Shape optimization using time evolution equations. (25th June 2018)

• Record Type: Journal Article
• Authors: Murai, Daisuke; Kawamoto, Atsushi; Kondoh, Tsuguo
• Is Part Of: International journal for numerical methods in engineering. Volume 115:Number 11(2018)
• Page Start: 1371
• Page End: 1382
• Publication Date: 2018-06-25
• Subjects: adjoint variable method -- partial differential equations -- shape optimization problems -- time evolution equations; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.5848
• Languages: English
• ISSNs: 0029-5981

Abstract

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.