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  • 1.
    Amouzgar, Kaveh
    et al.
    Jönköping University, School of Engineering, JTH. Research area Product Development - Simulation and Optimization.
    Strömberg, N.
    Radial basis functions with a priori bias in comparisonwith a posteriori bias under multiple modeling criteriaIn: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488Article in journal (Other academic)
  • 2.
    Amouzgar, Kaveh
    et al.
    Jönköping University, School of Engineering, JTH. Research area Product Development - Simulation and Optimization. School of Engineering Science, University of Skövde, Sweden.
    Strömberg, Niclas
    Department of Mechanical Engineering, School of Science and Technology, University of Örebro, Örebro, Sweden .
    Radial basis functions as surrogate models with a priori bias in comparison with a posteriori bias2017In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 55, no 4, p. 1453-1469Article in journal (Refereed)
    Abstract [en]

    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.

  • 3. Gustafsson, E
    et al.
    Strömberg, Niclas
    Jönköping University, School of Engineering, JTH, Mechanical Engineering. Jönköping University, School of Engineering, JTH. Research area Engineering mechanics and optimization.
    Shape optimization of castings by using successive response surface methodology2008In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 35, no 1, p. 11-28Article in journal (Refereed)
  • 4.
    Hofwing, Magnus
    et al.
    Jönköping University, School of Engineering, JTH, Mechanical Engineering. Jönköping University, School of Engineering, JTH. Research area Engineering mechanics and optimization.
    Strömberg, Niclas
    Jönköping University, School of Engineering, JTH, Mechanical Engineering. Jönköping University, School of Engineering, JTH. Research area Engineering mechanics and optimization.
    D-optimality of non-regular design spaces by using a Bayesian modification and a hybrid method2010In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 42, no 1, p. 73-88Article in journal (Refereed)
    Abstract [en]

    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.

  • 5.
    Klarbring, Anders
    et al.
    Linköping university.
    Strömberg, Niclas
    Jönköping University, School of Engineering, JTH. Research area Product Development - Simulation and Optimization.
    A Note on the Min-Max Formulation of Stiffness Optimization including Non-Zero Prescribed Displacements2012In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 45, no 1, p. 147-149Article in journal (Refereed)
    Abstract [en]

    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.

  • 6.
    Klarbring, Anders
    et al.
    Linköping university.
    Strömberg, Niclas
    Jönköping University, School of Engineering, JTH. Research area Product Development - Simulation and Optimization.
    Topology optimization of hyperelastic bodies including non-zero prescribed displacements2013In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 47, no 1, p. 37-48Article in journal (Refereed)
    Abstract [en]

    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.

  • 7.
    Klarbring, Anders
    et al.
    Division of Solid Mechanics, Linköping University, Linköping, Sweden.
    Torstenfelt, Bo
    Division of Solid Mechanics, Linköping University, Linköping, Sweden.
    Hansbo, Peter
    Jönköping University, School of Engineering, JTH, Product Development. Jönköping University, School of Engineering, JTH. Research area Product Development - Simulation and Optimization.
    Larson, Mats G.
    Department of Mathematics and Mathematical Statistics, Umeå University, Umeå, Sweden.
    Optimal design of fibre reinforced membrane structures2017In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 56, no 4, p. 781-789Article in journal (Refereed)
    Abstract [en]

    A design problem of finding an optimally stiff membrane structure by selecting one–dimensional fiber reinforcements is formulated and solved. The membrane model is derived in a novel manner from a particular three-dimensional linear elastic orthotropic model by appropriate assumptions. The design problem is given in the form of two minimization statements. After finite element discretization, the separate treatment of each of the two statements follows from classical results and methods of structural optimization: the stiffest orientation of reinforcing fibers coincides with principal stresses and the separate selection of density of fibers is a convex problem that can be solved by optimality criteria iterations. Numerical solutions are shown for two particular configurations. The first for a statically determined structure and the second for a statically undetermined one. The latter shows related but non-unique solutions. 

  • 8.
    Olofsson, Jakob
    et al.
    Jönköping University, School of Engineering, JTH, Materials and Manufacturing.
    Cenni, Riccardo
    Imola, Italy.
    Cova, Matteo
    Imola, Italy.
    Bertuzzi, Giacomo
    Imola, Italy.
    Salomonsson, Kent
    Jönköping University, School of Engineering, JTH, Materials and Manufacturing.
    Johansson, Joel
    Jönköping University, School of Engineering, JTH, Industrial Product Development, Production and Design.
    Multidisciplinary shape optimization of ductile iron castings by considering local microstructure and material behaviour2018In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 57, no 5, p. 1889-1903Article in journal (Refereed)
    Abstract [en]

    During the casting process and solidification of ductile iron castings, a heterogeneous microstructure is formed throughout the casting. This distribution is strongly influenced by the item geometry and the process related factors, as chemical composition and local solidification conditions. Geometrical changes to the geometry of the casting thus alters the local mechanical behavior and properties, as well as the distribution of stresses and strains when the casting is subjected to load. In order to find an optimal geometry, e.g. with reduced weight and increased load-bearing capacity, this interdependency between geometry and local material behavior needs to be considered and integrated into the optimization method. In this contribution, recent developments in the multidisciplinary integration of casting process simulation, solidification and microstructure modelling, microstructure-based material characterization, finite element structural analyses with local material behavior and structural optimization techniques are presented and discussed. The effect and relevance of considering the local material behavior in shape optimization of ductile iron castings is discussed and evidenced by an industrial application. It is shown that by adopting a multidisciplinary optimization approach by integration of casting simulation and local material behavior into shape optimization, the potential of the casting process to obtain components with high performance and reliability can be enabled and utilized. 

  • 9.
    Strömberg, Niclas
    Jönköping University, School of Engineering, JTH. Research area Engineering mechanics and optimization. Jönköping University, School of Engineering, JTH, Mechanical Engineering.
    Topology optimization of structures with manufacturing and unilateral contact constraints by minimizing an adjustable compliance–volume product2010In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 42, no 3, p. 341-350Article in journal (Refereed)
  • 10.
    Strömberg, Niclas
    et al.
    Jönköping University, School of Engineering, JTH, Mechanical Engineering. Jönköping University, School of Engineering, JTH. Research area Engineering mechanics and optimization.
    Klarbring, A
    Topology Optimization of Structures in Unilateral Contact2010In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 41, no 1, p. 57-64Article in journal (Refereed)
1 - 10 of 10
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