Вплив вм’ятин на напружений стан циліндричних обичайок апаратів високого тиску

Abstract

На поверхні корпусних оболонкових елементів сосудів високого тиску часто виявляють вм’ятини, які є концентраторами напружень. Розглядалася тонкостінна циліндрична оболонка (обичайка) під дією внутрішнього тиску, у якої вм’ятина є результатом плавного сполученнятрьох складових оболонок: циліндричної, сферичної і тороїдний. Основне диференціальне рівняння було подано в комплексній формі Новожилова. На базі умов сполучення складових оболонок було розроблено алгоритм визначення напружень у зоні вм’ятини, застосування якого у конкретному прикладі показало суттєве збільшення коефіцієнту їх концентрації. Indents are often found while examining high pressure vessels. The indents on the surface of case shell elements of these vessels are stress concentrators influencing stress strain behaviour of these elements. This can result in exceeding allowed tension values. There is virtually no research of this state in the indent regions at the moment, which has encouraged this work. The author has studied a thin-walled cylindrical shell under the effect of internal pressure. The shell has an indent resulting from the seamless joint of three shells: cylindrical, spherical and toroidal as a transition between the first two shells. The main differential equation for these shells has been presented in Novozhylov complex form. The general solution of this equation in complex function is provided as the sum of the general solution of homogeneous equation, defined by asymptotic method, and the specific solution of non-homogeneous equation, which satisfies membrane theory. Solutions for all three shells were presented in expressions with complex constants, derived from four conditions of these shell combinations. Joint parameters were defined as radial displacements, degrees of tangential rotation, radial stresses and bending moments. The systems of algebraic equations for Novozhylov functions and the functions themselves has been found. The latter determined stresses and moments in all shell components of the indent. Tension calculations of the indent t=0,02 m deep in the cylindrical shell h=0,02 m thick and RB=1,3 m in diameter, done under pressure p=1,2 MPa have the following results: being a stress concentrator, the indent causes tension increase. Concentration factor for tensile stresses was quite small (1,2), being rather substantial for bending stresses (5,3). Therefore, we think it is worthwhile to regulate geometrical parameters of indents in proper technical documentation.