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Suresh, S., Lindström, S. B., Thore, C.-J., Torstenfelt, B. & Klarbring, A. (2018). An Evolution-Based High-Cycle Fatigue Constraint in Topology Optimization. In: : . Paper presented at EngOpt 2018, Proceedings of the 6th International Conference on Engineering Optimization, Lisboa, Portugal, 17-19 September, 2018 (pp. 844-854). Cham, Switzerland
Open this publication in new window or tab >>An Evolution-Based High-Cycle Fatigue Constraint in Topology Optimization
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2018 (English)Conference paper, Published paper (Refereed)
Abstract [en]

We develop a topology optimization method including high-cycle fatigue as a constraint. The fatigue model is based on a continuous-time approach, which uses the concept of a moving endurance surface as a function of the stress history and back stress evolution. The development of damage only occurs when the stress state lies outside the endurance surface. Furthermore, an aggregation function, which approximates the maximum fatigue damage, is implemented. As the optimization workflow is sensitivity-based, the fatigue sensitivities are determined using an adjoint sensitivity analysis. The capabilities of the presented approach are tested on numerical models where the problem is to maximize the stiffness subject to high-cycle fatigue constraints.

Place, publisher, year, edition, pages
Cham, Switzerland: , 2018
Keywords
Endurance surface, High-cycle fatigue, Topology optimization, Adjoint sensitivity analysis, Aggregation function
National Category
Applied Mechanics
Identifiers
urn:nbn:se:liu:diva-155097 (URN)10.1007/978-3-319-97773-7_73 (DOI)978-3-319-97772-0 (ISBN)978-3-319-97773-7 (ISBN)
Conference
EngOpt 2018, Proceedings of the 6th International Conference on Engineering Optimization, Lisboa, Portugal, 17-19 September, 2018
Funder
Vinnova, 2016-05175EU, Horizon 2020, 738002
Available from: 2019-03-18 Created: 2019-03-18 Last updated: 2019-03-22Bibliographically approved
Daghighi, A., Tropp, H., Dahlström, N. & Klarbring, A. (2018). F.E.M. Stress-Investigation of Scolios Apex. Open Biomedical Engineering Journal, 12, 51-71
Open this publication in new window or tab >>F.E.M. Stress-Investigation of Scolios Apex
2018 (English)In: Open Biomedical Engineering Journal, ISSN 1874-1207, E-ISSN 1874-1207, Vol. 12, p. 51-71Article in journal (Refereed) Published
Abstract [en]

In scoliosis, kypholordos and wedge properties of the vertebrae should be involved in determining how stress is distributed in the vertebral column. The impact is logically expected to be maximal at the apex.

Place, publisher, year, edition, pages
Bentham Open, 2018
Keywords
Comsol model; FEM Stress-Investigation; Mechanical loading; Pathological mechanisms; Scoliosis; Thoracal Idiopathic
National Category
Computer Engineering
Identifiers
urn:nbn:se:liu:diva-152506 (URN)10.2174/1874120701812010051 (DOI)30258499 (PubMedID)
Available from: 2019-03-28 Created: 2019-03-28 Last updated: 2019-10-07
Holmberg, E., Thore, C.-J. & Klarbring, A. (2017). Game theory approach to robust topology optimization with uncertain loading. Structural and multidisciplinary optimization (Print), 55(4), 1383-1397
Open this publication in new window or tab >>Game theory approach to robust topology optimization with uncertain loading
2017 (English)In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 55, no 4, p. 1383-1397Article in journal (Refereed) Published
Abstract [en]

The paper concerns robustness with respect to uncertain loading in topology optimization problems with essentially arbitrary objective functions and constraints. Using a game theoretic framework we formulate problems, or games, defining Nash equilibria. In each game a set of topology design variables aim to find an optimal topology, while a set of load variables aim to find the worst possible load. Several numerical examples with uncertain loading are solved in 2D and 3D. The games are formulated using global stress, mass and compliance as objective functions or constraints.

