Publication: Optimal Sizing of Industrial Structural Mechanics Problems Using AD
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Optimal Sizing of Industrial Structural Mechanics Problems Using AD

- incollection -
 

Area
Computational Fluid Dynamics

Author(s)
Gundolf Haase , Ulrich Langer , Ewald Lindner , Wolfram Mühlhuber

Published in
Automatic Differentiation of Algorithms: From Simulation to Optimization

Editor(s)
George Corliss, Christèle Faure, Andreas Griewank, Laurent Hascoët, Uwe Naumann

Year
2002

Publisher
Springer

Abstract
We consider minimizing the mass of the frame of an injection moulding machine as an example of optimal sizing. The deformation of the frame is described by a generalized plane stress state with an elasticity modulus scaled by the thickness. The resulting constrained nonlinear optimization problem is solved by sequential quadratic programming (SQP), which requires gradients of the objective and the constraints with respect to the design parameters. As long as the number of design parameters is small, finite differences may be used. For several hundreds of varying thickness parameters, we use the reverse mode of automatic differentiation (ad). ad works fine but requires huge memory and disk capabilities and limits the use of iterative solvers for the governing state equations. Therefore, we combine ad with the adjoint method to get a fast and flexible hybrid gradient evaluation procedure. Numerical results show the potential of this approach and imply that this method can also be used for finding an initial guess for a shape optimization.

Cross-References
Corliss2002ADo

AD Tools
ADOL-C

BibTeX
@INCOLLECTION{
         Haase2002OSo,
       author = "Gundolf Haase and Ulrich Langer and Ewald Lindner and Wolfram
         M{\"u}hlhuber",
       title = "Optimal Sizing of Industrial Structural Mechanics Problems Using AD",
       pages = "181--188",
       chapter = "21",
       crossref = "Corliss2002ADo",
       booktitle = "Automatic Differentiation of Algorithms: From Simulation to Optimization",
       year = "2002",
       editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent
         Hasco{\"e}t and Uwe Naumann",
       series = "Computer and Information Science",
       publisher = "Springer",
       address = "New York, NY",
       abstract = "We consider minimizing the mass of the frame of an injection moulding machine as an
         example of optimal sizing. The deformation of the frame is described by a generalized plane stress
         state with an elasticity modulus scaled by the thickness. The resulting constrained nonlinear
         optimization problem is solved by sequential quadratic programming (SQP), which requires gradients
         of the objective and the constraints with respect to the design parameters. As long as the number of
         design parameters is small, finite differences may be used. For several hundreds of varying
         thickness parameters, we use the reverse mode of automatic differentiation (AD). AD works fine but
         requires huge memory and disk capabilities and limits the use of iterative solvers for the governing
         state equations. Therefore, we combine AD with the adjoint method to get a fast and flexible hybrid
         gradient evaluation procedure. Numerical results show the potential of this approach and imply that
         this method can also be used for finding an initial guess for a shape optimization.",
       referred = "[Klein2002DMf].",
       ad_area = "Computational Fluid Dynamics",
       ad_tools = "ADOL-C"
}


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