Control of the thermal stress state of elastic bodies in the case of a unidimensional temperature field. (English. Russian original) Zbl 0636.73008
Sov. Appl. Mech. 23, 165-170 (1987); translation from Prikl. Mekh., Kiev 23, No. 2, 67-72 (1987).
Optimization of the speed of response in the control of transient unidimensional temperature regimes, with restrictions of thermoelastic stresses during heating of the body to limit these stresses, basically involves controlling the stresses at a specified point or the most heavily stressed point of the body. The solution of the problem of controlling thermal stresses is of practical interest not only at an isolated point of a body, but over the entire region in which the stresses are determined. Thus, for a unidimensional transient temperature field we pose the problem of using the distribution of the specific capacity of internal heat sources to optimize control of the quasistatic thermoelastic stress state of an infinite layer, long cylinder, and sphere. A method is proposed for solving this problem, and the method is used, with realistic restrictions on the required thermal stress distribution in the body, to find the control which ensures attainment of the lower bound of the corresponding quadratic optimization functional.
MSC:
| 74F05 | Thermal effects in solid mechanics |
| 74S30 | Other numerical methods in solid mechanics (MSC2010) |
| 74A15 | Thermodynamics in solid mechanics |
| 49K20 | Optimality conditions for problems involving partial differential equations |
| 45B05 | Fredholm integral equations |
Keywords:
ill-posed inverse problem; second order boundary conditions; unidimensional transient temperature field; internal heat sources; optimize control; quasistatic thermoelastic stress state; infinite layer; long cylinder; sphere; lower bound; quadratic optimization functionalReferences:
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