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On vehicle crashworthiness design using structural optimization
Linköping University, Department of Mechanical Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
2004 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This dissertation addresses the problems and possibilities of using structural optimization in vehicle crashworthiness design. The first part of the thesis gives an introduction to vehicle crashworthiness design. The optimization methods presented are also used to exemplify how structural optimization and robustness analysis can be used in vehicle crashworthiness design.

In the second part of the thesis, five papers are appended, where different optimization methods are evaluated and improved for the usage in vehicle crashworthiness design. These papers concern the optimization methods Response Surface Methodology (RSM), Stochastic Optimization (SO) and Space Mapping (SM).

Each method has its advantages and disadvantages. The Response Surface Methodology is the easiest method to use and the method that most often finds the best design of these three methods. Generally RSM is rather expensive, especially when many design variables are used. Then, SO is an effective alternative because in this method the number of evaluations is independent of the number of design variables, which is not the case for RSM. Space Mapping is the cheapest method, because it needs only one or two evaluations per iteration. However, SM is generally a method to fmd an improved design with fulfilled constraints and sometimes not the absolute optimum solution but to a low cost. Hence, both RSM and SO may produce better designs but at the price of more response evaluations.

Place, publisher, year, edition, pages
Linköping: Linköpings univeristet , 2004. , 46 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 863
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-24070Local ID: 3630ISBN: 91-7373-898-0 (print)OAI: oai:DiVA.org:liu-24070DiVA: diva2:244386
Public defence
2004-03-12, Hörsal Planck, Fysikhuset, Linköpings Universitet, Linköping, 10:15 (Swedish)
Opponent
Available from: 2009-10-07 Created: 2009-10-07 Last updated: 2013-01-22
List of papers
1. Using the response surface methodology and the D-optimality criterion in crashworthiness related problems
Open this publication in new window or tab >>Using the response surface methodology and the D-optimality criterion in crashworthiness related problems
2002 (English)In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 24, no 3, 185-194 p.Article in journal (Refereed) Published
Abstract [en]

The aim of this paper is to determine the efficient number of experimental points when using the response surface methodology in crashworthiness problems.

The D-optimality criterion is used as experimental design method. Two application models have been studied, one square tube and one front rail from Saab Automobile AB. Both models were fully parameterized in the preprocessor LS-INGRID but only two design variables were used. The optimization package LS-OPT was used to determine the design of experiments using the D-optimality criterion. Both models were subjected to an impact into a rigid wall and the simulations were carried out using LS-DYNA. A general recommendation is to to use 1.5 times the minimum number of experimental points. A more specialized recommendation is for linear surfaces 1.5, elliptic surfaces 2.2 and for quadratic surfaces 1.6 times the minimum number of experimental points.

National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-35584 (URN)10.1007/s00158-002-0228-9 (DOI)27810 (Local ID)27810 (Archive number)27810 (OAI)
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2017-12-13
2. Using surrogate models and response surfaces in structural optimization: with application to crashworthiness design and sheet metal forming
Open this publication in new window or tab >>Using surrogate models and response surfaces in structural optimization: with application to crashworthiness design and sheet metal forming
2003 (English)In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 25, no 2, 129-140 p.Article in journal (Refereed) Published
Abstract [en]

The aim of this paper is to determine if the Space Mapping technique using surrogate models together with response surfaces is useful in the optimization of crashworthiness and sheet metal forming. In addition, the efficiency of optimization using Space Mapping will be compared to traditional structural optimization using the Response Surface Methodology (RSM). Five examples are used to study the algorithm: one optimization of an analytic function and four structural optimization problems. All examples are constrained optimization problems. In all examples, the algorithm converged to an improved design with all constraints fulfilled, even when a conventional RSM optimization failed to converge. For the crashworthiness design problems, the total computing time for convergence was reduced by 53% using Space Mapping compared to conventional RSM. For the sheet metal forming problems the total computing time was reduced by 63%. The conclusions are that optimization using Space Mapping and surrogate models can be used for optimization in crashworthiness design and sheet metal forming applications with a significant reduction in computing time.

