| 1. |
- Amouzgar, Kaveh, 1980-, et al.
(författare)
-
An approach towards generating surrogate models by using RBFN with a priori bias
- 2014
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Ingår i: Proceedings of the ASME International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, 2014, Vol. 2B. - New York, USA : ASME Press. - 9780791846322
-
Konferensbidrag (refereegranskat)abstract
- In this paper, an approach to generate surrogate modelsconstructed by radial basis function networks (RBFN) with a prioribias is presented. RBFN as a weighted combination of radialbasis functions only, might become singular and no interpolationis found. The standard approach to avoid this is to add a polynomialbias, where the bias is defined by imposing orthogonalityconditions between the weights of the radial basis functionsand the polynomial basis functions. Here, in the proposed a prioriapproach, the regression coefficients of the polynomial biasare simply calculated by using the normal equation without anyneed of the extra orthogonality prerequisite. In addition to thesimplicity of this approach, the method has also proven to predictthe actual functions more accurately compared to the RBFNwith a posteriori bias. Several test functions, including Rosenbrock,Branin-Hoo, Goldstein-Price functions and two mathematicalfunctions (one large scale), are used to evaluate the performanceof the proposed method by conducting a comparisonstudy and error analysis between the RBFN with a priori and aposteriori known biases. Furthermore, the aforementioned approachesare applied to an engineering design problem, that ismodeling of the material properties of a three phase sphericalgraphite iron (SGI) . The corresponding surrogate models arepresented and compared
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| 2. |
- Amouzgar, Kaveh, 1980-, et al.
(författare)
-
Multi-objective optimization of a disc brake system by using SPEA2 and RBFN
- 2013
-
Ingår i: ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. - New York : ASME Press. - 9780791855898
-
Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- Many engineering design optimization problems involve multiple conflicting objectives, which today often are obtained by computational expensive finite element simulations. Evolutionary multi-objective optimization (EMO) methods based on surrogate modeling is one approach of solving this class of problems. In this paper, multi-objective optimization of a disc brake system to a heavy truck by using EMO and radial basis function networks (RBFN) is presented. Three conflicting objectives are considered. These are: 1) minimizing the maximum temperature of the disc brake, 2) maximizing the brake energy of the system and 3) minimizing the mass of the back plate of the brake pad. An iterative Latin hypercube sampling method is used to construct the design of experiments (DoE) for the design variables. Next, thermo-mechanical finite element analysis of the disc brake, including frictional heating between the pad and the disc, is performed in order to determine the values of the first two objectives for the DoE. Surrogate models for the maximum temperature and the brake energy are created using RBFN with polynomial biases. Different radial basis functions are compared using statistical errors and cross validation errors (PRESS) to evaluate the accuracy of the surrogate models and to select the most accurate radial basis function. The multi-objective optimization problem is then solved by employing EMO using the strength Pareto evolutionary algorithm (SPEA2). Finally, the Pareto fronts generated by the proposed methodology are presented and discussed.
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| 3. |
- Amouzgar, Kaveh, 1980-, et al.
(författare)
-
Radial basis functions as surrogate models with a priori bias in comparison with a posteriori bias
- 2017
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Ingår i: Structural and multidisciplinary optimization (Print). - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 55:4, s. 1453-1469
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Tidskriftsartikel (refereegranskat)abstract
- In order to obtain a robust performance, the established approach when using radial basis function networks (RBF) as metamodels is to add a posteriori bias which is defined by extra orthogonality constraints. We mean that this is not needed, instead the bias can simply be set a priori by using the normal equation, i.e. the bias becomes the corresponding regression model. In this paper we demonstrate that the performance of our suggested approach with a priori bias is in general as good as, or even for many test examples better than, the performance of RBF with a posteriori bias. Using our approach, it is clear that the global response is modelled with the bias and that the details are captured with radial basis functions. The accuracy of the two approaches are investigated by using multiple test functions with different degrees of dimensionality. Furthermore, several modeling criteria, such as the type of radial basis functions used in the RBFs, dimension of the test functions, sampling techniques and size of samples, are considered to study their affect on the performance of the approaches. The power of RBF with a priori bias for surrogate based design optimization is also demonstrated by solving an established engineering benchmark of a welded beam and another benchmark for different sampling sets generated by successive screening, random, Latin hypercube and Hammersley sampling, respectively. The results obtained by evaluation of the performance metrics, the modeling criteria and the presented optimal solutions, demonstrate promising potentials of our RBF with a priori bias, in addition to the simplicity and straight-forward use of the approach.
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| 4. |
- 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
-
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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| 5. |
- Gustafsson, Erik, et al.
(författare)
-
Residual stresses in a stress lattice : experiments and finite element simulations
- 2009
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Ingår i: Journal of Materials Processing Technology. - : Elsevier. - 0924-0136 .- 1873-4774. ; 209:9, s. 4320-4328
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Tidskriftsartikel (refereegranskat)abstract
- In this work residual stresses in a stress lattice are studied. The residual stresses are both measured and simulated. The stress lattice is casted of low alloyed grey cast iron. In fact, nine similar lattices are casted and measured. The geometry of the lattice consists of three sections in parallel. The diameter of the two outer sections are thinner than the section in the middle. When the stress lattice cools down, this difference in geometry yields that the outer sections start to solidify and contract before the section in the middle. Finally, an equilibrium state, with tensile stresses in the middle and compressive stresses in the outer sections, is reached. The thermo-mechanical simulation of the experiments is performed by using Abaqus. The thermo-mechanical solidification is assumed to be uncoupled. First a thermal analysis, where the lattice is cooled down to room temperature, is performed. Latent heat is included in the analysis by letting the fraction of solid be a linear function of the temperature in the mushy zone. After the thermal analysis a quasi-static mechanical analysis is performed where the temperature history is considered to be the external force. A rate independent J2-plasticity model with isotropic hardening is considered, where the material data depend on the temperature. Tensile tests are performed at room temperature, 200°C, 400°C, 600°C and 800°C in order to evaluate the Young´s modulus, the yield strength and the hardening accurate. In addition, the thermal expansion coefficient is evaluated for temperatures between room temperature and 1000°C. The state of residual stresses is measured by cutting the mid section or the outer section. The corresponding elastic spring-back reveals the state of residual stresses. The measured stresses are compared to the numerical simulations. The simulations show good agreement with the results from the experiments.
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| 6. |
- Gustafsson, Erik, et al.