Place, publisher, year, edition, pages
Springer, 2017
Keywords
Topology optimization, Robust optimization, Game theory, Nash equilibrium, Stress constraints
National Category
Applied Mechanics
Identifiers
urn:nbn:se:liu:diva-123006 (URN)10.1007/s00158-016-1548-5 (DOI)000398951100015 ()
Note

Funding agencies: NFFP [2013-01221]; Swedish Armed Forces; Swedish Defence Materiel Administration; Swedish Governmental Agency for Innovation Systems; Swedish Foundation for Strategic Research [AM13-0029]

Available from: 2015-12-01 Created: 2015-12-01 Last updated: 2017-05-18Bibliographically approved
Spagnoli, A., Terzano, M., Klarbring, A. & Barber, J. R. (2016). Shakedown in an elastic-plastic solid with a frictional crack. In: Francesco Iacoviello (Ed.), Procedia Structural Integrity vol. 2: . Paper presented at 21st European Conference on Fracture, ECF21, 20-24 June 2016, Catani, Italy (pp. 2667-2673). Elsevier, 2
Open this publication in new window or tab >>Shakedown in an elastic-plastic solid with a frictional crack
2016 (English)In: Procedia Structural Integrity vol. 2 / [ed] Francesco Iacoviello, Elsevier, 2016, Vol. 2, p. 2667-2673Conference paper, Published paper (Refereed)
Abstract [en]

When subjected to periodic loading, elastic systems containing contact interfaces might exhibit frictional slip which ceases after some loading cycles. In such cases, it is said that the system shakes down. For elastic discrete systems presenting complete contacts, it has been proved that Melan’s theorem, originally proposed for elastic-plastic problems, offers a sufficient condition for the system to shake down, provided that the contact is of an uncoupled type. In the present paper, the application of Melan’s theorem is speculated for systems involving plasticity and friction. A finite element example of an elastic-plastic solid containing a frictional crack is discussed.

Place, publisher, year, edition, pages
Elsevier, 2016
Series
Procedia Structural Integrity, ISSN 2452-3216
Keywords
shakedown; Coulomb friction; Associate plasticity; Melan’s theorem
National Category
Applied Mechanics
Identifiers
urn:nbn:se:liu:diva-130797 (URN)10.1016/j.prostr.2016.06.333 (DOI)000387976802091 ()
Conference
21st European Conference on Fracture, ECF21, 20-24 June 2016, Catani, Italy
Note

Fulltext published by CC BY-NC-ND

Available from: 2016-08-24 Created: 2016-08-24 Last updated: 2017-05-15Bibliographically approved
Klarbring, A. (2015). Design optimization based on state problem functionals. Structural and multidisciplinary optimization (Print), 52(2), 417-425
Open this publication in new window or tab >>Design optimization based on state problem functionals
2015 (English)In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 52, no 2, p. 417-425Article in journal (Refereed) Published
Abstract [en]

This paper presents a general mathematical structure for design optimization problems, where state problem functionals are used as design objectives.It extends to design optimization the general model of physical theories pioneered by Tonti (1972, 1976) and Oden and Reddy (1974, 1983). It turns out that the classical structural optimization problem of compliance minimization is a member of the treated general class of problems. Other particular examples, discussed in the paper, are related to Darcy-Stokes flow and pipe flow models. A main novel feature of the paper is the unification of seemingly different design problems, but the general mathematical structure also explains some previously not fully understood phenomena. For instance, the self-penalization property of Stokes flow design optimization receives an explanation in terms of minimization of a concave function over a convex set.

Place, publisher, year, edition, pages
Springer Verlag (Germany), 2015
National Category
Computational Mathematics
Identifiers
urn:nbn:se:liu:diva-120336 (URN)10.1007/s00158-015-1240-1 (DOI)000357476900013 ()
Note

Funding Agencies|Swedish Foundation for Strategic Research [AM13-0029]; Swedish Research Council [Dnr: 621-2012-3117]

Available from: 2015-07-31 Created: 2015-07-31 Last updated: 2017-12-04
Lindström, S., Satha, G. & Klarbring, A. (2015). Extension of Murray's law including nonlinear mechanics of a composite artery wall. Biomechanics and Modeling in Mechanobiology, 14(1), 83-91
Open this publication in new window or tab >>Extension of Murray's law including nonlinear mechanics of a composite artery wall
2015 (English)In: Biomechanics and Modeling in Mechanobiology, ISSN 1617-7959, E-ISSN 1617-7940, Vol. 14, no 1, p. 83-91Article in journal (Refereed) Published
Abstract [en]

A goal function approach is used to derive an extension of Murray’s law that includes effects of nonlinear mechanics of the artery wall. The artery is modeled as a thin-walled tube composed of different species of nonlinear elastic materials that deform together. These materials grow and remodel in a process that is governed by a target state defined by a homeostatic radius and a homeostatic material composition. Following Murray’s original idea, this target state is defined by a principle of minimum work. We take this work to include that of pumping and maintaining blood, as well as maintaining the materials of the artery wall. The minimization is performed under a constraint imposed by mechanical equilibrium. We derive a condition for the existence of a cost-optimal homeostatic state. We also conduct parametric studies using this novel theoretical frame to investigate how the cost-optimal radius and composition of the artery wall depend on flow rate, blood pressure, and elastin content.

