TY - JOUR
T1 - Adjoint optimization of pressurized membrane structures using automatic differentiation tools
AU - Niewiarowski, Alexander
AU - Adriaenssens, Sigrid
AU - Pauletti, Ruy Marcelo
N1 - Funding Information:
This material is based upon work supported by the Princeton Environmental Institute at Princeton University , as well as the Princeton University-University of Sao Paulo Collaborative Partnership. The authors would also like to thank Alex Beatson for his advice regarding dolfin-adjoint.
Publisher Copyright:
© 2020 Elsevier B.V.
PY - 2020/12/1
Y1 - 2020/12/1
N2 - 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.
AB - 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.
KW - Dolfin-adjoint
KW - FEniCS
KW - Inflatable dams
KW - Kreisselmeier–Steinhauser function
KW - Shape optimization
KW - Storm-surge barriers
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U2 - 10.1016/j.cma.2020.113393
DO - 10.1016/j.cma.2020.113393
M3 - Article
AN - SCOPUS:85090335400
SN - 0045-7825
VL - 372
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
M1 - 113393
ER -