(författare)
-
Shape Optimization of Castings by using Successive Response Surface Methodology
- 2008
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Ingår i: Structural and multidisciplinary optimization (Print). - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 35:1, s. 11-28
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper, an optimization routine for a thermomechanical problem is presented. The optimization routine is based on the successive response surface methodology where the panning and zooming technique presented by Stander and Craig has been implemented and improved. The optimization routine has been applied to an optimization problem of a three-dimensional beam that undergoes a solidification process. The material in the beam is assumed to be low-alloyed gray iron. The thermomechanical solidification analysis is uncoupled where, first, a thermal analysis is performed to determine the thermal history. This thermal history is then used to calculate the residual stresses in the beam. The residual stresses are solved by using classical J 2-plasticity with temperature-dependent material properties. The residual stresses from solidification are then carried on to the structural analysis where a mechanical load is applied. These are all linked together via scripts, and the commercial FE software Abaqus is used as the FE solver. The obtained maximum von Mises stress and mass information for every set of parameters are then exported to Matlab where general quadratic response surfaces are fitted by a least square method. Taken together, these response surfaces define a minimum of weight problem, which is solved by using sequential linear programming. To minimize the number of evaluations needed, the parameters are chosen to be D-optimally selected. The numerical results show that the residual stresses from solidification might influence the optimal shape significantly. The residual stress results have been compared with those obtained from casting simulation softwares, and the results are similar. The optimization has been compared with a commercial optimization software and shows very promising results.
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| 7. |
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| 8. |
- Gustafsson, Erik, et al.
(författare)
-
Structural optimization of castings by using ABAQUS and Matlab
- 2005
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Ingår i: Competent Design by Castings. - Espoo, Finland : VTT. - 9513862984 - 9513862992 ; , s. 39-52
-
Konferensbidrag (refereegranskat)abstract
- In this work a general method for structural optimization of nonlinear structures is implemented using FE-analysis. The method utilizes the response surface methodology with polynomial surfaces and nonlinear programming. In such manner a method that is applicable for a large number of different classes of nonlinear problems is obtained. In this paper, the method is utilized to minimize weight of castings by including residual stresses from solidification. This is performed by first determine the residual stresses by a thermomechanical analysis of a metal structure that is cooled from a temperature above liquidus temperature down to room temperature. The thermomechanical analysis is uncoupled where the temperature distribution within the casting as a function of time is determined first and is later on used for residual stress calculations. These residual stresses are then included when the mechanical load is applied to the structure and the problem of minimum of weight is formulated. The structure shown in this paper is an example of a two dimensional geometry. The shape of the structures will of course affect the residual stress distribution during the optimization. The nonlinear models are then solved using ABAQUS/Standard. A set of solutions are generated by solving the model for a pre-defined set of parameters. In order to minimize the number of simulations and still achieve good surface approximations these parameters are taken to be D-optimal. The sets of solutions and parameters are in turn exported to Matlab where general quadratic response surfaces are fitted by the least square method. By utilizing these surfaces the problem of minimum of weight subjected to constraints on stresses is formulated. Finally, the nonlinear optimization problem is solved by sequential linear programming.
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| 9. |
- Gustafsson, Erik, et al.
(författare)
-
Structural optimization of castings by using Abaqus and Matlab
- 2005
-
Ingår i: Proceedings of the Abaqus World Users' Conference.
-
Konferensbidrag (refereegranskat)abstract
- In this work a general method for structural optimization of nonlinear structures is implemented using ABAQUS and Matlab. The method utilizes the response surface methodology with polynomial surfaces and nonlinear programming. In such manner a method that is applicable for a large number of different classes of nonlinear problems is obtained. For instance plasticity problems, thermomechanical problems and contact problems can be optimized using this strategy. In this paper, the method is utilized to minimize weight of castings by including residual stresses from solidification. This is performed by first determine the residual stresses by a thermomechanical analysis of a metal structure that is cooled down from a temperature above liquidus temperature down to room temperature. These residual stresses are then included when the problem of minimum of weight is formulated. The shape of the structure will of course affect the residual stress distribution during the optimization and the optimal shape will be different from the one obtained when residual stresses are not included in the analysis. The method is implemented by using a Python script and m-files. In such way a parameterized model can easily be treated in ABAQUS and Matlab during the optimization process. The parameterized geometry, loads, boundary conditions and mesh are first generated by the ABAQUS/CAE module. The nonlinear models are then solved using ABAQUS/Standard. A set of solutions are generated by solving the model for a pre-defined set of parameters. In order to minimize the number of simulations and still achieve good surface approximations these parameters are taken to be D-optimal. The sets of solutions and parameters are in turn exported to Matlab where general quadratic response surfaces are fitted by the least square method. By utilizing these surfaces the problem of minimum of weight subjected to constraints on stresses is formulated. Finally, the nonlinear optimization problem is solved by sequential linear programming where the linear part is solved using Matlab.
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| 10. |
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| 11. |
- Hofwing, Magnus, 1982-, et al.
(författare)
-
D-optimality of non-regular design spaces by using a Bayesian modification and a hybrid method
- 2010
-
Ingår i: Structural and multidisciplinary optimization (Print). - : Springer. - 1615-147X .- 1615-1488. ; 42:1, s. 73-88
-
Tidskriftsartikel (refereegranskat)abstract
- In this work a hybrid method of a genetic algorithm and sequential linear programming is suggested to obtain a D-optimal design of experiments. Regular as well as non-regular design spaces are considered. A D-optimal design of experiments maximizes the determinant of the information matrix, which appears in the normal equation. It is known that D-optimal design of experiments sometimes include duplicate design points. This is, of course, not preferable since duplicates do not add any new information to the response surface approximation and the computational effort is therefore wasted. In this work a Bayesian modification, where higher order terms are added to the response surface approximation, is used in case of duplicates in the design of experiments. In such manner, the draw-back with duplicates might be eliminated. The D-optimal problem, which is obtained by using the Bayesian modification, is then solved by a hybrid method. A hybrid method of a genetic algorithm that generates a starting point for sequential linear programming is developed. The genetic algorithm performs genetic operators such as cross-over and mutation on a binary version of the design of experiments, while the real valued version is used to evaluate the fitness. Next, by taking the gradient of the objective, a LP-problem is formulated which is solved by an interior point method that is available in Matlab. This is repeated in a sequence until convergence is reached. The hybrid method is tested for four numerical examples. Results from the numerical examples show a very robust convergence to a global optimum. Furthermore, the results show that the problem with duplicates is eliminated by using the Bayesian modification.
