| 1. |
- Holmberg, L. Joakim, 1971-
(författare)
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Musculoskeletal Biomechanics in Cross-country Skiing
- 2012
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Why copy the best athletes? When you finally learn their technique, they may have already moved on. Using muscluloskeletal biomechanics you might be able to add the "know-why" so that you can lead, instead of being left in the swells.This dissertation presents the theoretical framework of musculoskeletal modeling using inverse dynamics with static optimization. It explores some of the possibilities and limitations of musculoskeletal biomechanics in cross-country skiing, especially double-poling. The basic path of the implementation is shown and discussed, e.g. the issue of muscle model choice. From that discussion it is concluded that muscle contraction dynamics is needed to estimate individual muscle function in double-poling. Several computer simulation models, using The Anybody Modeling System™, have been created to study different cross-country skiing applications. One of the applied studies showed that the musculoskeletal system is not a collection of discrete uncoupled parts because kinematic differences in the lower leg region caused kinetic differences in the other end of the body. An implication of the results is that the kinematics and kinetics of the whole body probably are important when studying skill and performance in sports. Another one of the applied studies showed how leg utilisation may affect skiing efficiency and performance in double-poling ergometry. Skiing efficiency was defined as skiing work divided by metabolic muscle work, performance was defined as forward impulse. A higher utilization of the lower-body increased the performance, but decreased the skiing efficiency. The results display the potential of musculoskeletal biomechanics for skiing efficiency estimations. The subject of muscle decomposition is also studied. It is shown both analytically and with numerical simulations that muscle force estimates may be affected by muscle decomposition depending on the muscle recruitment criteria. Moreover, it is shown that proper choices of force normalization factors may overcome this issue. Such factors are presented for two types of muscle recruitment criteria.To sum up, there are still much to do regarding both the theoretical aspects as well as the practical implementations before predictions on one individual skier can be made with any certainty. But hopefully, this disseration somewhat furthers the fundamental mechanistic understanding of cross-country skiing, and shows that musculoskeletal biomechanics will be a useful complement to existing experimental methods in sports biomechanics.
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| 2. |
- Pettersson, Robert, 1981-
(författare)
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Simulation of Human Movements through Optimization
- 2012
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Optimization has been used to simulate human neural control and resulting movement patterns. The short term aim was to develop the methodology required for solving the movement optimization problem often arising when modelling human movements. A long term aim is the contribution to increased knowledge about various human movements, wherein postures is one specific case. Simulation tools can give valuable information to improve orthopeadic treatments and technique for training and performance in sports. In one study a static 3D model with 30 muscle groups was used to analyse postures. The activation levels of these muscles are minimized in order to represent the individual’s choice of posture. Subject specific data in terms of anthropometry, strength and orthopedic aids serve as input. The specific aim of this part was to study effects from orthopedic treatment and altered abilities of the subject. Initial validation shows qualitative agreement of posture strategies but further details about passive stiffness and anthropometry are needed, especially to predict pelvis orientation. Four studies dealt with movement optimization. The main methodological advance was to introduce contact constraints to the movement optimization. A freetime multiple phase formulation was derived to be able to analyse movements where different constraints and degrees of freedom are present in subsequent phases of the movements. The athletic long jump, a two foot high jump, a backward somersault and rowing were used as applications with their different need of formulation. Maximum performance as well as least effort cost functions have been explored. Even though it has been a secondary aim in this work the results show reasonable agreement to expected movements in reality. Case specific subject properties and inclusion of muscle dynamics are required to draw conclusions about improvements in the sport activity, respectively.
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| 3. |
- Rashid, Asim
(författare)
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Finite Element Modeling of Contact Problems
- 2016
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Contact is the principal way load is transferred to a body. The study of stresses and deformations arising due to contact interaction of solid bodies is thus of paramount importance in many engineering applications. In this work, problems involving contact interactions are investigated using finite element modeling.In the first part, a new augmented Lagrangian multiplier method is implemented for the finite element solution of contact problems. In this method, a stabilizing term is added to avoid the instability associated with overconstraining the non-penetration condition. Numerical examples are presented to show the influence of stabilization term. Furthermore, dependence of error on different parameters is investigated.In the second part, a disc brake is investigated by modeling the disc in an Eulerian framework which requires significantly lower computational time than the more common Lagrangian framework. Thermal stresses in the brake disc are simulated for a single braking operation as well as for repeated braking. The results predict the presence of residual tensile stresses in the circumferential direction which may cause initiation of radial cracks on the disc surface after a few braking cycles. It is also shown that convex bending of the pad is the major cause of the contact pressure concentration in middle of the pad which results in the appearance of a hot band on the disc surface. A multi-objective optimization study is also performed, where the mass of the back plate, the brake energy and the maximum temperature generated on the disc surface during hard braking are optimized. The results indicate that a brake pad with lowest possible stiffness will result in an optimized solution with regards to all three objectives. Finally, an overview of disc brakes and related phenomena is presented in a literature review.In the third part, a lower limb donned in a prosthetic socket is investigated. The contact problem is solved between the socket and the limb while taking friction into consideration to determine the contact pressure and resultant internal stress-strain in the soft tissues. Internal mechanical conditions and interface stresses for three different socket designs are compared. Skin, fat, fascia, muscles, large blood vessels and bones are represented separately, which is novel in this work.
