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Thermal deflection analysis of the solidified shell in continuous casting of slab

The thermal deformation problem in the continuous casting of a slab subjected to thermal loading because of the temperature gradient along the solidified shell thickness is investigated. On the basis of the reciprocal theorem of work or Betti-Maxwell’s reciprocal theorem and the superposition principle, the deflection expressions for a rectangular plate with the two opposite edges simply supported, and the other two opposite edges clamped under the action of the uniformly distributed load and nonuniform temperature field are derived respectively. The meaning of each term in the deflection expression obtained by the reciprocal theorem of work is explained. Then the practical example is given to calculate the thermal deformation and the bulging deformation of the solidified shell under three tension speeds. This research is useful for analyzing the bulging deformation in the continuous casting of a slab under the static pressure of the molten steel and the thermal loading because of the temperature gradient along the solidified shell thickness.