Place, publisher, year, edition, pages
Springer Berlin/Heidelberg, 2015
Keywords
Goal function, Murrays law, Constrained mixture theory, Artery
National Category
Mechanical Engineering
Identifiers
urn:nbn:se:liu:diva-113721 (URN)10.1007/s10237-014-0590-8 (DOI)000347250500008 ()24817182 (PubMedID)
Note

At the time for thesis presentation publication was in status: Manuscript

Funding Agencies|Swedish Research Council [621-2012-3117]

Available from: 2015-01-30 Created: 2015-01-29 Last updated: 2017-12-05Bibliographically approved
Thore, C.-J., Holmberg, E. & Klarbring, A. (2015). Large-scale robust topology optimization under load-uncertainty. In: Qing Li, Grant P Steven and Zhongpu (Leo) Zhang (Ed.), Advances in Structural and Multidisciplinary Optimization - Proceedings of the 11th World Congress of Structural and Multidisciplinary Optimization(WCSMO-11): . Paper presented at 11th World Congress on Structural and Multidisciplinary Optimization (WCSMO-11), Sydney Australia, 7–12 June (pp. 255-260).
Open this publication in new window or tab >>Large-scale robust topology optimization under load-uncertainty
2015 (English)In: Advances in Structural and Multidisciplinary Optimization - Proceedings of the 11th World Congress of Structural and Multidisciplinary Optimization(WCSMO-11) / [ed] Qing Li, Grant P Steven and Zhongpu (Leo) Zhang, 2015, p. 255-260Conference paper, Published paper (Refereed)
Abstract [en]

Structures designed by topology optimization (TO) are frequently sensitive to loads different from the ones accounted for in the optimization. In extreme cases this means that loads differing ever so slightly from the ones it was designed to carry may cause a structure to collapse. It is therefore clear that handling uncertainty regarding the actual loadings is important. To address this issue in a systematic  manner is one of the main goals in the field of robust TO. In this work we present a deterministic robust formulation of TO for maximum stiffness design which accounts for uncertain variations around a set of nominal loads. The idea is to find a design which minimizes the maximum compliance obtained as the loads vary in infinite, so-called uncertainty sets. This naturally gives rise to a semi-infinite optimization problem, which we here reformulate into a non-linear, semi-definite program. With appropriate numerical algorithms this optimization problem can be solved at a cost similar to that of solving a standard multiple load-case TO problem with the number of loads equal to the number of spatial dimensions plus one, times the number of nominal loads. In contrast to most previously suggested methods, which can only be applied to small-scale problems, the presented method is – as illustrated by a numerical example – well-suited for large-scale TO problems.

Keywords
Robust optimization, Topology optimization, Large-scale optimization, Non-linear semi-definite programming
National Category
Applied Mechanics
Identifiers
urn:nbn:se:liu:diva-123004 (URN)978-0-646-94394-7 (ISBN)
Conference
11th World Congress on Structural and Multidisciplinary Optimization (WCSMO-11), Sydney Australia, 7–12 June
Available from: 2015-12-01 Created: 2015-12-01 Last updated: 2017-05-15Bibliographically approved
Klarbring, A., Torstenfelt, B. & Satha, G. (2015). Nutrient modulated structural design with application to growth and degradation. Zeitschrift für angewandte Mathematik und Mechanik, 95(11), 1323-1334
Open this publication in new window or tab >>Nutrient modulated structural design with application to growth and degradation
2015 (English)In: Zeitschrift für angewandte Mathematik und Mechanik, ISSN 0044-2267, E-ISSN 1521-4001, Vol. 95, no 11, p. 1323-1334Article in journal (Refereed) Published
Abstract [en]