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| 12. |
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| 13. |
- Hofwing, Magnus, 1982-, et al.
(författare)
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Robustness of residual stresses in castings and an improved process window
- 2010
-
Ingår i: Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2009. - New York, N.Y. : ASME Press. - 9780791849026 ; , s. 1081-1091, s. 1081-1091
-
Konferensbidrag (refereegranskat)abstract
- In this work the robustness of residual stresses in finite element simulations with respect to deviations in mechanical parameters in castings is evaluated. Young's modulus, the thermal expansion coefficient and the hardening are the studied parameters. A 2D finite element model of a stress lattice is used. The robustness is evaluated by comparing purely finite element based Monte Carlo simulations and Monte Carlo simulations based on linear and quadratic response surfaces. Young's modulus, the thermal expansion coefficient and the hardening are assumed to be normal distributed with a standard deviation that is 10% of their nominal value at different temperatures. In this work an improved process window is also suggested to show the robustness graphically. By using this window it is concluded that least robustness is obtained for high hardening values in combination to deviations in Young's modulus and the thermal expansion coefficient. It is also concluded that quadratic response surface based Monte Carlo simulations substitute finite element based Monte Carlo simulations satisfactory. Furthermore, the standard deviation of the responses are evaluated analytically by using the Gauss formula, and are compared to results from Monte Carlo simulations. The analytical solutions are accurate as long as the Gauss formula is not utilized close to a stationary point.
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| 14. |
- Hofwing, Magnus, 1982-, et al.
(författare)
-
Simulation of residual stresses in stamping dies
- 2008
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Ingår i: Proceedings of the IDDRG 2008 Conference. - Olofström : Industriellt utvecklingscentrum i Olofström AB. - 9789163329487 ; , s. 765-776
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Konferensbidrag (refereegranskat)abstract
- In the past stamping dies have in principle been designed by rules of thumb and intuition. As the sheet metals in the vehicle industry have got increased mechanical properties in recent years the demands on the stamping dies have increased. For instance increase in stiffness is desirable in order to better control spring-back. The most simple way to satisfy this new demand would be to make the stamping dies even more heavy in order to be able to handle the new sheet metals. Since there are restrictions of the weight of the stamping dies in the stamping machines and since the overhead cranes usually have reached the limit of what they can handle, this is not a desirable solution. Another approach, in order to increase the stiffness without increasing the weight is to use topology optimization. Recently in a master thesis at Volvo Car Corporation a conceptual design of a stamping die has been done by topology optimization. In that work no consideration is taken to the fact that the stamping die is casted. Casting implies that residual stresses possibly are produced during the solidification and cooling process. The residual stresses might affect the fatigue life and the risk of failure of the stamping die.In this work the residual stress state after casting is analyzed for the original stamping die as well as the optimized stamping die from the master thesis discussed above. The analyses are performed using an uncoupled approach, where one thermal analysis is followed by a quasi-static elasto-plastic analysis. The thermal analysis simulates the solidification and cooling during the casting process, while the quasi-static elasto-plastic analysis uses the temperature history, obtained from the thermal analysis, in order to build up residual stresses. The thermal analysis includes the release of latent heat. Furthermore, the material properties included in the heat equation (density, conductivity, specific heat) are given as temperature dependent properties for the mould as well as the casting. In the quasi-static elasto-plastic analysis the plasticity is described by the von Mises yield surface in combination with isotropic hardening and the mechanical properties (thermal expansion coefficient, Young's modulus, yield stress, hardening parameter, Poisson's ratio) are given as temperature dependent properties. The simulations show high levels of residual stresses.
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| 15. |
- Ireman, Peter, et al.
(författare)
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Algorithms for thermoelastic wear problems
- 2002
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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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| 16. |
- 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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| 17. |
- Karlsson, Patrik, 1973-, et al.
(författare)
-
Generative Design Optimization and Characterization of Triple Periodic Lattice Structures in AlSi10Mg
- 2020
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Ingår i: Industrializing Additive Manufacturing. - Cham : Springer. - 9783030543334 - 9783030543341 ; , s. 3-16
-
Konferensbidrag (refereegranskat)abstract
- In this work, generative design optimization and characterization of triple periodic lattice structures in AlSi10Mg are considered. Structures with Gyroid, Schwarz-D and G-prime lattices are designed optimally by utilizing a generative design optimization approach. The approach is based on topology optimization, support vector machines (SVM), radial basis function networks (RBFN), morphing operations, design of experiments and metamodels. Firstly, topology optimization solutions are generated which are represented using SVM, secondly, sizing solutions obtained by setting the SIMP parameter equal to one are represented with RBFN. Thirdly, graded lattice structures using the RBFN are morphed together with the SVM to final conceptual designs. Fourthly, design of experiments of the conceptual designs are performed using non-linear finite element analyses (FEA) and, finally, metamodel-based design optimization is conducted using convex combinations of Kriging, RBFN, polynomial chaos expansion and support vector regression models. In order to validate the optimal designs, new tensile test specimens that include the periodic lattice structures are suggested. The specimens with all three lattices are manufactured in AlSi10Mg using direct metal laser sintering with an EOS M290 machine. Tensile tests of these specimens are then performed and validated using nonlinear FEA. The test specimens are also characterized with respect to geometry and defects by means of computed tomography, optical microscopy and scanning electron microscopy. The study demonstrates the high potential of using the proposed generative design optimization approach with triple periodic lattice structures for producing robust lightweight designs using additive manufacturing. In order to demonstrate the industrial relevance the established GE engine bracket is studied in the paper and discussed at the conference.
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| 18. |
- Klarbring, Anders, 1957-, et al.
(författare)
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A note on the min-max formulation of stiffness optimization including non-zero prescribed displacements
- 2012
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Ingår i: Structural and multidisciplinary optimization (Print). - : Springer. - 1615-147X .- 1615-1488. ; 45:1, s. 147-149
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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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| 19. |
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| 20. |
- Klarbring, Anders, 1957-, et al.
