Variance method of calculating the deflection rate of a rectangular plate in high-temperature creep conditions

Abstract

1. The variance approach to calculating the deflection rate of the crept sheet is more universal from the mathematical viewpoint than the previously used methods since it makes it possible to reject the assumptions on the reduction of the problem to unidimensional (disregarding the side edges of the billet) and on the coincidence of the tensor of the bending moments with the tensor for the elastic sheet, which distort the real situation. 2. The calculated results greatly increase the accuracy of the existing theoretical pattern of the deflection of the rectangular sheet. Specifically, the results show that at low values of the exponent α in the creep dependence the deflection rate in the center of the sheet stabilizes at a considerably higher ratio β of the long to the short side than at the value α=1 which corresponds to the elastic and linearly crept sheets. 3. Taking into account the assumption of the homogeneity of the material of the sheet, it is recommended to use the method in combination with the calculation models which take into account the heterogeneity of the material and the thickness of the sheet. 4. The proposed method can be used for the quantitative calculations of the deflection of the sheets with both the creep and plasticity properties with the exponential hardening law.