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| 4. |
- Schmidt, Peter, 1965-
(författare)
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Analysis of adhesively bonded joints : an asymptotic approach
- 2001
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Simulations using the Finite Element Method (FEM) play an increasingly important role in the design process of joints and fasteners in the aerospace industry. In order to utilize the potential of using adhesive bonding, there is an increasing need for effective and accurate computational methods. The geometry and the nature of an adhesive joint is, however, not so simple to describe effectively using regular FEM-codes. The main reason is that the very thin and soft adhesive layer must be modelled by a large number of FEM-elements in the thickness direction to achieve sufficiently accurate calculations. To overcome this difficulty, special FEM-elements can be developed that provides a material surface treatment of the adhesive and the joined parts. In order to create a model that reflects the above features one may introduce proper scalings on the geometry and on the material properties in terms of a perturbation parameter. Within the framework of three-dimensional elasticity, together with an asymptotic expansion method, a material surface model is obtained through a systematic procedure of derivation. In such derivation no a priori assumptions on the displacements or stress fields are needed. The final result is a variational equation posed over a single reference surface, which forms the basis of a structural element for the compound joint.
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| 5. |
- Ahn, Young Ju, et al.
(författare)
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Shakedown in frictional contact of discrete elastic systems: A review
- 2022
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Ingår i: International Journal of Solids and Structures. - : PERGAMON-ELSEVIER SCIENCE LTD. - 0020-7683 .- 1879-2146. ; 241
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Forskningsöversikt (refereegranskat)abstract
- When exposed to cyclic quasi-static loading, elastic bodies in contact may develop a favourable condition where slip ceases after a few cycles, an occurrence commonly known as frictional shakedown. If the amplitude of the cyclic load is greater than a so-called shakedown limit, shakedown cannot occur. In this review paper, the validity of shakedown theorems in the context of conforming contacts with a la Coulomb friction is first discussed. Then, an optimisation method for determining the shakedown limit of elastic discrete three-dimensional systems is reviewed. Finally, an incremental Gauss-Seidel algorithm, extended to three-dimensional systems, is here illustrated in details for the first time. The algorithm allows us to describe the transient response of normal-tangential coupled systems under a given cyclic loading scenario, and to determine their possible shakedown depending on the initial conditions. An example concerning a discrete conforming contact problem, where either coupling or uncoupling conditions can be imposed, is illustrated.
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| 6. |
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| 7. |
- Andersson, Lars-Erik, 1942-, et al.
(författare)
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A Survey of Basic Mathematical Results for Frictional Contact Problems
- 2001
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Ingår i: From Convexity to Nonconvexity. - Dordrecht/Boston/London : Kluwer. - 0792371445 - 9780792371441 ; , s. -392
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- Contains a collection of invited papers dedicated to the memory of two great mathematicians, Gaetano Fichera and Panagis Panagiotopoulos. The book is centered around the seminal research of G Fichera on the Signorini problem, hemivariational inequalities, nonsmooth global optimization, and regularity results for variational inequatities.
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| 8. |
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| 9. |
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| 10. |
- Andersson, Lars-Erik, 1942-, et al.
(författare)
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On the existence and uniqueness of steady state solutions in thermoelastic contact with frictional heating
- 2005
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Ingår i: Proceedings of the Royal Society of Edinburgh. Section A Mathematics. - : The Royal Society. - 0308-2105 .- 1473-7124. ; 461:2057, s. 1261-1282
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Tidskriftsartikel (refereegranskat)abstract
- It is well known that contact and friction in thermoelasticity result in mathematical problems which may lack solutions or have multiple solutions. Previously, issues related to thermal contact and issues related to frictional heating have been discussed separately. In this work, the two effects are coupled. Theorems of existence and uniqueness of solutions in two or three space dimensions are obtained - essentially extending, to frictional heating, results due to Duvaut, which were built on Barber's heat exchange conditions. Two qualitatively different existence results are given. The first one requires that the contact thermal resistance goes to zero at least as fast as the inverse of the contact pressure. The second existence theorem requires no such growth condition, but requires instead that the frictional heating, i.e. the sliding velocity times the friction coefficient, is small enough. Finally, it is shown that a solution is unique if the inverse of the contact thermal resistance is Lipschitz continuous and the Lipschitz constant, as well as the frictional heating, is small enough.
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| 11. |
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| 12. |
- Andersson, Lars-Erik, 1942-, et al.
(författare)
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Thermoelastic Contact with Frictional Heating
- 2006
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Ingår i: Nonsmooth Mechanics and Analysis,2003. - New York : Springer Science+business Media, inc.. ; , s. 61-
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Konferensbidrag (refereegranskat)
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| 13. |
- Barber, J.R., et al.