Phenomena such as biological growth and damage evolution can be thought of as time evolving processes, the directions of which are governed by descendent of certain goal functions. Mathematically this means using a dynamical systems approach to optimization. We extend such an approach by introducing a field quantity, representing nutrients or other non-mechanical stimuli, that modulate growth and damage evolution. The derivation of a generic model is systematic, starting from a Lyaponov-type descent condition and utilizing a Coleman-Noll strategy. A numerical algorithm for finding stationary points of the resulting dynamical system is suggested and applied to two model problems where the influence of different levels of nutrient sensitivity are observed. The paper demonstrates the use of a new modeling technique and shows its application in deriving a generic problem of growth and damage evolution. (C) 2014 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim

Place, publisher, year, edition, pages
WILEY-V C H VERLAG GMBH, 2015
Keywords
topology optimization; biological growth; structural damage; nutrient
National Category
Mechanical Engineering
Identifiers
urn:nbn:se:liu:diva-122786 (URN)10.1002/zamm.201400008 (DOI)000363885300019 ()
Note

Funding Agencies|Swedish Research Council [Dnr: 621-2012-3117]

Available from: 2015-11-23 Created: 2015-11-23 Last updated: 2017-12-01
Holmberg, E., Thore, C.-J. & Klarbring, A. (2015). Worst-case topology optimization of self-weight loaded structures using semi-definite programming. Structural and multidisciplinary optimization (Print), 52(5), 915-928
Open this publication in new window or tab >>Worst-case topology optimization of self-weight loaded structures using semi-definite programming
2015 (English)In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 52, no 5, p. 915-928Article in journal (Refereed) Published
Abstract [en]

The paper concerns worst-case compliance optimization by finding the structural topology with minimum compliance for the loading due to the worst possible acceleration of the structure and attached non-structural masses. A main novelty of the paper is that it is shown how this min-max problem can be formulated as a non-linear semi-definite programming (SDP) problem involving a small-size constraint matrix and how this problem is solved numerically. Our SDP formulation is an extension of an eigenvalue problem seen previously in the literature; however, multiple eigenvalues naturally arise which makes the eigenvalue problem non-smooth, whereas the SDP problem presented in this paper provides a computationally tractable problem. Optimized designs, where the uncertain loading is due to acceleration of applied masses and the weight of the structure itself, are shown in two and three dimensions and we show that these designs satisfy optimality conditions that are also presented.

Keywords
Topology optimization; Semi-definite programming; Worst-case compliance; Self-weight; Robust optimization
National Category
Applied Mechanics Computational Mathematics
Identifiers
urn:nbn:se:liu:diva-123002 (URN)10.1007/s00158-015-1285-1 (DOI)000366590800006 ()
Available from: 2015-12-01 Created: 2015-12-01 Last updated: 2017-12-01Bibliographically approved
Satha, G., Lindström, S. B. & Klarbring, A. (2014). A goal function approach to remodeling of arteries uncovers mechanisms for growth instability. Biomechanics and Modeling in Mechanobiology, 13(6), 1243-1259
Open this publication in new window or tab >>A goal function approach to remodeling of arteries uncovers mechanisms for growth instability
2014 (English)In: Biomechanics and Modeling in Mechanobiology, ISSN 1617-7959, E-ISSN 1617-7940, Vol. 13, no 6, p. 1243-1259Article in journal (Refereed) Published
Abstract [en]

A novel, goal function-based formulation for the growth dynamics of arteries is introduced, and used for investigating the development of growth instability in blood vessels. Such instabilities would lead to abnormal growth of the vessel, reminiscent of an aneurysm. The blood vessel  is modeled as a thin-walled cylindrical tube and the constituents that form the vessel wall are assumed to deform together as a constrained mixture. The growth dynamics of the composite material of the vessel wall is described by an evolution equation, where the effective area of each constituent changes in the direction of steepest descent of a goal function. This goal function is formulated in such way that the constituents grow toward a target potential energy and a target composition. The convergence of the simulated response of the evolution equation toward a target homeostatic state is investigated for a range of isotropic and orthotropic material models. These simulations suggest that elastin-deficient vessels are more prone to growth instability. Increased stiffness of the vessel wall, on the other hand, gives a more stable growth process. Another important finding is that an increased rate of degradation of materials impairs growth stability.

Place, publisher, year, edition, pages
Springer, 2014
Keywords
Goal function, Constrained mixture theory, Stability, Growth and remodeling, Blood vessel, Artery
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-104186 (URN)10.1007/s10237-014-0569-5 (DOI)000343210900007 ()
Available from: 2014-02-10 Created: 2014-02-10 Last updated: 2017-12-06Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0001-8460-0131

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