Тернопiльський національний технiчний унiверситет iменi Iвана Пулюя
Abstract
Розглянуто задачу про напружений стан пологої ортотропної оболонки двоякої кривини з двома колінеарними прямолінійними тріщинами різної довжини, коли до їх берегів прикладене самозрівноважене згинальне навантаження. Задачу сформульовано у двовимірній постановці на основі моделі контакту вздовж лінії на одній з лицьових поверхонь оболонки. Система сингулярних інтегральних рівнянь розв’язана чисельно за допомогою методу механічних квадратур. Досліджено вплив кривини оболонки, взаємного розміщення колінеарних тріщин, механічних властивостей матеріалу в околі вершин тріщин на коефіцієнти інтенсивності моментів. Отримані результати співпадають з відомими в літературі частинними розв’язками.In this paper we present the analytically and numerically study of the problem of the stress state of the shallow orthotropic dual curvature shell with two collinear rectilinear through thickness cracks of different lengths, when applied to their shores self-balanced load. The thin shells are widely used in hydraulic engineering, aerospace engineering, shipbuilding and aircraft construction, engineering and others areas of modern construction. By using of advanced composite materials the strength of structure is increased and the weight is reduced. As an example, the use of carbon plastic in the construction of Boeing and Airbus aircrafts; the housing of water version «Formula 1» is reinforced with carbon fibers; details of the internal combustion engine (pistons, connecting rods), and others. Reliability and durability of constructions like shells depends on the availability of various types of defects that occur at the stage of the manufacture of parts yet and avoid this impossible. So analysis of stress state of orthotropic dual curvature shell with closure cracks is an important task of mechanics.
The problem presented in this paper was formulated in a two-dimensional statement by means of the contact model along a line in one of the facial surfaces of a shell (internal or external). The problem statement is reduced to the solution of system of two integral equations. The independent variables in the equations are leaps of rotation angles of cracks, while leaps of movements on the lines of cracks are functions which are dependent on them. The system of singular integral equations is solved numerically using the method of mechanical quadratures. Was investigated the influence of the shell curvature, mutual location of collinear cracks, crack length, the mechanical properties of the orthotropic material in the vicinity of the crack tip on the stress intensity factors and moment intensity factors. In particular cases of the problem was obtained results for cylindrical, spherical and pseudo spherical shells. In case when cracks have same length in spherical shell was obtained known in the literature results
