Publication: Adjoint optimization of pressurized membrane structures using automatic differentiation tools
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Adjoint optimization of pressurized membrane structures using automatic differentiation tools

- Article in a journal -
 

Area
Shape optimization

Author(s)
Alexander Niewiarowski , Sigrid Adriaenssens , Ruy Marcelo Pauletti

Published in
Computer Methods in Applied Mechanics and Engineering

Year
2020

Abstract
This paper presents an adjoint-based method for solving optimization problems involving pressurized membrane structures subject to external pressure loads. Shape optimization of pressurized membranes is complicated by the fact that, lacking bending stiffness, their three-dimensional shape must be sustained by the internal pressure of the inflation medium. The proposed method treats the membrane structure as an immersed manifold and employs a total Lagrangian kinematic description with an analytical pressure–volume relationship for the inflating medium. To demonstrate the proposed method, this paper considers hydrostatically loaded inflatable barriers and develops an application-specific shape parametrization based on the analytical inhomogeneous solution for the inflated shape of cylindrical membranes. Coupling this shape parametrization approach with the adjoint method for computing the gradients of functionals enables a computationally efficient optimization of pressurized membrane structures. Numerical examples include minimization and minimax problems with inequality and state constraints, which are solved considering both plane strain and general plane stress conditions. The numerical implementation leverages the high-level mathematical syntax and automatic differentiation features of the finite-element library FEniCS and related library dolfin-adjoint. The overall techniques generalize to a broad range of structural optimization problems involving pressurized membrane and thin shell structures.

AD Tools
dolfin-adjoint

BibTeX
@ARTICLE{
         Niewiarowski2020Aoo,
       title = "Adjoint optimization of pressurized membrane structures using automatic
         differentiation tools",
       journal = "Computer Methods in Applied Mechanics and Engineering",
       volume = "372",
       pages = "113393",
       year = "2020",
       issn = "0045-7825",
       doi = "10.1016/j.cma.2020.113393",
       url = "http://www.sciencedirect.com/science/article/pii/S0045782520305788",
       author = "Alexander Niewiarowski and Sigrid Adriaenssens and Ruy Marcelo Pauletti",
       keywords = "Storm-surge barriers, Inflatable dams, Shape optimization,
         Kreisselmeier–Steinhauser function, FEniCS, Dolfin-adjoint",
       abstract = "This paper presents an adjoint-based method for solving optimization problems
         involving pressurized membrane structures subject to external pressure loads. Shape optimization of
         pressurized membranes is complicated by the fact that, lacking bending stiffness, their
         three-dimensional shape must be sustained by the internal pressure of the inflation medium. The
         proposed method treats the membrane structure as an immersed manifold and employs a total Lagrangian
         kinematic description with an analytical pressure–volume relationship for the inflating
         medium. To demonstrate the proposed method, this paper considers hydrostatically loaded inflatable
         barriers and develops an application-specific shape parametrization based on the analytical
         inhomogeneous solution for the inflated shape of cylindrical membranes. Coupling this shape
         parametrization approach with the adjoint method for computing the gradients of functionals enables
         a computationally efficient optimization of pressurized membrane structures. Numerical examples
         include minimization and minimax problems with inequality and state constraints, which are solved
         considering both plane strain and general plane stress conditions. The numerical implementation
         leverages the high-level mathematical syntax and automatic differentiation features of the
         finite-element library FEniCS and related library dolfin-adjoint. The overall techniques generalize
         to a broad range of structural optimization problems involving pressurized membrane and thin shell
         structures.",
       ad_area = "Shape optimization",
       ad_tools = "dolfin-adjoint"
}


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