(författare)
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Topology optimization of hyperelastic bodies including non-zero prescribed displacements
- 2013
-
Ingår i: Structural and multidisciplinary optimization (Print). - : Springer. - 1615-147X .- 1615-1488. ; 47:1, s. 37-48
-
Tidskriftsartikel (refereegranskat)abstract
- Stiffness topology optimization is usually based on a state problem of linear elasticity, and there seems to be little discussion on what is the limit for such a small rotation-displacement assumption. We show that even for gross rotations that are in all practical aspects small (<3 deg), topology optimization based on a large deformation theory might generate different design concepts compared to what is obtained when small displacement linear elasticity is used. Furthermore, in large rotations, the choice of stiffness objective (potential energy or compliance), can be crucial for the optimal design concept. The paper considers topology optimization of hyperelastic bodies subjected simultaneously to external forces and prescribed non-zero displacements. In that respect it generalizes a recent contribution of ours to large deformations, but we note that the objectives of potential energy and compliance are no longer equivalent in the non-linear case. We use seven different hyperelastic strain energy functions and find that the numerical performance of the Kirchhoff–St.Venant model is in general significantly worse than the performance of the other six models, which are all modifications of this classical law that are equivalent in the limit of infinitesimal strains, but do not contain the well-known collapse in compression. Numerical results are presented for two different problem settings.
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| 21. |
- Lundvall, Olle, et al.
(författare)
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A flexible multi-body approach for frictional contact in spur gears
- 2004
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Ingår i: Journal of Sound and Vibration. - : Elsevier. - 0022-460X .- 1095-8568. ; 278:3, s. 479-499
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Tidskriftsartikel (refereegranskat)abstract
- In the present paper, a large rotational approach for dynamic contact problems with friction is proposed. The approach is used for modelling a spur gear pair with shafts and bearings. The model is obtained by superposing small displacement elasticity on rigid-body motions, and postulating tribological laws on the gear flanks. The finite element method is used to model the elastic properties of the gear pair. Shafts and bearings are represented by linear springs. The tribological laws of the contact interface are Signorini's contact law and Coulomb's law of friction. An important feature of the approach is that the difficulties of impacting mass nodes are avoided. The governing equations of the model are numerically treated by use of the augmented Lagrangian approach. In such manner the geometry of the gear flanks are well represented in the numerical simulations. It is possible to study accurately the consequences of different types of profile modifications as well as flank errors. In this work, the dynamic transmission error is studied. For instance, it turns out that the effect from profile modification is less significant for the transmission error when frictional effects are included.
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| 22. |
- Rashid, Asim, 1978-, et al.
(författare)
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An Efficient Sequential Approach for Simulation of Thermal Stresses in Disc Brakes
- 2012
-
Ingår i: Nordtrib 2012, 15th Nordic Symposium on Tribology, 2012.
-
Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- In this paper an efficient approach to simulate thermal stresses due to frictional heating of disc brakes is presented. Inthe approach thermal and stress analysis are performed sequentially. The frictional heat analysis is based on the Eulerianmethod, which requires significantly low computational time as compared to the Lagrangian approach. Completethree-dimensional geometries of a disc and a pad are considered for the numerical simulations. The contact forcesare computed at each time step taking the thermal deformations of the disc into account. The nodal temperaturehistory is recorded at each time step and is used in sequentially coupled stress analysis, where a temperature dependentelasto-plastic material model is used to compute the stresses in a disc brake. The results show that during hard braking,high compressive stresses are generated on the disc surface in circumferential direction which cause plastic yielding. Butwhen the disc cools down, the compressive stresses transform to tensile stresses. Such thermoplastic stress history maycause cracks on disc surface after a few braking cycles. These results are in agreement with experimental observationsavailable in the literature.
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| 23. |
- Rashid, Asim, 1978-, et al.
(författare)
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Sequential simulation of thermal stresses in disc brakes for repeated braking
- 2013
-
Ingår i: Proceedings of the Institution of mechanical engineers. Part J, journal of engineering tribology. - London, United Kingdom : Sage Publications. - 1350-6501 .- 2041-305X. ; 227:8, s. 919-929
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, an efficient sequential approach for simulating thermal stresses in brake discs for repeated braking is presented. First, a frictional heat analysis is performed by using an Eulerian formulation of the disc. Then, by using the temperature history from the first step of the sequence, a plasticity analysis with temperature dependent material data is performed in order to determine the corresponding thermal stresses. Three-dimensional geometries of a disc and a pad to a heavy truck are considered in the numerical simulations. The contact forces are computed at each time step taking the thermal deformations of the disc and pad into account. In such manner, the frictional heat power distribution will also be updated in each time step, which in turn will influence the development of heat bands. The plasticity model is taken to be the von Mises yield criterion with linear kinematic hardening, where both the hardening and the yield limit are temperature dependent. The results show that during hard braking, high compressive stresses are generated on the disc surface in the circumferential direction which cause yielding. But when the disc cools down, these compressive stresses transform to tensile residual stresses. For repeated hard braking when this kind of stress history is repeated, we also show that stress cycles with high amplitudes are developed which might generate low cycle fatigue cracks after a few braking cycles.
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| 24. |
- Rashid, Asim, 1978-, et al.
(författare)
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Thermomechanical Simulation of Wear and Hot Bands in a Disc Brake by Adopting an Eulerian Approach
- 2013
-
Ingår i: Eurobrake 2013. - : FISITA.
-
Konferensbidrag (refereegranskat)abstract
- In this paper frictional heating of a disc brake is simulated while taking wear into account. By performing thermomechanical finite element analysis, it is studied how the wear history will influence the development of hot bands. The frictional heat analysis is based on an Eulerian formulation of the disc, which requires significantly lower computational time as compared to a standard Lagrangian approach. A real disc-pad system to a heavy truck is considered, where complete three-dimensional geometries of the ventilated disc and pad are used in the simulations. A sequential approach is adopted, where the contact forces are computed at each time step taking the wear and thermal deformations of the mating parts into account. After each brake cycle, the wear profile of the pad is updated and used in subsequent analysis. The results show that when wear is considered, different distributions of the temperature on disc are obtained for each new brake cycle. After a few braking cycles two hot bands appear on the disc surface instead of only one. These results are in agreement with experimental observations.
