting, studied by the author and co-workers in [2,3,4], is a two-player Nash game formulation for robust TO wherein a "designer" controls the design variables in x and "nature" the load variables in r. Assuming the same pay-off functional f for both players a Nash equilibrium (x * , r * ) is defined by…”