Structural Design Optimization

Arbitrary nonlinear optimization
Size optimization (parametric)
Topometry optimization (shell thickness)
Topography optimization (beads)
Shape optimization by mesh morphing
Topology optimization of plates and solids
Topology optimization of trusses
Material optimization
Design space exploration (variational analysis, design of experiments, response surfaces, ...)

Application Cases

Identification of Ogden Material Properties

The Ogden material model is frequently used in finite element programs to simulate the behavior of non-linear elastomers. The values of the material parameters of the Ogden model are highly material dependent. The main challenge in using the Ogden model in finite element simulations, is to find reliable estimates for the values of the Ogden material parameters. The relation between an imposed displacement and the resulting reaction force can be used to identify these material parameters using a mixed numerical-experimental approach. In this approach, the objective is to fit the simulated reaction force curve onto the measured reaction force curve. The computationally most efficient way of doing that is by using a gradient-based optimization strategy.

Such identification routine was implemented using FEMtools Script for the process identification part, FEMtools Optimization for the optimizer routines, and used MSC.Marc to compute the reaction force curves. More information can be found in the following application note:

Identification of Ogden Material Parameters using FEMtools, October 2008.
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Optimization of the Dynamic Response of a Complete Exhaust System

An optimization approach can be used for tailoring the dynamic response of a complete exhaust system using finite element modeling.

Before the optimization procedure is started, the FE-model is updated using modal test data. This preliminary step is required to ensure the validity of the initial FE model. The actual optimization routine consists of two iteration loops: an inner and an outer loop. The inner iteration loop performs the optimization using a modal domain modification technique to predict the change of the dynamic response of the structure. In this way the structure can be optimized in a computational efficient way. However, the modal domain prediction is only accurate within a limited parameter range. Therefore, the outer iteration loop re-evaluates the full finite element model once the parameter changes exceed the trust-region bounds of the modal domain prediction. The solution of the re-evaluation is then used as improved base for the modal domain prediction in the inner iteration loop.

The suggested optimization approach is illustrated on a finite element model of an exhaust system of a passenger car. The exhaust system is connected to the car body using four isolators. The optimization is performed to keep the force transmitted by the exhaust system through the isolators to the car body below the design specifications, optimizing the stiffness of the decoupling elements. The goal is to ensure a good NVH (Noise Vibration Harshness) performance of the exhaust system.

A complete overview of the application is presented in the following paper:

T. Lauwagie, J. Strobbe, E. Dascotte, J. Clavier, M. Monteagudo, Optimization of the Dynamic Response of a Complete Exhaust System, presented at the International Seminar on Modal Analysis 2008 (ISMA), September 15-17, 2008, Leuven, Belgium.
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Other References Related to Optimization

E. Dascotte, Integration of FE Model Validation, Uncertainty Analysis and Design Improvement using the FEMtools Framework Toolbox, Presented at the OPTECH04 conference, May 2004, Breckenridge, Colorado.
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T. Koizumi, N.Tsujiuchi (Doshisha University), I. Kubomoto, E. Ishida (Kubota Corp.), F. Ohtani, Optimizing a Tractor Frame for Improved Cabin NVH, SAE Off Highway Engineering, September 2000, pp 45-49.