Shape optimization using time evolution equations

Summary In this study, we deal with a numerical solution based on time evolution equations to solve the optimization problem for finding the shape that minimizes the objective function under given constraints. The design variables of the shape optimization problem are defined on a given original dom...

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Bibliographic Details
Published in:International journal for numerical methods in engineering 2018-09, Vol.115 (11), p.1371-1382
Main Authors: Murai, Daisuke, Kawamoto, Atsushi, Kondoh, Tsuguo
Format: Article
Language:English
Subjects:
adjoint variable method
Boundary value problems
Design optimization
Evolution
Partial differential equations
Shape optimization
shape optimization problems
Thermal resistance
time evolution equations
Time integration
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Summary:Summary In this study, we deal with a numerical solution based on time evolution equations to solve the optimization problem for finding the shape that minimizes the objective function under given constraints. The design variables of the shape optimization problem are defined on a given original domain on which the boundary value problems of partial differential equations are defined. The variations of the domain are obtained by the time integration of the solution to derive the time evolution equations defined in the original domain. The shape gradient with respect to the domain variations are given as the Neumann boundary condition defined on the original domain boundary. When the constraints are satisfied, the decreasing property of the objective function is guaranteed by the proposed method. Furthermore, the proposed method is used to minimize the heat resistance under a total volume constraint and to solve the minimization problem of mean compliance under a total volume constraint.
ISSN:0029-5981
1097-0207
DOI:10.1002/nme.5848