(författare)
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Shakedown in frictional contact problems
- 2007
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Ingår i: 2007 Proceedings of the ASME/STLE International Joint Tribology Conference. - 0791838110 - 0791848108 ; , s. 517-519
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- If a linear elastic system with frictional interfaces is subjected to periodic loading, any slip which occurs generally reduces the tendency to slip during subsequent cycles and in some circumstances the system ‘shakes down’ to a state without slip. It has often been conjectured that a frictional Melan’s theorem should apply to this problem — i.e. that the existence of a state of residual stress sufficient to prevent further slip is a sufficient condition for the system to shake down. Here we discuss recent proofs that this is indeed the case for ‘complete’ contact problems if there is no coupling between relative tangential displacements at the interface and the corresponding normal contact tractions. By contrast, when coupling is present, the theorem applies only for a few special two-dimensional discrete cases. Counter-examples can be generated for all other cases. These results apply both in the discrete and the continuum formulation.
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| 14. |
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| 15. |
- Bendsoe, MP, et al.
(författare)
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Joakim Petersson 1968-2002 - Obituary
- 2003
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Ingår i: Structural and multidisciplinary optimization (Print). - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 25:3
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Annan publikation (övrigt vetenskapligt/konstnärligt)
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| 16. |
- Christensen, Peter, et al.
(författare)
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An introduction to structural optimization
- 2009. - 1
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Bok (övrigt vetenskapligt/konstnärligt)abstract
- Mechanical and structural engineers have always strived to make as efficient use of material as possible, e.g. by making structures as light as possible yet able to carry the loads subjected to them. In the past, the search for more efficient structures was a trial-and-error process. However, in the last two decades computational tools based on optimization theory have been developed that make it possible to find optimal structures more or less automatically. Due to the high cost savings and performance gains that may be achieved, such tools are finding increasing industrial use.This textbook gives an introduction to all three classes of geometry optimization problems of mechanical structures: sizing, shape and topology optimization. The style is explicit and concrete, focusing on problem formulations and numerical solution methods. The treatment is detailed enough to enable readers to write their own implementations. On the book's homepage, programs may be downloaded that further facilitate the learning of the material covered.The mathematical prerequisites are kept to a bare minimum, making the book suitable for undergraduate, or beginning graduate, students of mechanical or structural engineering. Practicing engineers working with structural optimization software would also benefit from reading this book."--Publisher's website.
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| 17. |
- Christensen, P. W., et al.
(författare)
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Formulation and comparison of algorithms for frictional contact problems
- 1998
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Ingår i: International Journal for Numerical Methods in Engineering. - : John Wiley & Sons. - 0029-5981 .- 1097-0207. ; 42:1, s. 145-173
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Tidskriftsartikel (refereegranskat)abstract
- This paper presents two algorithms for solving the discrete, quasi-static, small-displacement, linear elastic, contact problem with Coulomb friction. The algorithms are adoptions of a Newton method for solving B-differentiable equations and an interior point method for solving smooth, constrained equations. For the application of the former method, the contact problem is formulated as a system of B-differentiable equations involving the projection operator onto sets with simple structure; for the application of the latter method, the contact problem is formulated as a system of smooth equations involving complementarity conditions and with the non-negativity of variables treated as constraints. The two algorithms are numerically tested for two-dimensional problems containing up to 100 contact nodes and up to 100 time increments. Results show that at the present stage of development, the Newton method is superior both in robustness and speed. Additional comparison is made with a commercial finite element code.
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| 18. |
- Ciavarella, M., et al.
(författare)
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Interaction of thermal contact resistance and frictional heating in thermoelastic instability
- 2003
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Ingår i: International Journal of Solids and Structures. - 0020-7683 .- 1879-2146. ; 40:21, s. 5583-5597
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Tidskriftsartikel (refereegranskat)abstract
- Thermoelastic contact problems can posess non-unique and/or unstable steady-state solutions if there is frictional heating or if there is a pressure-dependent thermal contact resistance at the interface. These two effects have been extensively studied in isolation, but their possible interaction has never been investigated. In this paper, we consider an idealized problem in which a thermoelastic rod slides against a rigid plane with both frictional heating and a contact resistance. For sufficiently low sliding speeds, the results are qualitatively similar to those with no sliding. In particular, there is always an odd number of steady-state solutions, if the steady-state is unique it is stable and if it is non-unique, stable and unstable solutions alternate, with the outlying solutions being stable. However, we identify a sliding speed V0 above which the number of steady states is always even (including zero, implying possible non-existence of a steady-state) and again stable and unstable states alternate. A parallel numerical study shows that for V > V0 there are some initial conditions from which the contact pressure grows without limit in time, whereas for V < V0 the system will always tend to one of the stable steady states. © 2003 Elsevier Ltd. All rights reserved.
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| 19. |
- Daghighi, Abtin, et al.
(författare)
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F.E.M. Stress-Investigation of Scolios Apex
- 2018
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Ingår i: Open Biomedical Engineering Journal. - : Bentham Open. - 1874-1207. ; 12, s. 51-71
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 20. |
- Eriksson, Robert, et al.
