| Speaker : |
Prof. Huaxiong HUANG(York University, Toronto) |
| Subject : |
Thermal Stress Reduction for a Czochralski Grown Single Crystal |
| Date : |
June 23, 2005 3:00pm-4:30pm (Seminar room 2, Faculty of Engineering bldg.2, Hongo campus) |
| Outline : |
In this talk we present an optimal control approach for the reduction of thermal stress inside a Czochralski grown single crystal. Using the lateral heat flux as a control variable, we derive an optimal control formulation for minimizing thermal stress with a given crystal shape. Since crystal shape has a significant effect on thermal stress, the stress can also be reduced by finding a suitable crystal shape. Using crystal shape as a control variable, we derive a similar optimal control formulation for stress reduction. In both cases, von Mises stress is used as an objective function of the constrained optimization problem. Euler-Lagrange equations are derived using the calculus of variations and the method of Lagrange multipliers. Various stress reduction strategies are explored by solving the Euler-Lagrange equations numerically. |
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