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Topology optimization using a continuous-time high-cycle fatigue model
Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-1503-8293
Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, Faculty of Science & Engineering.
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2020 (English)In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 61, no 3, p. 1011-1025Article in journal (Refereed) Published
Abstract [en]

We propose a topology optimization method that includes high-cycle fatigue as a constraint. The fatigue model is based on a continuous-time approach where the evolution of damage in each point of the design domain is governed by a system of ordinary differential equations, which employs the concept of a moving endurance surface being a function of the stress and back stress. Development of fatigue damage only occurs when the stress state lies outside the endurance surface. The fatigue damage is integrated for a general loading history that may include non-proportional loading. Thus, the model avoids the use of a cycle-counting algorithm. For the global high-cycle fatigue constraint, an aggregation function is implemented, which approximates the maximum damage. We employ gradient-based optimization, and the fatigue sensitivities are determined using adjoint sensitivity analysis. With the continuous-time fatigue model, the damage is load history dependent and thus the adjoint variables are obtained by solving a terminal value problem. The capabilities of the presented approach are tested on several numerical examples with both proportional and non-proportional loads. The optimization problems are to minimize mass subject to a high-cycle fatigue constraint and to maximize the structural stiffness subject to a high-cycle fatigue constraint and a limited mass.

Place, publisher, year, edition, pages
SPRINGER , 2020. Vol. 61, no 3, p. 1011-1025
Keywords [en]
Continuous-time approach; Endurance surface; High-cycle fatigue; Topology optimization; Adjoint sensitivity analysis; Aggregation function
National Category
Applied Mechanics
Identifiers
URN: urn:nbn:se:liu:diva-164857DOI: 10.1007/s00158-019-02400-wISI: 000519378000009OAI: oai:DiVA.org:liu-164857DiVA, id: diva2:1417688
Available from: 2020-03-30 Created: 2020-03-30 Last updated: 2020-05-05
In thesis
1. Topology Optimization for Additive Manufacturing Involving High-Cycle Fatigue
Open this publication in new window or tab >>Topology Optimization for Additive Manufacturing Involving High-Cycle Fatigue
2020 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

Additive Manufacturing (AM) is gaining popularity in aerospace and automotive industries. This is a versatile manufacturing process, where highly complex structures are fabricated and together with topology optimization, a powerful design tool, it shares the property of providing a very large freedom in geometrical form. The main focus of this work is to introduce new developments of Topology Optimization (TO) for metal AM.

The thesis consists of two parts. The first part introduces background and theory, where TO and adjoint sensitivity analysis are described. Furthermore, methodology used to identify surface layer and high-cycle fatigue are introduced. In the second part, three papers are appended, where the first paper presents the treatment of surface layer effects, while the second and third papers provide high-cycle fatigue constraint formulations.

In Paper I, a TO method is introduced to account for surface layer effects, where different material properties are assigned to bulk and surface regions. In metal AM, the fabricated components in as-built surface conditions significantly affect mechanical properties, particularly fatigue properties. Furthermore, the components are generally in-homogeneous and have different microstructures in bulk regions compared to surface regions. We implement two density filters to account for surface effects, where the width of the surface layer is controlled by the second filter radius. 2-D and 3-D numerical examples are treated, where the structural stiffness is maximized for a limited mass.

For Papers II and III, a high-cycle fatigue constraint is implemented in TO. A continuous-time approach is used to predict fatigue-damage. The model uses a moving endurance surface and the development of damage occurs only if the stress state lies outside the endurance surface. The model is applicable not only for isotropic materials (Paper II) but also for transversely isotropic material properties (Paper III). It is capable of handling arbitrary load histories, including non-proportional loads. The anisotropic model is applicable for additive manufacturing processes, where transverse isotropic properties are manifested not only in constitutive elastic response but also in fatigue properties. Two optimization problems are solved: In the first problem the structural mass is minimized subject to a fatigue constraint while the second problem deals with stiffness maximization subjected to a fatigue constraint and mass constraint. Several numerical examples are tested with arbitrary load histories.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2020. p. 41
Series
Linköping Studies in Science and Technology. Licentiate Thesis, ISSN 0280-7971 ; 1878
National Category
Applied Mechanics
Identifiers
urn:nbn:se:liu:diva-165503 (URN)10.3384/lic.diva-165503 (DOI)9789179298500 (ISBN)
Presentation
2020-05-27, Online: Var vänlig kontakta Anders Klarbring för mer information, anders.klarbring@liu.se, 10:15 (English)
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Supervisors
Available from: 2020-05-05 Created: 2020-05-05 Last updated: 2020-05-05Bibliographically approved

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Suresh, ShyamLindström, StefanThore, Carl-JohanTorstenfelt, BoKlarbring, Anders
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