TY - GEN

T1 - Modelling and process optimization for functionally graded materials

AU - Bellur-Ramaswamy, Ravi S.

AU - Haber, Robert

AU - Sobh, Nahil A.

AU - Tortorelli, Daniel A.

PY - 2001

Y1 - 2001

N2 - We optimize continuous quench process parameters to produce functionally graded aluminum alloy extrudates. To perform this task, an optimization problem is defined and solved using a standard nonlinear programming algorithm. Ingredients of this algorithm include 1) the process parameters to be optimized, 2) a cost function: the weighted average of the precipitate number density distribution, 3) constraint functions to limit the temperature gradient (and hence distortion and residual stress) and exit temperature, and 4) their sensitivities with respect to the process parameters. The cost and constraint functions are dependent on the temperature and precipitate size which are obtained by balancing energy to determine the temperature distribution and by using a reaction-rate theory to determine the precipitate particle sizes and their distributions. Both the temperature and the precipitate models are solved via the discontinuous Galerkin finite element method. The energy balance incorporates nonlinear boundary conditions and material properties. The temperature field is then used in the reaction rate model which has as many as 105 degrees-of-freedom per finite element node. After computing the temperature and precipitate size distributions we must compute their sensitivities. This seemingly intractable computational task is resolved thanks to the discontinuous Galerkin finite element formulation and the direct differentiation sensitivity method. A three-dimension example is provided to demonstrate the algorithm.

AB - We optimize continuous quench process parameters to produce functionally graded aluminum alloy extrudates. To perform this task, an optimization problem is defined and solved using a standard nonlinear programming algorithm. Ingredients of this algorithm include 1) the process parameters to be optimized, 2) a cost function: the weighted average of the precipitate number density distribution, 3) constraint functions to limit the temperature gradient (and hence distortion and residual stress) and exit temperature, and 4) their sensitivities with respect to the process parameters. The cost and constraint functions are dependent on the temperature and precipitate size which are obtained by balancing energy to determine the temperature distribution and by using a reaction-rate theory to determine the precipitate particle sizes and their distributions. Both the temperature and the precipitate models are solved via the discontinuous Galerkin finite element method. The energy balance incorporates nonlinear boundary conditions and material properties. The temperature field is then used in the reaction rate model which has as many as 105 degrees-of-freedom per finite element node. After computing the temperature and precipitate size distributions we must compute their sensitivities. This seemingly intractable computational task is resolved thanks to the discontinuous Galerkin finite element formulation and the direct differentiation sensitivity method. A three-dimension example is provided to demonstrate the algorithm.

UR - http://www.scopus.com/inward/record.url?scp=0035789596&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035789596&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0035789596

SN - 0873395131

T3 - Proceedings of the Conference on Computational Modeling of Materials, Minerals and Metals Processing

SP - 65

EP - 84

BT - Proceedings of the Conference on Computational Modeling of Materials, Minerals and Metals Processing

A2 - Cross, M.

A2 - Evans, J.W.

A2 - Bailey, C.

A2 - Cross, M.

A2 - Evans, J.W.

A2 - Bailey, C.

T2 - Proceedings of Conference on Computational Modeling of Materials, Minerals and Metals Processing

Y2 - 23 September 2001 through 26 September 2001

ER -