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Robust optimisation of structures: Evaluation and incorporation of variations in simulation based design
Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology. (Hållfasthetslära)
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis concerns the robustness of structures considering various uncertainties. The overall objective is to evaluate and develop simulation based design methods in order to find solutions that are optimal both in the sense of handling typical load cases and minimising the variability of the response, i.e. robust optimal designs. Conventionally optimised structures may show a tendency of being sensitive to small perturbations in the design or loading conditions. These variations are of course inevitable. To create robust designs, it is necessary to account for all conceivable variations (or at least the influencing ones) in the design process. The thesis is divided into two parts. The first part serves as a theoretical background for this work. It includes introductions to the concept of robust design, basic statistics, optimisation theory and metamodelling. The second part consists of five appended papers on the topic.

The first and third papers focuse on the evaluation of robustness, given some dispersions in the input data. Established existing methods are applied, and for paper three, comparisons with experimentally evaluated dispersions on a larger system are made.

The second and fourth paper introduce two new approaches to perform robust optimisation, i.e. optimisations where the mean performance and the robustness in the objectives are simultaneously optimised. These methods are demonstrated both on an analytical example and on a Finite Element model design example. The fifth paper studies the variations in mechanical properties between several different batches of the same steel grade. A material model is fitted to each batch of material, whereby dispersions seen in test specimens are transferred to material model parameter variations. The correlations between both test and material model parameters are studied.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press , 2011. , 39 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1382
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-70199ISBN: 978-91-7393-129-8 (print)OAI: oai:DiVA.org:liu-70199DiVA: diva2:436728
Public defence
2011-09-23, C3, Hus C, Campus Valla, Linköpings universitet, Linköping, 10:15 (Swedish)
Opponent
Supervisors
Available from: 2011-08-24 Created: 2011-08-24 Last updated: 2011-09-07Bibliographically approved
List of papers
1. Finite element based robustness study of a truck cab subjected to impact loading
Open this publication in new window or tab >>Finite element based robustness study of a truck cab subjected to impact loading
2009 (English)In: International Journal of Crashworthiness, ISSN 1358-8265, E-ISSN 1754-2111, Vol. 14, no 2, 111-124 p.Article in journal (Refereed) Published
Abstract [en]

Optimised designs have a tendency of being sensitive to variations. It is therefore of great importance to analyse this sensitivity to assure that a design is robust, i.e. sufficiently insensitive to variations. To analyse robustness, variations are introduced in model parameters and their influences on simulation responses are studied. This is usually achieved using the Monte Carlo method. Though, due to the large number of simulations needed, the Monte Carlo method is very costly for problems requiring a long computing time. Therefore, in this work a meta model-based Monte Carlo method is used to evaluate the robustness of a vehicle structure. That is, the Monte Carlo analysis is performed on a surface approximation of the true response, over the domain of interest. The methodology used is to first identify the variables that influence the response the most, referred to as a screening, using simple linear response surfaces. This is followed by a more detailed sensitivity analysis using only the identified variables and a quadratic response surface, thereby incorporating second order effects. A truck cab model exposed to a pendulum impact load is used as an evaluation of this method, and the important variables and their influence on the response are identified. The effect of including results from forming simulations is also evaluated using the truck cab model. Variations are introduced before forming simulations, thereby taking forming effects into account in the sensitivity analysis. The method was found to be a good tool to identify important dispersion variables and to give an approximate result of the total dispersion, all with a reasonable amount of simulations.

Place, publisher, year, edition, pages
Taylor & Francis, 2009
Keyword
Monte Carlo, meta model, robust design, response surface method, sensitivity analysis, robustness
National Category
Applied Mechanics
Identifiers
urn:nbn:se:liu:diva-15474 (URN)10.1080/13588260802412992 (DOI)
Projects
ROBDES
Note
On the day of the defence date the status of this article was: Accepted.Available from: 2008-11-11 Created: 2008-11-11 Last updated: 2017-12-14Bibliographically approved
2. An approach to robust optimization of impact problems using random samples and meta-modelling
Open this publication in new window or tab >>An approach to robust optimization of impact problems using random samples and meta-modelling
2010 (English)In: International Journal of Impact Engineering, ISSN 0734-743X, E-ISSN 1879-3509, Vol. 37, no 6, 723-734 p.Article in journal (Refereed) Published
Abstract [en]

Conventionally optimized structures may show a tendency to be sensitive to variations, for instance in geometry and loading conditions. To avoid this, research has been carried out in the field of robust optimization where variations are taken into account in the optimization process. The overall objective is to create solutions that are optimal both in the sense of mean performance and minimum variability. This work presents an alternative approach to robust optimization, where the robustness of each design is assessed through multiple sampling of the stochastic variables at each design point. Meta-models for the robust optimization are created for both the mean value and the standard deviation of the response. Furthermore, the method is demonstrated on an analytical example and an example of an aluminium extrusion with quadratic cross-section subjected to axial crushing. It works well for the chosen examples and it is concluded that the method is especially well suited for problems with a large number of random variables, since the computational cost is essentially independent of the number of random variables. In addition, the presented approach makes it possible to take into consideration variations that cannot be described with a variable. This is demonstrated in this work by random geometrical perturbations described with the use of Gaussian random fields.

