Approximate Evaluation of Shrinkage due to Spot Heating on a Rectangular Plate (Report No.2)

Abstract

In the previous reports, an analytical method was proposed to study shrinkage distortion due to spot heating on a rectangular plate. First, a method for exact analysis was presented. Then several methods of approximate anlyses were sought for.
In this report, approximate formulae were deduced by combining the results from the rigorous and the approximate analyses with those of numerical calculations. These formulae are simple and self-explanatory, therefore very convenient to apply in practice. They also lead to a clear understanding of characteristic features of shrinkage distortion in rectagular plates.
For example, the formulae indicate that the shrinkages chiefly depend on the breadth of the plate, while they are little affected by the length. It is also shown that if heat is applied on a point far away from the plate edges, the length of the plate reduces approximately by 27πδ/2bE, where-δ, 2 b and E designate the magnitude of shrinkage source, the breadth and Young's modulus of the plate, respectively. The quantity 2δ/2bE is the fundamental value which appears in all the exact or approximate expressions.
Calculated values from the approximate formulae satisfactorily agreed with experimental ones.
The results obtained through the present investigation are expected to provide a basis for the analysis of shrinkages in any locally heated plates.