Ajg Bert Schoofs

Optimization of multibody systems using approximation concepts

Sequential approximate optimization is used to solve multibody optimum design problems. The transient optimization problem is formulated such that approximation concepts can be incorporated. Two multibody design examples illustrate the effectiveness of the approach.

Experimental design and structural optimization

Structural optimization problems are mostly solved iteratively by combining finite element and mathematical progamming methods.

Crash worthiness design optimization using multipoint sequential linear programming

A design optimization tool has been developed for the crash victim simulation software MADYMO. The crash worthiness optimization problem is characterized by a noisy behaviour of objective function and constraints. Additionally, objective function and constraint values follow from a computationally expensive numerical analysis. Sequential approximate optimization is used to deal with both the noisy functional behaviour and the high computational costs. By means of multipoint approximations, a sequence of linear programming problems is generated that can be easily solved. The optimization approach is illustrated for an analytical test problem and an industrial crash worthiness design problem.

Use of Design Sensitivity Information in Response Surface and Kriging Metamodels

Metamodels based on responses from designed (numerical) experiments may form efficient approximations to functions in structural analysis. They can improve the efficiency of Engineering Optimization substantially by uncoupling computationally expensive analysis models and (iterative) optimization procedures. In this paper we focus on two strategies for building metamodels, namely Response Surface Methods (RSM) and kriging. We discuss key-concepts for both approaches, present strategies for model training and indicate ways to enhance these metamodeling approaches by including design sensitivity data. The latter may be advantageous in situations where information on design sensitivities is readily available, as is the case with e.g. Finite Element Models. Furthermore, we illustrate the use of RSM and kriging in a numerical model study and conclude with some remarks on their practical value.

Approximation of structural optimization problems by means of designed numerical experiments

In this paper we describe an approach in which the Experimental Design Theory (EDT) (see Montgomery and Wiley 1984; Kiefer and Wolfowitz 1959; Fedorov 1972) is used as a tool in building approximate analysis models to be applied in structural optimization problems. This theory has been developed for the planning and analysis of comprehensive physical experiments in order to reduce the number of required experiments while preserving the amount of information that can be extracted from them. This situation is very similar to that of structural optimization, where the number of expensive finite element (FEM) analyses has to be minimized (Schoofs 1987). FEM computations can be regarded as numerical experiments, where the design variables are treated as input quantities. All computable properties of the structure, such as weight, displacements, stresses, etc. can be regarded as response quantities of the numerical experiment. The approximating models will be derived for these responses by using regression techniques, and they can be substituted in the optimization problem for the definition of the objective and the constraint functions. The application of the proposed method is illustrated with two case studies.

A general purpose two-dimensional mesh generator

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Design Optimization of Multibody Systems by Sequential Approximation

Design optimization of multibody systems is usually established by a direct coupling of multibody system analysis and mathematical programming algorithms. However, a direct coupling is hindered by the transient and computationally complex behavior of many multibody systems. In structural optimization often approximation concepts are used instead to interface numerical analysis and optimization. This paper shows that such an approach is valuable for the optimization of multibody systems as well. A design optimization tool has been developed for multibody systems that generates a sequence of approximate optimization problems. The approach is illustrated by three examples: an impact absorber, a slider-crank mechanism, and a stress-constrained four-bar mechanism. Furthermore, the consequences for an accurate and efficient accompanying design sensitivity analysis are discussed.

Global and Mid-Range Function Approximation for Engineering Optimization

Global and mid-range approximation concepts are used in engineering optimisation in those cases were the commonly used local approximations are not available or applicable. In this paper the response surface method is discussed as a method to build both global and mid-range approximations of the objective and constraint functions. In this method analysis results in multiple design points are fitted on a chosen approximation model function by means of regression techniques. Especially global approximations rely heavily on appropriate choices of the model functions. This builds a serious bottleneck in applying the method. In mid-range approximations the model selection is much less critical. The response surface method is illustrated at two relatively simple design problems. For building global approximations a new method was developed by Sacks and co-workers, especially regarding the nature of computer experiments. Here, the analysis results in the design sites are exactly predicted, and model selection is more flexible compared to the response surface method. The method will be applied to an analytical test function and a simple design problem. Finally the methods are discussed and compared.

Design of a Stroke Dependent Damper for the Front Axle Suspension of a Truck Using Multibody System Dynamics and Numerical Optimization

Summary A stroke dependent damper is designed for the front axle suspension of a truck. The damper supplies extra damping for inward deflections rising above 4 cm. In this way the damper should reduce extreme suspension deflections without deteriorating the comfort of the truck. But the question is which stroke dependent damping curve yields the best compromise between suspension deflection working space and comfort. Therefore an optimization problem is defined to minimize the maximum inward suspension deflection subject to constraints on the chassis acceleration for three typical road undulations. The optimization problem is solved using sequential linear programming (SLP) and multibody dynamics simulation software. Several optimization runs have been carried out for a small two degree of freedom vehicle model and a large full-scale model of the truck semi-trailer combination. The results show that the stroke dependent damping can reduce large deflections at incidental road disturbances, but that the optimum stroke dependent damping curve is related to the acceleration bound. By means of vehicle model simulation and numerical optimization we have been able to quantify this trade-off between suspension deflection working space and truck comfort.

Optimization of structural and acoustical parameters of bells

Citation for published version (APA): Schoofs, A. J. G., Kroon, P. J. M., & Campen, van, D. H. (1994). Optimization of structural and acoustical parameters of bells. In A collection of technical papers of the 5th AIAA/USAF/NASA/ISSMO symposium on multidisciplinary analysis and optimization, September 7-9, 1994, Panama City Beach, Fla. Part 2 (pp. 11671180). Washington, DC: American Institute of Aeronautics and Astronautics Inc. (AIAA).