(författare)
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OPTIMIZING THERMAL BARRIER COATING DESIGN USING STRUCTURAL OPTIMIZATION METHODS
- 2017
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Ingår i: PROCEEDINGS OF THE ASME TURBO EXPO: TURBINE TECHNICAL CONFERENCE AND EXPOSITION, 2017, VOL 6. - : AMER SOC MECHANICAL ENGINEERS. - 9780791850916
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Konferensbidrag (refereegranskat)abstract
- Thermal barrier coatings (TBCs) are used in gas turbines to reduce creep, thermo-mechanical fatigue, and oxidation, or to allow for reduced air cooling. TBCs may fail due to fatigue. Structural optimization methods were applied to optimize the. TBC thickness in such a way as to increase the life of the TBC. The TBC thickness was varied for three cases: 1) minimizing TBC volume, 2) minimizing TBC maximum effective stress, and 3) minimizing compliance (minimizing the strain energy). The results from the optimization were used to estimate the relative change in TBC life via a strain energy based failure criterion and a Coffin-Manson-like expression. Minimization of volume had limited use due to limitations in the current implementation. Minimization of effective stress did not give any significant increase in life. The minimization of compliance increased the estimated TBC life at highly stressed regions.
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| 21. |
- Fredricson, Harald, et al.
(författare)
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Topology optimization of frame structures with flexible joints
- 2003
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Ingår i: Structural and multidisciplinary optimization (Print). - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 25:3, s. 199-214
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Tidskriftsartikel (refereegranskat)abstract
- A method for structural topology optimization of frame structures with flexible joints is presented. A typical frame structure is a set of beams and joints assembled to carry an applied load. The problem considered in this paper is to find the stiffest frame for a given mass. By introducing design variables for beams and joints, a mass distribution for optimal structural stiffness can be found. Each beam can have several design variables connected to its cross section. One of these is an area-type design variable which is used to represent the global size of the beam. The other design variables are of length ratio type, controlling the cross section of the beam. Joints are flexible elements connecting the beams in the structure. Each joint has stiffness properties and a mass. A framework for modelling these stiffnesses is presented and design variables for joints are introduced. We prove a theorem which can be interpreted as the fact that the removal of structural elements, e.g. joints or beams, can be modelled by a small strictly positive material amount assigned to the element. This is needed for the computations of sensitivities used in the applied gradient based iterative method. Both two and three dimensional problems, as well as multiple load cases and multiple mass constraints, are treated.
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| 22. |
- Haveroth, G. A., et al.
(författare)
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Topology optimization including a model of the layer-by-layer additive manufacturing process
- 2022
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - : ELSEVIER SCIENCE SA. - 0045-7825 .- 1879-2138. ; 398
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Tidskriftsartikel (refereegranskat)abstract
- A topology optimization formulation including a model of the layer-by-layer additive manufacturing (AM) process is considered. Defined as a multi-objective minimization problem, the formulation accounts for the performance and cost of both the final and partially manufactured designs and allows for considering AM-related issues such as overhang and residual stresses in the optimization. The formulation is exemplified by stiffness optimization in which the overhang is limited by adding mechanical or thermal compliance as a measure of the cost of partially manufactured designs. Convergence of the model as the approximate layer-by-layer model is refined is shown theoretically, and an extensive numerical study indicates that this convergence can be fast, thus making it a computationally viable approach useful for including AM-related issues into topology optimization. The examples also show that drips and sharp corners associated with some geometry-based formulations for overhang limitation can be avoided. The codes used in this article are written in Python using only open sources libraries and are available for reference.
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| 23. |
- Hilding, D., et al.
(författare)
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A computational methodology for shape optimization of structures in frictionless contact
- 2001
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - 0045-7825 .- 1879-2138. ; 190:31, s. 4043-4060
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Tidskriftsartikel (refereegranskat)abstract
- This paper presents a computational methodology for shape optimization of structures in frictionless contact, which provides a basis for developing user-friendly and efficient shape optimization software. For evaluation it has been implemented as a subsystem of a general finite element software. The overall design and main principles of operation of this software are outlined. The parts connected to shape optimization are described in more detail. The key building blocks are: analytic sensitivity analysis, an adaptive finite element method, an accurate contact solver, and a sequential convex programing optimization algorithm. Results for three model application examples are presented, in which the contact pressure and the effective stress are optimized. cr 2001 Elsevier Science B.V. All rights reserved.
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| 24. |
- Hilding, Daniel, et al.
(författare)
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Optimization of structures in frictional contact
- 2012
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - : Elsevier. - 0045-7825 .- 1879-2138. ; 205-208:S1, s. 83-90
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Tidskriftsartikel (refereegranskat)abstract
- This paper describes a new approach to optimization of linear elastic structures in frictional contact. It uses a novel method to determine an, in a specified sense, likely equilibrium state of the structure, using only the static equilibrium conditions. That is, no complex dynamic/quasi-static analyses have to be performed. The approach has the advantage that it is not necessary to know the complete load history, which is most often unknown for practical problems. To illustrate the theory, numerical results are given for the optimal design problem of sizing a truss to attain a more uniform normal contact force distribution.
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| 25. |
- Holmberg, Erik, et al.
