Educational and Research Materials

We have created this area to help educators, researchers, and students exchange educational materials that will allow them to teach and apply optimization more effectively. If you are currently teaching an optimization class using HEEDS, and wish to share your curriculum and/or sample problems, please send them to

Educational Materials
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Technical Papers

Below you'll find technical papers describing work performed with HEEDS. If you have conducted research using HEEDS that has been published in a technical journal or conference proceedings, let us know! We'd love to add a link to your work.
Erik Wendeberg
Master’s Thesis in the Automotive Engineering Programme
Department of Applied Mechanics
Division of Vehicle Engineering and Autonomous Systems
Vehicle Dynamics Group

Computer aided engineering is becoming an increasingly important tool in the automotive industry since it can reduce development time of new vehicles. However, in order to draw the same conclusions from test and simulation results it is important that the behaviour and characteristics of a simulation model match test data. Traditionally, to ensure that a suspension simulation model is accurate, it is correlated by a manual adjustment of the parameters in the model. This is time-consuming and error-prone. By automating the correlation process using a suitable optimization technique and a properly defined procedure, the process can be performed faster and the quality of the results can be improved since more parameters and objectives can be included. The aim of this study was to develop a well-defined correlation procedure, with minimal user input, that optimizes parameters in a suspension model so the behaviour of the model matches test data. A design of experiment study was conducted to analyse the influence of suspension parameters on corresponding suspension characteristics, and based on this a suitable correlation method and optimization model setup could be defined. By running the correlation procedure in the optimization software HEEDS MDO, connected with ADAMS/Car, suspension characteristics could be correlated to measurement data. The defined auto-correlation procedure was found to be effective and a front suspension assembly was successfully correlated to physical kinematics and compliance measurement results. However, the baseline suspension model has to be modelled correctly and include all the necessary variables in order to fully correlate the suspension simulation model. Some of the correlated suspension parameters were found to have optimized values outside normal production tolerances, in order to compensate for limitations in the simulation model, such as rigid modelling of components. By using the defined auto-correlation procedure, the correlation time was reduced and it is recommended that HEEDS MDO is used for future correlation of suspension assemblies. If the setup of the optimization model is adjusted, the defined correlation procedure can also be used to create suspension simulation models of competitor vehicles or optimizing suspension design concepts to meet requirements.
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Abvabi, Akbar, Rolfe, Bernard, Hodgson, Peter D., Weiss, Matthias
Presented at Esaform 2013 Conference, April 2013, Aveiro, Portugal

Bending and reverse bending are the dominant material deformations in roll forming, and hence property data derived from bend tests could be more relevant than tensile test data for numerical simulation of a roll forming process. Recent investigations have shown that residual stresses change the material behavior close to the yield in a bending test. So, residual stresses introduced during prior steel processing operations may affect the roll forming process, and therefore they need to be included in roll forming simulations to achieve improved model accuracy. Measuring the residual stress profile experimentally is time consuming and has limited accuracy while analytical models that are available require detailed information about the pre-processing conditions that is generally not available for roll forming materials. The main goal of this study is to develop an inverse routine that determines a residual stress profile through the material thickness based on experimental pure bend test data. A numerical model of the skin passing (temper rolling) process is performed to introduce a residual stress profile in DP780 steel sheet. The skin passed strips are used in a pure bending simulation to record moment-curvature data and this data is then applied in an inverse analysis to predict the residual stress profile in the material. Comparison of the residual stress profile predicted by the inverse routine with that calculated by finite element analysis (FEA) indicates an inverse approach combined with pure bend test may present an alternative to predict residual stresses in sheet metals.
Manufacturing, Marc, Nonlinear Stress, Parameter Estimation

Lee, Jin Woo, M.S., Embry-Riddle Aeronautical University, 2011, 159 pages; AAT EP33513

Development of a multidisciplinary design optimization (MDO) of a large scale hybrid composite wind turbine blade is performed. Multiple objectives are considered in the MDO process to maximize annual energy production and lifetime profit, minimize weight and power production rate. A wind turbine blade is divided into regions and the layup sequences for each region are considered as design variables. The scale of wind turbine blade is also considered to find the optimum size of a wind turbine blade. Applied loads due to extreme wind conditions for rotor rotation and rotor stop condition are considered for finite element analysis (FEA) to evaluate the structural strength. The designed structural strength and stiffness are demonstrated to withstand the loads due to harmonic excitation from rotor rotation. An MDO process for obtaining an optimum hybrid composite laminate layup and an optimum length of a wind turbine blade is developed and illustrated in this research. The finite element (FE) model and cost estimation model are calibrated and the developed MDO process is verified for an optimum design. The optimum hybrid composite layup sequence and size of a large scale wind turbine blade are highlighted in this research.
Energy, Excel, FEMAP, Linear Stress, Nastran