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Optimization and Robustness of Structural Product Families
Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis concerns structural optimization and robustness evaluations, and new methods are presented that considerably reduce the computational cost of these evaluations.

Optimization is an effective tool in the design process and the interest from industry of its usage is quickly increasing. However, the usage would probably have grown faster if the required number of computationally costly finite element analyses could be reduced. Especially in the case of product family optimization, the problem size can easily get too large to be solved within a reasonable time. This is sometimes also true for robustness evaluations. To enable the usage of optimization and robustness evaluations also for large scale industrial problems, two new methods are here presented, which require a considerably smaller number of finite element analyses.

The first method concerns structural optimization of product families subjected to multiple crash load cases. Here, the number of required finite element analyses are considerably reduced by only considering the critical constraint in each iteration step.

The second method is an approach to approximate the variable sensibility based on the distribution of internal energy in a structure. The method can be used to evaluate the relative robustness of different design proposals or for structural optimization. Since the method is independent of the number of parameters and design variables the computational cost of such evaluations is drastically reduced for computationally large problems.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press , 2011. , 50 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1397
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-70372ISBN: 978-91-7393-072-7 (print)OAI: oai:DiVA.org:liu-70372DiVA: diva2:438635
Public defence
2011-10-18, Planck, Fysikhuset, Campus Valla, Linköpings universitet, Linköping, 10:15 (English)
Opponent
Supervisors
Available from: 2011-09-05 Created: 2011-09-05 Last updated: 2011-09-19Bibliographically 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, 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: 2011-09-19Bibliographically approved
2. Structural optimization of product families subjected to multiple crash load cases
Open this publication in new window or tab >>Structural optimization of product families subjected to multiple crash load cases
2010 (English)In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 41, no 5, 797-815 p.Article in journal (Refereed) Published
Abstract [en]

This paper discusses the problem of structural optimization of product families subjected to multiple load cases, evaluated by computationally costly finite element analysis. Product families generally have a complex composition of shared components that makes individual product optimization difficult as the relation between the shared variables is not always intuitive. More optimal is to treat the problem as a product family optimization problem. Though, for product families subjected to multiple and computationally costly crash loads, the optimization problem takes too long time to solve with traditional methods. Therefore, a new optimization algorithm is presented that decomposes the family problem into sub-problems and iteratively reduces the number of sub-problems, decouple and solve them. The algorithm is applicable for module based product families with predefined composition of generalized commonality, subjected to multiple load cases that can be analyzed separately. The problem reduction is performed by only considering the constraints that are critical in the optimal solution. Therefore the optimization algorithm is called the Critical Constraint Method, CCM. Finally the CCM algorithm is evaluated by two product family optimization problems.

Place, publisher, year, edition, pages
Springer Science Business Media, 2010
Keyword
Product family optimization, Multiple crash loads, Nonlinear systems, Response surface methodology, Meta model approximations, Critical constraints
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-54846 (URN)10.1007/s00158-009-0471-4 (DOI)000276075900011 ()
Available from: 2010-04-16 Created: 2010-04-16 Last updated: 2011-09-19Bibliographically approved
3. An improved critical constraint method for structural optimization of product families
Open this publication in new window or tab >>An improved critical constraint method for structural optimization of product families
2012 (English)In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 45, no 2, 235-246 p.Article in journal (Refereed) Published
Abstract [en]

This paper discusses important improvements in the efficient Critical Constraint Method (CCM) for the optimization of structural product families subjected to multiple crash load cases. The method was first presented by Öman and Nilsson (Struct Multidisc Optim 41(5):797–815, 2010). However, the algorithm often converged towards an infeasible solution, which considerably limited the applicability of the method. Therefore, improvements are presented here to make the method more robust regarding feasible solutions, resulting in only a minor decrease in efficiency compared to the original method. The improvements include; a penalty approach to control the feasibility of the method by continuously pushing the solution out of the infeasible region, a dynamic contraction algorithm to increase the accuracy and robustness of the method by considering the optimization progress and variable history in the reduction of the step size, and the implementation of a parallel approach to further increase the efficiency of the method by enabling the full potential of large-scale computer clusters. Finally, the potential of the improved CCM algorithm is demonstrated on a large-scale industrial family optimization problem and it is concluded that the high efficiency of the method enables the usage of large product family optimization in the design process.

Place, publisher, year, edition, pages
Springer-Verlag, 2012
Keyword
Product family optimization – Multiple crash loads – Nonlinear systems – Response surface methodology – Meta model approximations – Critical constraints
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-70787 (URN)10.1007/s00158-011-0689-9 (DOI)000298500500006 ()
Available from: 2011-09-19 Created: 2011-09-19 Last updated: 2017-12-08Bibliographically approved
4. Evaluation of structural robustness basedon internal energy distribution
Open this publication in new window or tab >>Evaluation of structural robustness basedon internal energy distribution
2011 (English)Manuscript (preprint) (Other academic)
Abstract [en]

Robustness evaluations give valuable information about the sensitivity of a structure to stochastic variation of design parameters, but are in general expensive to perform due to the extensive number of function evaluations required. Therefore, an Internal Energy Based (IEB) method is presented here, in which the structural sensitivity to variation of each thickness parameter is estimated based on the internal energy distribution obtained from one single function evaluation. In this way, the cost of such structural robustness evaluations is significantly reduced. However, the accuracy of the IEB method depends on the structural behaviour. Here it is tested for two structures with nonlinear displacement responses caused by impact loads. The method is however believed to be applicable to any structure exposed to a single load acting on a limited area of the structure, and for response functions related to the displacement of the loaded area.

Keyword
Robustness evaluations, Internal energy based gradients, Internal energy distribution, Internal energy based method, Structural robustness
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-70788 (URN)
Available from: 2011-09-19 Created: 2011-09-19 Last updated: 2011-09-19Bibliographically approved
5. Structural optimization based on internal energy distribution
Open this publication in new window or tab >>Structural optimization based on internal energy distribution
2011 (English)Manuscript (preprint) (Other academic)
Abstract [en]

Structural optimization is a valuable tool to improve the performance of products, but it is in general expensive to perform due to the required extensive number of function evaluations. Therefore, an approximate method based on the internal energy distribution, which only requires a small number of function evaluations, is presented here. By this method, structural optimization can be enabled already in the initial steps in the design of new products when fast, but not necessarily precise, results are often desired. However, the accuracy of the approximate solution depends on the structural behaviour. The internal energy based optimization method is here validated for three structures, but it is believed to be applicable to any structure subjected to a single load where the functions considered are related to the displacement of the loaded area and/or the material thicknesses of the structural parts.

Keyword
Structural Optimization, Internal Energy Gradients, Internal Energy Based Method, Internal Energy Distribution, Product Family Optimization
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-70789 (URN)
Available from: 2011-09-19 Created: 2011-09-19 Last updated: 2011-09-19Bibliographically approved

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