(författare)
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Fatigue constrained topology optimization
- 2014
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Ingår i: Structural and multidisciplinary optimization (Print). - : Springer-Verlag New York. - 1615-147X .- 1615-1488. ; 50:2, s. 207-219
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Tidskriftsartikel (refereegranskat)abstract
- We present a contribution to a relatively unexplored application of topology optimization: structural topology optimization with fatigue constraints. A probability based high-cycle fatigue analysis is combined with principal stress calculations in order to find the topology with minimal mass that can withstand prescribed loading conditions for a specific life time. This allows us to generate optimal conceptual designs of structural components where fatigue life is the dimensioning factor.We describe the fatigue analysis and present ideas that makes it possible to separate the fatigue analysis from the topology optimization. The number of constraints is kept low as they are applied to stress clusters, which are created such that they give adequate representations of the local stresses. Optimized designs constrained by fatigue and static stresses are shown and a comparison is also made between stress constraints based on the von Mises criterion and the highest tensile principal stresses.
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| 26. |
- Holmberg, Erik, et al.
(författare)
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Game theory approach to robust topology optimization with uncertain loading
- 2017
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Ingår i: Structural and multidisciplinary optimization (Print). - : Springer. - 1615-147X .- 1615-1488. ; 55:4, s. 1383-1397
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 27. |
- Holmberg, Erik, et al.
(författare)
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Global and clustered approaches for stress constrained topology optimization and deactivation of design variables
- 2013
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- We present a global (one constraint) version of the clustered approach previously developed for stress constraints, and also applied to fatigue constraints, in topology optimization. The global approach gives designs without large stress concentrations or geometric shapes that would cause stress singularities. For example, we solve the well known L-beam problem and obtain a radius at the internal corner.The main reason for using a global stress constraint in topology optimization is to reduce the computational cost that a high number of constraints impose. In this paper we compare the computational cost and the results obtained using a global stress constraint versus using a number of clustered stress constraints.We also present a method for deactivating those design variables that are not expected to change in the current iteration. The deactivation of design variables provides a considerable decrease of the computational cost and it is made in such a way that approximately the same final design is obtained as if all design variables are active.
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| 28. |
- Holmberg, Erik
(författare)
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Stress and fatigue constrained topology optimization
- 2013
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis concerns structural optimization in conceptual design stages, for which constraints that are adapted to industrial requirements have been developed for topology optimization problems. The objective of the project has been to identify and solve problems that today prevent structural optimization from being used in a broader sense in the avionic industry; the main focus has been on stress and fatigue constraints in topology optimization.The thesis consists of two parts. The rst part gives an introduction to topology optimization and describes the developed methods for stress and fatigue constraints. In the second part, two papers are included, where the stress and fatigue constraints are evaluated, respectively.In the rst paper, a clustered approach is presented, where stress constraints are applied to stress clusters, rather than points on the structure. This allows for a trade-o between computational time and accuracy, as the number of clusters and thus constraints can be varied. Dierent approaches for how to sort stress evaluation points into clusters and how to update the clusters, such that the results are suciently accurate for conceptual designs, are developed and evaluated. The two-dimensional examples conrm the theoretical discussions and the designs that are obtained have managed to avoid large stress concentrations, even for problems with an initial stress singularity. Compared to the traditional stiness based designs, the stress constrained designs are considered to be closer to a nal design, which will decrease the total product development time.The second paper uses the methodology developed in the rst paper and applies it to high-cycle fatigue constraints. Using loads described by a variable load spectrum and material data from fatigue tests, the tensile principal stresses are constrained by a limit that is determined such that fatigue failure will not occur. In the examples, where the mass is minimized subjected to fatigue and static stress constraints, simple topologies are obtained and the structural parts are sized with respect to the critical fatigue stress and the yield limit. Stress concentrations are again avoided, for example by the creation of a radius around an internal corner. A comparison between static stress constraints based on the von Mises criterion and the highest tensile principal stresses is given and the examples clearly show the characteristics of the two formulations.
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| 29. |
- Holmberg, Erik, et al.
(författare)
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Stress constrained topology optimization
- 2013
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Ingår i: Structural and multidisciplinary optimization (Print). - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 48:1, s. 33-47
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Tidskriftsartikel (refereegranskat)abstract
- This paper develops and evaluates a method for handling stress constraints in topology optimization. The stress constraints are used together with an objective function that minimizes mass or maximizes stiffness, and in addition, the traditional stiffness based formulation is discussed for comparison. We use a clustering technique, where stresses for several stress evaluation points are clustered into groups using a modified P-norm to decrease the number of stress constraints and thus the computational cost. We give a detailed description of the formulations and the sensitivity analysis. This is done in a general manner, so that different element types and 2D as well as 3D structures can be treated. However, we restrict the numerical examples to 2D structures with bilinear quadrilateral elements. The three formulations and different approaches to stress constraints are compared using two well known test examples in topology optimization: the L-shaped beam and the MBB-beam. In contrast to some other papers on stress constrained topology optimization, we find that our formulation gives topologies that are significantly different from traditionally optimized designs, in that it actually manage to avoid stress concentrations. It can therefore be used to generate conceptual designs for industrial applications.
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| 30. |
- Holmberg, Erik, 1985-
(författare)
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Topology optimization considering stress, fatigue and load uncertainties
- 2016
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)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.The third paper introduces load uncertainties and stiffness optimization considering the worst possible loading is then formulated as a semi-definite programming problem, which is solved very efficiently. The load is due to acceleration of point masses attached to the structure and the mass of the structure itself, and the uncertainty concerns the direction of the acceleration. The fourth paper introduces an extension to the formulated semi-definite programming problem such that both fixed and uncertain loads can be optimized for simultaneously.Game theory is used in the fifth paper to formulate a general framework, allowing essentially any differentiable objective and constraint functions, for topology optimization under load uncertainty. Two players, one controlling the structure and one the loads, are in conflict such that a solution to the game, a Nash equilibrium, is a design optimized for the worst possible load.