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| 25. |
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| 26. |
- Strömberg, Niclas, 1968-
(författare)
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A Generative Design Optimization Approach for Additive Manufacturing
- 2019
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Ingår i: Second International Conference on Simulation for Additive Manufacturing. - Barcelona, Spain : International Centre for Numerical Methods in Engineering (CIMNE). - 9788494919480 ; , s. 130-141
-
Konferensbidrag (refereegranskat)abstract
- In this paper, we present a generative design optimization (GDO) approach for additive manufacturing (AM) by using topology optimization, support vector machines, cellular lattice structures (CLS), design of experiments, morphing and metamodel-based design optimization. By starting from appropriate design domains, a trade-off curve of design concepts is generated by SIMP-based topology optimization (TO). Then, a smooth implicit representation of the TO-solution is established by classifying the discrete density values using soft non-linear support vector machines (SVM). Instead of using the standard soft non-linear SVM of Cortez and Vapnik, we classify the TO solutions by using the 1-norm SVM of Mangasarian. In such manner, the classification is obtained by linear programming instead ofquadratic programming. The implicit SVM-model is further modified by incorporating cellular lattice structures, such as e.g. Gyroid lattice structures, by applying boolean operators. Design of experiments using finite element analysis are then set up by morphing the CLS-modified SVM models for different volume fractions. Finally, metamodel-based design optimization is performed by using optimal ensembles of polynomial regression models, Kriging, radial basis function networks, polynomial chaos expansion and support vector regression. The steps presented above constitute our proposed generative design optimization approach for additive manufacturing and are presented in more detail in the paper.
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| 27. |
- Strömberg, Niclas, 1968-, et al.
(författare)
-
A Layer-by-Layer Approach for Simulating Residual Stresses in AM
- 2017
-
Ingår i: 11th European LS-DYNA Conference.
-
Konferensbidrag (refereegranskat)abstract
- Distortions and residual stresses developed during additive manufacturing(AM) might be so severe that the design does not meet tolerance requirementsor even cracks and fail. Predictions of such distortions andresidual stressesby finite element analysis are therefore preferable performed early during thedesign development in order to reduce such problems. One approach for thiskind of analysis is to apply techniques from welding simulations letting theGoldak heat source move over each layer of the material. However, this iscomputationally most costly and one might also argue how well this actuallyrepresent the AM process. We suggest to simplify this boundary conditionto instead apply the heat layer-by-layer. We mean that this will represent theAM process as well as an approach of using the Goldak heat source and it ismuch more computational efficient than applying Goldaks heat source. Themodel is simply obtained by slicing the geometry in several layers using anin-house script. Then, a volume heat source is applied layer-by-layer, whereeach layer is activated starting from the build plate until the final build layer.Sequentially thermomechanical analysis using LS-Dyna is applied, wherethe heat capacity, conductivity, Youngs modulus, Poissonsratio, expansioncoefficient, yield stress, and the hardening modulus are given as functionsof temperature. The classical heat equation and J2-plasticity with kinematicor isotropic hardening are adopted by using*MATTHERMALCWMand*MATCWM,which makes the activation of the layers straight-forward using the ghostfeature implemented in these material models. After all layers are activatedand heated, a restart of cooling analysis is performed and, finally, the partis cut from the building plate using a third restart analysis. The approachis demonstrated for a benchmark of an open cylinder printed in Inconel 718showing the development of distortions and residual stresses in all stages ofthe AM process from heating during building until the final cut from the buildplate. We suggest that this benchmark can serve as an experimental setup inorder to validate the suggested approach. This is discussedin the paper andis a topic for future work.
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| 28. |
- Strömberg, Niclas, 1968-
(författare)
-
A Multi-scale Topology Optimization Approach for Optimal Macro-layout and Local Grading of TPMS-based Lattices
- 2021
-
Ingår i: Proceedings of ASME 2021 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC-CIE2021) (Volume 3). - : American Society of Mechanical Engineers. - 9780791885383
-
Konferensbidrag (refereegranskat)abstract
- The use of lattice structures in design for additive manufacturing has quickly emerged as a popular and efficient design alternative for creating innovative multifunctional lightweight solutions. In particular, the family of triply periodic minimal surfaces (TPMS) studied in detail by Schoen for generating frame-or shell-based lattice structures seems extra promising. In this paper a multi-scale topology optimization approach for optimal macro-layout and local grading of TPMS-based lattice structures is presented. The approach is formulated using two different density fields, one for identifying the macro-layout and another one for setting the local grading of the TPMS-based lattice. The macro density variable is governed by the standard SIMP formulation, but the local one defines the orthotropic elasticity of the element following material interpolation laws derived by numerical homogenization. Such laws are derived for frame- and shell-based Gyroid, G-prime and Schwarz-D lattices using transversely isotropic elasticity for the bulk material. A nice feature of the approach is that the lower and upper additive manufacturing limits on the local density of the TMPS-based lattices are included properly. The performance of the approach is excellent, and this is demonstrated by solving several three-dimensional benchmark problems, e.g., the optimal macro-layout and local grading of Schwarz-D lattice for the established GE-bracket is identified using the presented approach.
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| 29. |
- Strömberg, Niclas, 1968-
(författare)
-
A new multi-scale topology optimization framework for optimal combinations of macro-layouts and local gradings of TPMS-based lattice structures
- 2024
-
Ingår i: Mechanics based design of structures and machines. - : Taylor & Francis Group. - 1539-7734 .- 1539-7742. ; 52:1, s. 257-274
-
Tidskriftsartikel (refereegranskat)abstract
- In this work, optimal combinations of macro-layouts and local gradings of triply periodic minimal surface (TPMS)-based lattice structures are obtained by using multi-scale topology optimization. A new innovative framework is proposed by using two density variables in each finite element. The first variable is the local relative lattice density and it sets the effective orthotropic elastic properties of the element, which in turn are obtained by using numerical homogenization of representative volume elements of the particular TPMS-based lattice structure of interest. The second variable is a standard topology optimization macro density variable, which defines if the element should be treated as a void or contain the graded lattice structure by letting this variable be governed by the rational approximation of material properties (RAMP) model. By using such density variables for all elements, the compliance is minimized by separately constraining the volume of lattice structure and the volume of macro-layout by using two independent constraints. For benchmarks in 3 D, it is demonstrated that the stiffness is increased significantly by including local grading of the lattice structure compared to using a constant lattice density. It is also demonstrated how ultra-lightweight designs can be generated using the multi-scale formulation, and how the optimal multi-scale solutions easily can be realized to printable stl-files by using implicit based geometry modeling. Finally, the new multi-scale topology optimization framework is utilized to generate an optimal design combination of macro-layout and local grading of frame-based Gyroid structure for the established GE-bracket benchmark.
