On an optimal shape design problem to control a thermoelastic deformation under a prescribed thermal treatment

Mehne, Hamed Hashemi; Farahi, Mohammad Hadi; Esfahani, Javad Abolfazli

doi:10.1016/j.apm.2005.12.001

Cited by 9 publications

(8 citation statements)

References 6 publications

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“…Now it is necessary to verify the existence of a solution for this problem. Proof The proof is similar to Theorems 6.1 and 6.2 of [11].…”

Section: Optimization In Measure Spacementioning

confidence: 85%

“…(ii) α(·) is a decreasing differentiable function and satisfy the relations (4), (5), (9), (10), (11) and (12).…”

Section: Lemma 31 a Necessary And Sufficient Condition For Holding Tmentioning

confidence: 99%

“…Thus, one can interpret the shape optimization problem (7) as an optimal control problem consisting of minimizing the cost functional (6), subject to the constraints (4), (5), (9), (10), (11) and (12). Definition 3.…”

Section: Lemma 31 a Necessary And Sufficient Condition For Holding Tmentioning

confidence: 99%

“…The procedure to construct a piecewise constant control function from the solution {κ l , λ m } of linear programming problem (49)-(54) which approximate the action of the optimal measure, is based on the analysis in [11].…”

Section: Finite-dimensional Approximation Of the Infinite-dimensionalmentioning

confidence: 99%

“…Now if one can find optimal measure, obviously optimal shape is obtained. This procedure presented in [10][11][12][13][14][15], is followed.…”

mentioning

confidence: 99%

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Control the Fibre Orientation Distribution at the Outlet of Contraction

Nazemi

Farahi

2008

Acta Appl Math

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A two dimensional model of the orientation distribution of fibres in a paper machine headbox is studied. The goal is to control the fibre orientation distribution at the outlet of contraction by changing its shape. The mathematical formulation leads to an optimization problem with control in coefficients of a linear convection-diffusion equation as the state problem. Then, the problem is expressed as an optimal control problem governed by variational forms. By using an embedding method, the class of admissible shapes is replaced by a class of positive Radon measures. The optimization problem in measure space is then approximated by a linear programming problem. The optimal measure representing optimal shape is approximated by the solution of this linear programming problem. In this paper, we have shown that the embedding method (embedding the admissible set into a subset of measures), successfully can be applied to shape variation design to a one dimensional headbox. The usefulness of this idea is that the method is not iterative and it does not need any initial guess of the solution.

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“…Now it is necessary to verify the existence of a solution for this problem. Proof The proof is similar to Theorems 6.1 and 6.2 of [11].…”

Section: Optimization In Measure Spacementioning

confidence: 85%

“…(ii) α(·) is a decreasing differentiable function and satisfy the relations (4), (5), (9), (10), (11) and (12).…”

Section: Lemma 31 a Necessary And Sufficient Condition For Holding Tmentioning

confidence: 99%

Section: Lemma 31 a Necessary And Sufficient Condition For Holding Tmentioning

confidence: 99%

Section: Finite-dimensional Approximation Of the Infinite-dimensionalmentioning

confidence: 99%

“…Now if one can find optimal measure, obviously optimal shape is obtained. This procedure presented in [10][11][12][13][14][15], is followed.…”

mentioning

confidence: 99%

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Control the Fibre Orientation Distribution at the Outlet of Contraction

Nazemi

Farahi

2008

Acta Appl Math

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Shape optimization of an airfoil in the presence of compressible and viscous flows

Farhadinia

2009

Comput Optim Appl

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LP Modelling for the Time Optimal Control Problem of the Heat Equation

Nazemi

2011

J Math Model Algor

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On an optimal shape design problem to control a thermoelastic deformation under a prescribed thermal treatment

Cited by 9 publications

References 6 publications

Control the Fibre Orientation Distribution at the Outlet of Contraction

Control the Fibre Orientation Distribution at the Outlet of Contraction

Shape optimization of an airfoil in the presence of compressible and viscous flows

LP Modelling for the Time Optimal Control Problem of the Heat Equation

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