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| 31. |
- Holmberg, Erik, et al.
(författare)
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Worst-case topology optimization of self-weight loaded structures using semi-definite programming
- 2015
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Ingår i: Structural and multidisciplinary optimization (Print). - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 52:5, s. 915-928
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 32. |
- Holmberg, Joakim L., 1971-
(författare)
-
Computational Biomechanics in Cross-country Skiing
- 2008
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Traditionally, research on cross‐country skiing biomechanics is based mainly on experimental testing alone. Trying a different approach, this thesis explores the possibilities of using computational musculoskeletal biomechanics for cross‐country skiing. As far as the author knows, this has not been done before.Cross‐country skiing is both fast and powerful, and the whole body is used to generate movement. Consequently, the computational method used needs to be able to handle a full‐body model with lots of muscles. This thesis presents several simulation models created in the AnyBody Modeling System, which is based on inverse dynamics and static optimization. This method allows for measurementdriven full‐body models with hundreds of muscles and rigid body segments of all major body parts.A major result shown in the thesis is that with a good simulation model it is possible to predict muscle activation. Even though there is no claim of full validity of the simulation models, this result opens up a wide range of possibilities for computational musculoskeletal biomechanics in cross‐country skiing. Two example of new possibilities are shown in the thesis, finding antagonistic muscle pairs and muscle load distribution differences in different skiing styles. Being able to perform optimization studies and asking and answering “what if”‐questions really gives computational methods an edge compared to traditional testing.To conclude, a combination of computational and experimental methods seems to be the next logical step to increase the understanding of the biomechanics of crosscountry skiing.
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| 33. |
- Holmberg, L. Joakim, 1971-, et al.
(författare)
-
Muscle decomposition and recruitment criteria influence muscle force estimates
- 2012
-
Ingår i: Multibody system dynamics. - : Springer. - 1384-5640 .- 1573-272X. ; 28:3, s. 283-289
-
Tidskriftsartikel (refereegranskat)abstract
- It has recently been pointed out that muscle decomposition influence muscle force estimates in musculoskeletal simulations. We show analytically and with numerical simulations that this influence depends on the recruitment criteria. Moreover, we also show that the proper choices of force normalization factors may overcome the issue. Such factors for the minmax and the polynomial criteria are presented.
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| 34. |
- Hozić, Dženan
(författare)
-
Composite Structure Optimization using a Homogenized Material Approach
- 2014
-
Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The increasing use of bre-reinforced composite materials in the manufacturing of high performance structures is primarily driven by their superior strength-toweight ratio when compared to traditional metallic alloys. This provides the ability to design and manufacture lighter structures with improved mechanical properties. However, the specic manufacturing process of composite structures, along with the orthotropic material properties exhibited by bre-reinforced composite materials, result in a complex structural design process where a number of dierent design parameters and manufacturing issues, which aect the mechanical properties of the composite structure, have to be considered. An ecient way to do this is to implement structural optimization techniques in the structural design process thus improving the ability of the design process to nd design solutions which satisfy the structural requirements imposed on the composite structure.This thesis describes a two phase composite structure optimization method based on a novel material homogenization approach. The proposed method consists of a stiness optimization problem and a lay-up optimization problem, respectively, with the aim to obtain a manufacturable composite structure with maximized stiness properties. The homogenization material approach is applied in both optimization problems, such that the material properties of the composite structure are homogenized. In the proposed method the stiness optimization problem provides a composite structure with maximized stiness properties by nding the optimal distribution of composite material across the design domain. The aim of the lay-up optimization problem is to obtain a manufacturable lay-up sequence of bre-reinforced composite plies for the composite structure which, as far as possible, retains the stiness properties given by the stiness optimization problem. The ability of the composite structure optimization method to obtain manufacturable composite structures is tested and conrmed by a number of numerical tests.
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| 35. |
- Hozić, Dženan, et al.
(författare)
-
Density Filter Control of Thickness-to-Length Change of Composite Structures
- 2013
-
Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- The homogenized material optimization (HMO) problem is a novel structural optimization problem that we have developed for optimization of fiber reinforced composite structures. In the HMO problem we apply a smeared-out approach to model the material properties of fiber reinforced composite materials. The objective of the HMO problem is to maximize the stiffness of a composite structure by means of finding the optimal distribution of composite material, belonging to a fixed set of fiber orientations, across the design domain. In order to obtain manufacturable solutions, we have introduced a linear density filter as a restriction method to control the thickness variation across the design domain. To examine the effect of the density filter on the thickness variation and the objective function value of composite structures, obtained in the HMO problem, we have performed numerical tests for different load cases, mesh densities and range of the filter radius.It is observed that for the present problem the thickness variation was mesh-independent. Both the thickness variation and objective function value depend on the load case used in the HMO problem. For all load cases the thickness variations exhibits an approximately piece-wise linear behaviour for increased filter radius. Furthermore, it was observed that an increase of filter radius would result in an moderate increase in objective function value for the solutions obtained from the HMO problem. From these results we conclude that by using a density filter, the HMO problem can be used to obtain manufacturable designs for composite structures.