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| 30. |
- Strömberg, Niclas, 1968-
(författare)
-
A Newton method for three-dimensional fretting problems
- 1999
-
Ingår i: International Journal of Solids and Structures. - : Elsevier. - 0020-7683 .- 1879-2146. ; 36:14, s. 2075-2090
-
Tidskriftsartikel (refereegranskat)abstract
- The present paper concerns the numerical treatment of fretting problems using a finite element analysis. The governing equations resulting from a formal finite element discretization of an elastic body with a potential contact surface are considered in a quasi-static setting. The constitutive equations of the potential contact surface are Signorini's contact conditions, Coulomb's law of friction and Archard's law of wear. Using a backward Euler time discretization and an approach based on projections, the governing equations are written as an augmented Lagrangian formulation which is implemented and solved using a Newton algorithm for three-dimensional fretting problems of didactic nature. Details concerning the implementation are provided.
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| 31. |
- Strömberg, Niclas, 1968-, et al.
(författare)
-
A soft contact formulation for modelling thin coatings
- 2005
-
Ingår i: Computer methods and experimental measurements for surface effects and contact mechanics VII. - Southampton : WIT Press. - 9781845640224 ; , s. 211-218
-
Konferensbidrag (refereegranskat)abstract
- Today, high-performance machine components are often improved by coatings. For instance, thin layers can increase the life-time by reducing friction and wear. An example of this is the spline joint in the suspension system of a truck. This joint, which is placed at the output of the gearbox, allows relative translation in the axial direction. In order to improve performance, this spline can be coated with a thin layer of polyamide. In such a manner, the life-time of the joint is increased by decreasing friction and wear. This type of coatings may be optimized by performing finite element contact analysis. However, when performing such an analysis, it can be difficult to obtain a good mesh due to the very thin layer. An approach to avoid this difficulty is to instead include the elastic properties of the coating in the contact formulation. Such a soft contact formulation is suggested and solved in this paper. The formulation is obtained by adding an elastic part to the free energy corresponding to Signorini’s contact conditions. In such a manner a new soft contact law is derived by taking the subdifferential of the free energy. In this law two new constitutive parameters appear. The first parameter describes the elastic response of the thin layer and the second one is taken to be equal to the thickness of the layer. In the event, when the layer is completely penetrated, hard contact is developed following a classical Lagrange formulation of Signorini.A numerical method for solving the new contact formulation is also developed. The method is obtained by following the augmented Lagrangian approach. In such a way an equivalent setting of equations is derived which in turn is solved by using a non-smooth Newton method. The method is implemented in a Matlab toolbox. The method is robust and produces accurate results. This is shown by comparing numerical results with solutions obtained by using a penalty formulation in Abaqus.
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| 32. |
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| 33. |
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| 34. |
- Strömberg, Niclas, 1968-
(författare)
-
An augmented Lagrangian method for fretting problems
- 1997
-
Ingår i: European journal of mechanics. A, Solids. - : Gauthier-Villars. - 0997-7538 .- 1873-7285. ; 16:4, s. 573-593
-
Tidskriftsartikel (refereegranskat)abstract
- The present work concerns the numerical treatment of fretting in the interface between a body and a rigid foundation. Starting from a variational formulation of a fretting model given in a framework of continuum thermodynamics, an augmented Lagrangian formulation is derived by introducing finite element discretizations in space and a finite difference discretization in time. The augmented Lagrangian formulation is implemented and solved by a Newton method for the two-dimensional case.
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| 35. |
- Strömberg, Niclas, 1968-
(författare)
-
An Efficient Tradeoff Approach for Topology Optimization with Manufacturing Constraints
- 2010
-
Ingår i: Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. - : ASME Press. - 9780791844090 ; , s. 1171-1179
-
Konferensbidrag (refereegranskat)abstract
- In this paper an efficient approach for generating tradeoff curves when performing topology optimization with manufacturing constraints is presented. By minimizing a new stiffness-volume ratio, or in-fact a new compliance-volume product, the tradeoff curve is generated by changing a new design parameter. The volume appearing in the objective is raised to the power of this new design parameter In such manner different conceptual designs can be generated By adopting a nested approach, the problem is easily solved by a simple numerical scheme. This is a nice feature of the approach which makes the numerical performance most efficient and robust. This feature makes it also easy to include manufacturing constraints by simply updating the move limits such that these constraints are satisfied The design parametrization is done by the SIMP-model and patterns of checker-boards are prevented by adopting Sigmund's filter. The efficiency of the approach is demonstrated by presenting tradeoff curves for both 2D- and 3D-problems.
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| 36. |
- Strömberg, Niclas, 1968-
(författare)
-
An Eulerian approach for simulating frictional heating in disc-pad systems
- 2011
-
Ingår i: European journal of mechanics. A, Solids. - : Elsevier. - 0997-7538 .- 1873-7285. ; 30:5, s. 673-683
-
Tidskriftsartikel (refereegranskat)abstract
- Thermal stresses as a result from frictional heating must be considered when designing disc brakes, clutches or other rotating machine components with sliding contact conditions. The rotational symmetry of the disc in these kind of applications makes it possible to model these systems using an Eulerian approach instead of a Lagrangian framework. In this paper such an approach is developed and implemented. The disc is formulated in an Eulerian frame where the convective terms are defined by the angular velocity. By utilizing the Eulerian framework, a node-to-node formulation of the contact interface is obtained, producing most accurate frictional heat power solutions. The energy balance of the interface is postulated by introducing an interfacial temperature. Both frictional power and contact conductances are included in this energy balance. The contact problem is solved by a non-smooth Newton method. By adopting the augmented Lagrangian approach, this is done by rewriting Signorini’s contact conditions to an equivalent semi-smooth equation. The heat transfer in the disc is discretized by a Petrov–Galerkin approach, i.e. the numerical difficulties due to the non-symmetric convective matrix appearing in a pure Galerkin discretization is treated by following the streamline-upwind approach. In such manner a stabilization is obtained by adding artificial conduction along the streamlines. For each time step the thermo-elastic contact problem is first solved for the temperature field from the previous time step. Then, the heat transfer problem is solved for the corresponding frictional power. In such manner a temperature history is obtained sequentially via the trapezoidal rule. In particular the parameter is set such that both the Crank–Nicolson and the Galerkin methods are utilized. The method seems very promising. This is demonstrated by solving a two-dimensional benchmark as well as a real disc brake system in three dimensions.
