Analytical Aspects and Practical Pitfalls in Technical Applications of Automatic Differentiation
by
Florian Dignath
Institute B of Mechanics, University of Stuttgart
Coauthors: Dr. Peter Eberhard (Institute B of Mechanics, University of Stuttgart), Axel Fritz (Institute B of Mechanics, University of Stuttgart)

In this paper, the application of Automatic Differentiation to three technical problems from multibody dynamics, vehicle dynamics and finite element material modelling will be presented. The first analysis investigates the application of threshold and maximum--value optimization criteria in direct representation using AD for the sensitivity analysis.

Secondly, an adaptive cruise controller of a vehicle convoy is optimized with respect to control error and control effort. Two experimental cars equipped with state-of-the- art sensors and actuators are used to verify the designed controllers. Since the engine voltage of the considered actuator model is restricted to +/- 10 V, a non- differentiable point in the time trajectory exists. After an appropriate definition of the derivative at that point, AD techniques can be used. Thirdly, Automatic Differentiation is used for the evaluation of constitutive relations for hyperelastic materials. Some important continuum mechanical quantities correspond to the first and second derivatives of the scalar stored energy function with respect to the strain tensor. These quantities can be derived analytically using complicated analysis but it is fascinating that with minimal preparation and few mathematical insight exactly the same vectors can be computed using AD methods.

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Date received: December 23, 1999