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| 36. |
- Hozić, Dženan, et al.
(författare)
-
Stiness and Lay-up Optimization of Composite Structures based on a Homogenized Material Approach
- 2013
-
Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- In the present work we propose a two phase composite structure optimization method based on a novel material homogenization approach. It consists of a stiffness and a lay-up optimization problem, respectively, with the aim of obtaining manufacturable composite structures with maximized stiffness properties. The method is applied to a cantilever plate, and numerical tests were performed for three load cases and for a number of parameters settings. The results show that the proposed method can obtain manufacturable composite structures with maximized stiffness properties. In the first phase of the method, the stiffness optimization problem provides an optimal distribution of the composite material, such that the stiffness properties of the structureare maximized. The second phase, the lay-up optimization problem, provides a manufacturable lay-up sequence of discrete plies which attempts to retain the stiffness properties of the structure from the first phase.
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| 37. |
- Ireman, Peter, et al.
(författare)
-
A model of damage coupled to wear
- 2003
-
Ingår i: International Journal of Solids and Structures. - : Elsevier. - 0020-7683 .- 1879-2146. ; 40:12, s. 2957-2974
-
Tidskriftsartikel (refereegranskat)abstract
- The present paper presents a model of damage coupled to wear. The damage model is based on a continuum model including the gradient of the damage variable. Such a model is non-local in the sense that the evolution of damage is governed by a boundary-value problem instead of a local evolution law. Thereby, the well-known mesh-dependency observed for local damage models is removed. Another feature is that the boundary conditions can be used to introduce couplings between bulk damage and processes at the boundary. In this work such a coupling is suggested between bulk damage and wear at the contact interface. The model is regarded as a first attempt to formulate a continuum damage model for studying crack initiation in fretting fatigue. The model is given within a thermodynamic framework, where it is assured that the principles of thermodynamics are satisfied. Furthermore, two variational formulations of the full initial boundary value problem, serving as starting points for finite element discretization, are presented. Finally, preliminary numerical results for a simple one-dimensional example are presented and discussed. It is qualitatively shown how the evolution of damage may influence the wear behaviour and how damage may be initiated by the wear process. © 2003 Elsevier Science Ltd. All rights reserved.
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| 38. |
- Ireman, Peter, et al.
(författare)
-
Algorithms for thermoelastic wear problems
- 2002
-
Ingår i: Contact mechanics. - Dordrecht : Kluwer Academic. - 9781402008115 - 1402008112 ; , s. 363-370
-
Konferensbidrag (refereegranskat)abstract
- This contribution concerns the numerical treatment of discrete thermoelastic wear problems. Two different approaches, both utilizing a non-smooth Newton method as non-linear equation solver, are outlined and compared. Furthermore, a numerical example shows how the predicted wear gap is influenced by the bulk properties of the contacting bodies.
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| 39. |
- Ireman, Peter, et al.
(författare)
-
Finite element algorithms for thermoelastic wear problems
- 2002
-
Ingår i: European journal of mechanics. A, Solids. - : Elsevier. - 0997-7538 .- 1873-7285. ; 21:3, s. 423-440
-
Tidskriftsartikel (refereegranskat)abstract
- In the present paper three algorithms are applied to a finite element model of two thermoelastic bodies in frictional wearing contact. All three algorithms utilize a modification of a Newton method for B-differentiable equations as non-linear equation solver. In the first algorithm the fully-coupled system of thermomechanical equations is solved directly using the modified method, while in the other two algorithms the equation system is decoupled in one mechanical part and another thermal part which are solved using an iterative strategy of Gauss-Seidel type. The two iterative algorithms differ in which order the parts are solved. The numerical performance of the algorithms are investigated for two two-dimensional examples. Based on these numerical results, the behaviour of the model is also discussed. It is found that the iterative approach where the thermal subproblem is solved first is slightly more efficient for both examples. Furthermore, it is shown numerically how the predicted wear gap is influenced by the bulk properties of the contacting bodies, in particular how it is influenced by thermal dilatation. © 2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved.
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| 40. |
- Ireman, Peter, et al.