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| 37. |
- Strömberg, Niclas, 1968-
(författare)
-
An Eulerian-based Thermo-Flexible Multi-Body Approach for Simulating Rig Testing of Disc Brakes
- 2018
-
Ingår i: Advances in Computational Coupling and Contact Mechanics. - : World Scientific. - 9781786344779 - 9781786344793 ; , s. 179-195
-
Bokkapitel (refereegranskat)abstract
- In this chapter, we propose an Eulerian-based thermo-flexible multi-body approach in order to simulate rig testing of disc brake systems accurately and efficiently. A multi-body model of the disc, an assembly of flywheels and the shaft connecting the disc and flywheels is coupled to an Eulerian-based thermo-mechanical finite element model of the disc-pad system. By utilizing the Eulerian framework of the disc, the contact interface is modelled most accurately with Signorini contact, Coulomb frictional heating with a new temperature-dependent friction model that includes fading at high temperatures and Archard wear with a temperature-dependent wear coefficient. The governing equations are treated with a sequential approach, where first the mechanical contact problem is solved using the augmented Lagrangian approach with a non-smooth Newton method. Then, the multi-body model is solved for the brake moment obtained from the mechanical contact analysis using the average acceleration method. Finally, heat balance for the system including the frictional power from the two previous steps is obtained with the trapezoidal rule and formulating the nonlinear equations as a system of linear equations. Here, the non-symmetric convection matrix is stabilized by adding artificial conduction according to the streamline-upwind approach. The proposed sequential approach is implemented in an in-house code and utilized to study a vented disc-pad system to a heavy truck. This is discussed at the end of the chapter, showing the development of heat bands, hot spots and corresponding residual stresses.
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| 38. |
- Strömberg, Niclas, 1968-
(författare)
-
An implicit method for frictional contact, impact and rolling
- 2005
-
Ingår i: European journal of mechanics. A, Solids. - : Elsevier. - 0997-7538 .- 1873-7285. ; 24:6, s. 1016-1029
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper an implicit method for frictional contact, impact and rolling is suggested. A nonclassical formulation of a two-dimensional hyperelastic body unilaterally constrained to rigid supports is proposed by following the ideas of Moreau and Jean. A total Lagrangian formulation of the system is given. The elastic properties are defined by coupling the second Piola–Kirchhoff stress to the Green–Lagrange strain via the Kirchhoff–St. Venant law. The equation of motion is written in the spirit of Moreau by using the mean value impulses introduced by Jean. The mean value impulses appear explicitly in the equation of motion. In such manner the treatment of nonconstant kinematic transformation matrices becomes straightforward. The rigid supports are described by smooth functions. By utilizing these functions and the mean value impulses, new contact/impact laws of Signorini and Coulomb type are formulated. The governing equations are solved by a nonsmooth Newton method. This is performed by following the augmented Lagrangian approach and deriving the consistent stiffness matrix as well as the contact stiffness matrices. Three two-dimensional examples are solved by the method: a contact problem, an impact problem and a rolling contact problem.
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| 39. |
- Strömberg, Niclas, 1968-
(författare)
-
Automatic Postprocessing of Topology Optimization Solutions by Using Support Vector Machines
- 2018
-
Ingår i: Proceedings of the ASME Design Engineering Technical Conference. - : American Society of Mechanical Engineers (ASME).
-
Konferensbidrag (refereegranskat)abstract
- The postprocessing step from the density result in topology optimization to a parametric CAD model is typically most time consuming and usually involves several hands on maneuvers by an engineer. In this paper we propose an approach in order to automate this step by using soft non-linear support vector machines (SVM). Our idea is to generate the boundaries separating regions of material (elements with densities equal to one) and no material (elements with densities equal zero) obtained from topology optimization automatically by using SVM. The hypersurface of the SVM can then in the long run be explicitly implemented in any CAD software. In this work we generate these hypersurfaces by solving the dual formulation of the SVM with soft penalization and nonlinear kernel functions using quadratic programming or the sequential minimal optimization approach. The proposed SVM-based postprocessing approach is studied on topology optimization results of orthotropic elastic design domains with mortar contact conditions studied most recently in a previous work. The potential energy of several bodies with non matching meshes is maximized. In such manner no extra adjoint equation is needed. Intermediate density values are penalized using SIMP or RAMP, and the regularization is obtained by applying sensitivity or density filters following the approaches of Sigmund and Bourdin. The study demonstrates that the SVM-based postprocessing approach automatically generates proper hypersurfaces which can be used efficiently in the CAD modelling.
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| 40. |
- Strömberg, Niclas, 1968-
(författare)
-
Comparison of optimal linear, affine and convex combinations of metamodels
- 2021
-
Ingår i: Engineering optimization (Print). - : Taylor & Francis. - 0305-215X .- 1029-0273. ; 53:4, s. 702-718
-
Tidskriftsartikel (refereegranskat)abstract
- In this article, five different formulations for establishing optimal ensembles of metamodels are presented and compared. The comparison is done by minimizing different norms of the residual vector of the leave-one-out cross-validation errors for linear, affine and convex combinations of 10 metamodels. The norms are taken to be the taxicab, the Euclidean and the infinity norm, respectively. The ensemble of metamodels consists of quadratic regression, Kriging with linear or quadratic bias, radial basis function networks with a-priori linear or quadratic bias, radial basis function networks with a-posteriori linear or quadratic bias, polynomial chaos expansion, support vector regression and least squares support vector regression. Eight benchmark functions are studied as ‘black-boxes’ using Halton and Hammersley samplings. The optimal ensembles are established for either one of the samplings and then the corresponding root mean square errors are established using the other sampling and vice versa. In total, 80 different test cases (5 formulations, 8 benchmarks and 2 samplings) are studied and presented. In addition, an established design optimization problem is solved using affine and convex combinations. It is concluded that minimization of the taxicab or Euclidean norm of the residual vector of the leave-one-out cross-validation errors for convex combinations of metamodels produces the best ensemble of metamodels.
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| 41. |
- Strömberg, Niclas, 1968-
(författare)
-
Contact, impact and rolling of a nonlinear elastic body on rigid foundations
- 2005
-
Ingår i: Multibody Dynamics 2005.
