Premium
Shape optimization using time evolution equations
Author(s) -
Murai Daisuke,
Kawamoto Atsushi,
Kondoh Tsuguo
Publication year - 2018
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5848
Subject(s) - mathematics , boundary value problem , mathematical optimization , constraint (computer aided design) , shape optimization , domain (mathematical analysis) , neumann boundary condition , optimization problem , boundary (topology) , fictitious domain method , function (biology) , partial differential equation , mathematical analysis , geometry , finite element method , physics , evolutionary biology , biology , thermodynamics
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.