Keyword
Robust optimisation, geometric imperfections, meta model, robustness
National Category
Applied Mechanics
Identifiers
urn:nbn:se:liu:diva-15478 (URN)10.1016/j.ijimpeng.2009.07.002 (DOI)
Projects
ROBDES
Note
Tidigare titel: Robust optimisation methodology using random samples and meta modelling Available from: 2008-11-11 Created: 2008-11-11 Last updated: 2017-12-14Bibliographically approved
3. Experimental and finite element robustness studies of a bumper system subjected to an offset impact loading
Open this publication in new window or tab >>Experimental and finite element robustness studies of a bumper system subjected to an offset impact loading
2011 (English)In: International Journal of Crashworthiness, ISSN 1358-8265, E-ISSN 1754-2111, Vol. 16, no 2, 155-168 p.Article in journal (Refereed) Published
Abstract [en]

A product of high quality is a product that performs well, not only in exactly the situations it was designed to handle but also in slightly different situations that arise in the usage of the product. As a specific example, the performance of a bumper system should not depend on small fluctuations in the manufacturing process or on small variations in the impact event. In this work, the robustness of an existing vehicle bumper system subjected to a crash load has been evaluated both experimentally and numerically. In the latter case, different widely used approaches to numerically assess the robustness have been utilised. A reliable numerical robustness study provides the designer with a valuable tool for improving a design, and an evaluation of these methods in this context is therefore of interest. It is concluded that for the example under study, both the Monte Carlo method and the metamodel-based Monte Carlo methods work well. Furthermore, for moderate dispersions levels, i.e. a small design space with no bifurcation in the deformation pattern, a linear response approximation is shown to have a sufficient accuracy to be used in the metamodel-based robustness analysis. The performed numerical robustness studies also point out that the performance of a nominal simulation, i.e. a simulation conducted with mean values for all variables, does not in general predict the mean performance of the finite element model. Finally, some possible design improvements for the bumper system under study are also identified

Place, publisher, year, edition, pages
Abingdon, Oxford, UK: Taylor & Francis Group, 2011
Keyword
experimental robustness, numerical robustness, Monte Carlo, metamodel, sensitivity analysis
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-70195 (URN)10.1080/13588265.2010.539339 (DOI)
Available from: 2011-08-24 Created: 2011-08-24 Last updated: 2017-12-08
4. Robust optimisation of front members in a full frontal car impact
Open this publication in new window or tab >>Robust optimisation of front members in a full frontal car impact
(English)Manuscript (preprint) (Other academic)
Abstract [en]

In the search of a lightweight design of automobiles, it is necessary to assure that a robust crashworthiness performance is achieved. Structures that are optimised to handle a finite number of load cases may perform poorly when subjected to various dispersions. Thus, uncertainties must be accounted for in the optimisation process. This paper presents an approach to optimisation where all design evaluations include an evaluation of the robustness. Metamodel approximations are applied both to the design space and the robustness evaluations, using Artifical Neural Networks and polynomials, respectively. The features of the robust optimisation approach are displayed in an analytical example, and further demonstrated in a large scale design example of front side members of a car. Different optimisation formulations are applied and it is shown that the proposed approach works well. It is also concluded that a robust optimisation puts higher demands on the FE model performance than normally.

Keyword
Robust optimisation; dual response surface; metamodel; genetic algorithm
National Category
Materials Engineering
Identifiers
urn:nbn:se:liu:diva-70192 (URN)
Available from: 2011-08-24 Created: 2011-08-24 Last updated: 2011-09-07Bibliographically approved
5. An evaluation of the statistics of steel material model parameters
Open this publication in new window or tab >>An evaluation of the statistics of steel material model parameters
2012 (English)In: Journal of Materials Processing Technology, ISSN 0924-0136, E-ISSN 1873-4774, Vol. 212, no 6, 1288-1297 p.Article in journal (Refereed) Published
Abstract [en]

In robustness studies, variations of material properties are often represented by simple assumptions, such as scaling of stress-strain relations, often due to lack of knowledge or deeper understanding of the material physics and the material model applied. By performing material characterisation tests on several batches of a DP600 steel and fitting a phenomenological material model to each batch, this paper studies the dispersion of material model parameters, as well as correlations between both experimental and model parameters. It is concluded that some of the charcterisation tests may be omitted in the future, due to correlations found between parameters. The results may also be applied in a robustness study by inversely using the retrieved statistics to generate reasonable new sets of material model parameters. The methodology presented may be adopted for any other type of material characterisation process.

Place, publisher, year, edition, pages
Elsevier, 2012
Keyword
Robustness studies, material model parameter variations, dual phase steel
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-70193 (URN)10.1016/j.jmatprotec.2012.01.016 (DOI)000303176900008 ()
Note
funding agencies|SFS ProViking project Super Light Steel Structures||Available from: 2011-08-24 Created: 2011-08-24 Last updated: 2017-12-08Bibliographically approved

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