-
Konferensbidrag (refereegranskat)abstract
- In this paper a method for frictional contact, impact and rolling of a two-dimensional hyperelastic body on rigid foundations is presented. A total Lagrangian formulation of the system is given. The elastic properties of the body are defined by coupling the second Piola-Kirchhoff stress to the Green-Lagrange strain via the Kirchhoff-St.Venant law. The rigid supports are described by smooth functions. By introducing the mean value impulses, these functions are utilized to formulate the contact/impact laws. The support functions appear explicitly in the variational formulation of Signorini, and implicitly in the maximal dissipation principle of Coulomb. An attractive property of this approach is that no search algorithm is needed. Another attractive property is that the normal and tangential directions of the supports are well defined. The above constitutive assumptions together with the law of motion, which is written on velocity form, define the governing equations of the system. The governing equations are solved by a nonsmooth Newton method. This is performed by following the augmented Lagrangian approach and deriving the consistent stiffness matrix as well as the contact stiffness matrices. The method is implemented in TriLab. TriLab is a toolbox for simulating contact problems. TriLab is developed using Matlab and Visual Fortran. The Fortran code is linked to Matlab as mex-files. The code is vectorized and the sparsity is utilized. By using TriLab, the presented method will be demonstrated by solving structural dynamic contact problems, impact problems as well as rolling contact problems
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| 42. |
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| 43. |
- Strömberg, Niclas, 1968-, et al.
(författare)
-
Derivation and analysis of a generalized standard model for contact, friction and wear
- 1996
-
Ingår i: International Journal of Solids and Structures. - : Elsevier. - 0020-7683 .- 1879-2146. ; 33:13, s. 1817-1836
-
Tidskriftsartikel (refereegranskat)abstract
- A model for mechanical contact including friction, wear and heat generation is proposed. By defining an internal state variable for the wear process, a generalized standard model for contact, friction and wear is derived from the principle of virtual power and the fundamental laws of thermodynamics. Within the frame of the generalized standard model some specific constitutive models are presented. For instance, a free energy corresponding to an extension of Signorini's unilateral contact conditions to include the wear process at the interface and having a linear tangential compliance between the relative tangential displacement and the tangential contact traction is suggested. Furthermore, a dual pseudo-potential with a friction and wear limit criterion in agreement with Coulomb's law of friction Archard's law of wear is given. In order to study existence and uniqueness questions, this pair of free energy and dual pseudo-potential is analysed in a one point elastic quasi-static contact problem with two degrees of freedom and thermal effects neglected. The so-called rate problem is solved.
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| 44. |
- Strömberg, Niclas, 1968-
(författare)
-
Development and Implementation of an Eulerian Approach for Efficient Simulation of Frictional Heating in Sliding Contacts
- 2011
-
Ingår i: Computational methods for coupled problems in science and engineering IV. - Barcelona : International Center for Numerical Methods in Engineering (CIMNE). - 9788489925786 ; , s. 1136-1146
-
Konferensbidrag (refereegranskat)abstract
- Thermal stresses as a result from frictional heating must be considered when designing disc brakes. The rotational symmetry of a disc brake makes it possible to model this system using an Eulerian approach instead of a Lagrangian framework. In this paper such an approach is developed. The sliding object is formulated in an Eulerian frame where the convective terms are defined by the sliding velocity. A node-to-node formulation of the contact interface is utilized. The energy balance of the interface is stated by introducing an interfacial temperature. Both frictional power and contact conductance are included in this energy balance. The contact problem is solved by a non-smooth Newton method. By adopting the augmented Lagrangian approach, this is done by rewriting Signorini's contact conditions to a system of semi-smooth equations. The heat transfer in the sliding body is discretized by a Petrov-Galerkin approach, i.e. the numerical difficulties due to the non-symmetric convective matrix appearing in a pure Galerkin discretization is treated by following the streamline-upwind approach. In such manner a stabilization is obtained by adding artificial conduction along the streamlines. For each time step the thermoelastic contact problem is first solved for the temperature field from the previous time step. Then, the heat transfer problem is solved for the corresponding frictional power. In such manner a temperature history is obtained via the trapezoidal rule. In particular the parameter is set such that both the Crank-Nicolson and the Galerkin methods are utilized. The method seems very promising. The method is demonstrated for two-dimensional benchmarks as well as a real disc brake system in three dimension.
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| 45. |
- Strömberg, Niclas, 1968-
(författare)
-
Efficient detailed design optimization of topology optimization concepts by using support vector machines and metamodels
- 2019
-
Ingår i: Engineering optimization (Print). - : Taylor & Francis. - 0305-215X .- 1029-0273.
-
Tidskriftsartikel (refereegranskat)abstract
- In this article, an approach for metamodel-based design optimization (MBDO) of topology optimization (TO) concepts is proposed by using support vector machines (SVMs) as geometric models of the concepts instead of traditional parametric computer aided design (CAD) models. In such a manner, an efficient approach for the MBDO-driven design of TO-based concepts is obtained. An implicit hypersurface representing the TO-based concept is generated by classifying the TO-solutions of zeros and ones by using the 1-norm SVM of Mangasarian. The implicit SVM-based hypersurfaces are then utilized to set up designs of experiments of nonlinear finite element analyses by morphing the TO-based concepts by using Boolean and blending operations. Finally, MBDO is performed by using an ensemble of metamodels consisting of quadratic regression, Kriging, radial basis function networks, polynomial chaos expansion and support vector regression models. The proposed MBDO framework is demonstrated by minimizing the mass of a three-dimensional design domain with a constraint on the plastic limit load. The performance of the approach is most promising.
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| 46. |
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| 47. |
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| 48. |
- Strömberg, Niclas, 1968-
(författare)
-
Finite element treatment of tribological problems
- 2000
-
Ingår i: Proceedings of the First International Symposium on Impact and Friction of Solids, Structures and Machines. - Singapore : World Scientific. - 9810243707 - 9812792511 ; , s. 277-280
-
Konferensbidrag (refereegranskat)abstract
- The present paper concerns the numerical treatment of contact, friction and wear between a thermoelastic body and a rigid foundation. The governing equations of thermoelasticity, Signorini contact, Coulomb friction and Archard wear are put together to a system of equations which is solved by using a Newton method.
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| 49. |
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| 50. |
- Strömberg, Niclas, 1968-
(författare)
-
Finite element treatment of two-dimensional thermoelastic wear problems
- 1999
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - : Elsevier. - 0045-7825 .- 1879-2138. ; 177:3-4, s. 441-455
-
Tidskriftsartikel (refereegranskat)abstract
- The present paper concerns the numerical treatment of thermoelastic wear problems. The governing equations of thermoelasticity coupled to Signorini contact, Coulomb's friction and Archard's wear are formulated as a system of discrete equations. This equation system is solved, using a Bouligand differentiable Newton method, for five problems of didactic nature.
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