Diagnosis of tensions according to thickness of shell structures which work under pressure

Abstract

Tension and deformations which appear in the structures elements have a great impact on their durability, production accuracy and bearing capacity. The aim of this work is to develop the calculation and experimental approach to determine the distribution of circumferential tensions according to the thickness in shell structures. It is important to find the connection between the averaged values of tensions and their distribution according to the thickness using the method of supersonic tensometry to measure the tension state of thick-wall shells. First of all, the solution to the Lame problem has been written down in order to determine the radial tensions in the cylinder. The inner wall of the cylinder is under the regular pressure. Further, in the result of the integration of this solution within the range from r min to r max , the formula has been obtained to determine the average value of tensions according to the wall thickness. The same averaged parameters are obtained after those tensions have been determined by means of the supersonic method. The value the quantity of which one can describe as a coefficient of the K transition from the average integral of circumferential tensions to their real distribution over the wall thickness is obtained in the result of the formulas relation to determine the circumferential tensions. Those numbers are relevant when using the non-destructive methods which carry the information regarding the tension condition of outer layers. The formula is derived to determine the distribution of the circumferential tensions over the wall of thick-wall shells based upon the average integral value of circumferential tension. Using the experimental methods the formulae are obtained to calculate the maximum and minimum values of circumferential tensions.