Combining response surface optimization and stochastic analysis for crashworthiness design -- an introductory study

Article type: Research Article

Authors: Fredriksson, Lars A. | Schramm, Uwe

Affiliations: Altair Engineering GmbH, Calwer Str.7, D-71034 B\"oblingen, Germany. E-mail: Fredriks@altair-gmbh.de | Altair Engineering, Inc., 2070 Business Center Dr, Irvine, CA 92612, USA. E-mail: Schramm@altair.com

Abstract: Objective of the design process are cost effective designs that meet certain expectations with respect to functionality and appearance. Designs are created in an iterative process where analyses of the structural behavior lead to changes in the design. The use of optimization technology makes design changes to be driven directly by analysis results. The application of optimization allows an efficient search for the right combination of design variables for a certain design. Additional use of stochastic methods in order to analyze the design from a statistical standpoint adds robustness to the design and prevents unpleasant surprises in later physical testing. This paper discusses methodology to optimize structures that undergo impact loading. Objective and constraints are transient dynamic responses. The optimization problem is solved using a sequential response surface method. An explicit finite element code is used to solve the transient dynamic problem. The optimization is not performed on results from single simulations but on statistical results from a stochastic analysis. The stochastic analysis is driven using a Monte Carlo method. Commercial software is used for the implementation of the methodology. The results from the study indicate that a combination of optimization and stochastic analysis can add safety margins to a design with respect to robustness against physical errors in the design itself and against changes in load levels and load cases. However, this initial study must be followed up by more in-depth investigations to fully understand the benefits of combined optimization-stochastic analysis.

Keywords: structural optimization, response surface methods, stochastical analysis, crashworthiness design

Journal: Shock and Vibration, vol. 8, no. 1, pp. 21-31, 2001