Keyword
Crashworthiness, Finite element, Optimization, Response surface, Sheet metal forming, Space mapping
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-46579 (URN)10.1007/s00158-002-0279-y (DOI)
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2017-12-13
3. Optimization of the new Saab 9-3 exposed to impact load using a space mapping technique
Open this publication in new window or tab >>Optimization of the new Saab 9-3 exposed to impact load using a space mapping technique
2004 (English)In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 27, no 5, 411-420 p.Article in journal (Refereed) Published
Abstract [en]

The aim of this work is to illustrate how a space mapping technique using surrogate models together with response surfaces can be used for structural optimization of crashworthiness problems. To determine the response surfaces, several functional evaluations must be performed and each evaluation can be computationally demanding. The space mapping technique uses surrogate models, i.e. less costly models, to determine these surfaces and their associated gradients. The full model is used to correct the gradients from the surrogate model for the next iteration. Thus, the space mapping technique makes it possible to reduce the total computing time needed to find the optimal solution. First, two analytical functions and one analytical structural optimization problem are presented to exemplify the idea of space mapping and to compare the efficiency of space mapping to traditional response surface optimization. Secondly, a sub-model of a complete vehicle finite element (FE) model is used to study different objective functions in vehicle crashworthiness optimization. Finally, the space mapping technique is applied to a structural optimization problem of a large industrial FE vehicle model, consisting of 350.000 shell elements and a computing time of 100 h. In this problem the intrusion in the passenger compartment area was reduced by 32% without compromising other crashworthiness parameters.

Keyword
crashworthiness, finite element, optimization, response surface, space mapping
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-46216 (URN)10.1007/s00158-004-0396-x (DOI)
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2017-12-13
4. An investigation of structural optimization in crashworthiness design using a stochastic approach
Open this publication in new window or tab >>An investigation of structural optimization in crashworthiness design using a stochastic approach
2004 (English)In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 27, no 6, 446-459 p.Article in journal (Refereed) Published
Abstract [en]

In this paper the response surface methodology (RSM) and stochastic optimization (SO) are compared with regard to their efficiency and applicability in crashworthiness design. Optimization of simple analytic expressions and optimization of a front rail structure are the applications used to assess the respective qualities of both methods. A low detail vehicle structure is optimized to demonstrate the applicability of the methods in engineering practice. The investigations reveal that RSM is better compared to SO for fewer than 10–15 design variables. The convergence behaviour of SO improves compared to RSM when the number of design variables is increased. A novel zooming method is proposed which improves the convergence behaviour. A combination of both the RSM and the SO is efficient, stochastic optimization could be used in order to determine appropriate starting points for an RSM optimization, which continues the optimization. Two examples are investigated using this combined method.

Keyword
finite element analysis, response surface methodology, stochastic optimization, structural optimization
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-46208 (URN)10.1007/s00158-004-0400-5 (DOI)
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2017-12-13
5. A multipoint version of space mapping optimization applied to vehicle crashworthiness design
Open this publication in new window or tab >>A multipoint version of space mapping optimization applied to vehicle crashworthiness design
2006 (English)In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 31, no 2, 134-146 p.Article in journal (Refereed) Published
Abstract [en]

In this paper, space mapping (SM) technique is combined with response surface methodology (RSM). SM is an optimization method well suited for very costly problems to find an improved design with fulfilled constraints. The SM technique use less costly models, which complements the correct models. The theory is established and compared to the corrected RSM. A multipoint version of SM is presented, where a separate evaluation is done in each iteration to improve the mapping function. Using this additional evaluation to update the mapping function, generally, the number of iterations to find the optimum solution can be reduced. Thus, the elapsed time to solve the optimization problem can be reduced if a parallel computer is utilized. Finally, one engineering optimization problem is solved to illustrate the application of SM in vehicle crashworthiness structural optimization.

National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-33878 (URN)10.1007/s00158-005-0544-y (DOI)19954 (Local ID)19954 (Archive number)19954 (OAI)
Available from: 2009-10-09 Created: 2009-10-09 Last updated: 2017-12-13

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