(författare)
-
Gradient theory of damage coupled to frictional contact and wear, and its numerical treatment
- 2009
-
Ingår i: CMES - Computer Modeling in Engineering & Sciences. - : Tech Science Press. - 1526-1492 .- 1526-1506. ; 52:2, s. 125-158
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper finite element approaches for fretting fatigue are proposed on the basis of a non-local model of continuum damage coupled to friction and wear. The model is formulated in the frame-work of a standard material. In a previous paper this was done in the spirit of Maugin, where an extra entropy flux is introduced in the second law in order to include the gradient of the internal variable in a proper manner. In this paper we follow instead the ideas of Frémond and others, where this extra entropy flux is no longer needed, but instead new non-classical balance laws associated to damage, friction and wear, respectively, are derived from the principle of virtual power. The standard material is then defined as usual by state laws based on free energies and complementary laws based on dissipation potentials. In particular, we pick free energies and dissipation potentials that correspond to a non-local continuum damage model coupled to friction and wear. In addition, the boundary conditions at the contact interface creates a coupling between damage and wear. This is a key feature of our model, which makes it very useful in studies of fretting fatigue. By starting from a variational formulation of the governing equations, two different finite element algorithms are implemented. Both algorithms are based on a Newton method for semi-smooth equations. In the first algorithm the Newton method is applied to the entire system of equations, while in the second algorithm the system of equations is split into two different parts such that an elastic wear problem is solved for fixed damage followed by the solution of the damage evolution problem for the updated displacements and contact forces in an iterative process. The latter algorithm can be viewed as a Gauss-Seidel scheme. The numerical performance of the algorithms is investigated for three twodimensional examples of increasing complexity. Based on the numerical solutions, the behavior of the model is also discussed. For instance, it is shown numerically how the initiation of damage depends on the contact geometry, the coefficient of friction and the evolution of wear.
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| 41. |
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| 42. |
- Johansson, Leif, et al.
(författare)
-
Study of frictional impact using a nonsmooth equations solver
- 2000
-
Ingår i: Journal of applied mechanics. - : ASME International. - 0021-8936 .- 1528-9036. ; 67:2, s. 267-273
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper a mathematical formulation and a numerical algorithm for the analysis of impact of rigid bodies against rigid obstacles are developed. The paper concentrates on three-dimensional motion using a direct approach where the impenetrability condition and Coulomb's law of friction are formulated as equations, which are not differentiable in the usual sense, and solved together with the equations of motion and necessary kinematical relations using Newton's method. An experiment has also been performed and compared with predictions of the algorithm, with favorable results.
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| 43. |
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| 44. |
- Klarbring, Anders, 1957-, et al.
(författare)
-
A note on the min-max formulation of stiffness optimization including non-zero prescribed displacements
- 2012
-
Ingår i: Structural and multidisciplinary optimization (Print). - : Springer. - 1615-147X .- 1615-1488. ; 45:1, s. 147-149
-
Tidskriftsartikel (refereegranskat)abstract
- The present theoretical note shows how a naturalobjective function in stiffness optimization, including bothprescribed forces and non-zero prescribed displacements,is the equilibrium potential energy. It also shows how theresulting problem has a saddle point character that may beutilized when calculating sensitivities.
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| 45. |
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| 46. |
- Klarbring, Anders, 1957-, et al.
(författare)
-
Asymptotic Modelling of Adhesive Joints
- 1999
-
Ingår i: Mechanics of materials. - 0167-6636 .- 1872-7743. ; 28, s. 137-145
-
Tidskriftsartikel (populärvet., debatt m.m.)
|
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| 47. |
- Klarbring, Anders
(författare)
-
Design optimization based on state problem functionals
- 2015
-
Ingår i: Structural and multidisciplinary optimization (Print). - : Springer Verlag (Germany). - 1615-147X .- 1615-1488. ; 52:2, s. 417-425
-
Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 48. |
- Klarbring, Anders, et al.
(författare)
-
Dynamical systems and topology optimization
- 2010
-
Ingår i: Structural and multidisciplinary optimization (Print). - : Springer Science Business Media. - 1615-147X .- 1615-1488. ; 42:2, s. 179-192
-
Tidskriftsartikel (refereegranskat)abstract
- This paper uses a dynamical systems approach for studying the material distribution (density or SIMP) formulation of topology optimization of structures. Such an approach means that an ordinary differential equation, such that the objective function is decreasing along a solution trajectory of this equation, is constructed. For stiffness optimization two differential equations with this property are considered. By simple explicit Euler approximations of these equations, together with projection techniques to satisfy box constraints, we obtain different iteration formulas. One of these formulas turns out to be the classical optimality criteria algorithm, which, thus, is receiving a new interpretation and framework. Based on this finding we suggest extensions of the optimality criteria algorithm. A second important feature of the dynamical systems approach, besides the purely algorithmic one, is that it points at a connection between optimization problems and natural evolution problems such as bone remodeling and damage evolution. This connection has been hinted at previously but, in the opinion of the authors, not been clearly stated since the dynamical systems concept was missing. To give an explicit example of an evolution problem that is in this way connected to an optimization problem, we study a model of bone remodeling. Numerical examples, related to both the algorithmic issue and the issue of natural evolution represented as bone remodeling, are presented.
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| 49. |
- Klarbring, Anders, et al.
(författare)
-
Dynamical systems, SIMP, bone remodeling and time dependent loads
- 2012
-
Ingår i: Structural and multidisciplinary optimization (Print). - : Springer Verlag (Germany). - 1615-147X .- 1615-1488. ; 45:3, s. 359-366
-
Tidskriftsartikel (refereegranskat)abstract
- The dynamical systems approach to sizing and SIMP topology optimization, introduced in a previous paper, is extended to the case of time-varying loads. A general dynamical system, satisfying a Lyaponov-type descent condition, is derived and specialized to a goal function combining stiffness and mass. For a cyclic time-dependent load it is indicated how, in the limit of short cycles compared to the overall time scale, this can be handled by multiple load cases. Numerical examples, both for a convex and a non-convex case, illustrates the theory.
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| 50. |
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