Elastoplastic deformation of conical shells with two circular holes

Abstract

The elastoplastic state of thin conical shells with two circular holes is analyzed. The stress distribution in the stress-concentration zone is examined using a proposed technique. The stress-strain state around the two circular holes in shells under internal pressure is analyzed taking plastic strains into account. Numerical results are presented in a tableIntroduction. Study of the interaction between the boundaries of holes in thin-walled conical shells is an important task of solid mechanics. Most results on stress concentration around curvilinear and rectangular holes in conical shells made of metals and composites were obtained by solving linear elastic problems with analytic, variational, and numerical methods and are most fully reported in [2,3,9,13].Also of great interest are the solutions of two-dimensional problems for thin shells with holes of various shapes under high surface and boundary loads, which makes it necessary to take into account both the real properties of materials (plastic strains) and deformation behavior (finite deflections).Physically nonlinear cases of stress-concentration in conical shells with holes were examined in few publications. This is because the system of governing equations becomes very complicated when nonlinear factors are allowed for and there are holes in the lateral walls. Therefore, most studies of the nonlinear deformation of conical shells with holes use mesh-based methods [14]. Note that most results on the nonlinear deformation of conical shells were obtained for the case of one hole. For example, numerical results were obtained, using a variational difference method, for an elastoplastic isotropic conical shell with rectangular [4] and circular [15] holes and for a nonlinear elastic orthotropic shell with a circular hole [1]. The combined effect of plastic strains and finite deflections on the stress-strain state of a conical shell with an elliptic or circular hole was studied in [7,8]. Numerical finite-element analyses were conducted for shells subject to uniform internal pressure. Two-dimensional nonlinear problems for a shell with a circular hole under axial forces were solved numerically in [6].Most numerical results on the stress-strain state around two circular holes were obtained for spherical [11,12] and cylindrical [10] shells. The FEM was used to analyze the effect of nonlinear factors on stress concentration and the interaction of the edges of holes in shells under known uniform internal pressure. For a cylindrical shell, the case of axial tension was numerically analyzed as well. The influence of plastic strains on the stress concentration around two circular holes in the lateral wall of a conical shell under tensile forces was studied in [5].Here we formulate elastoplastic problems for isotropic conical shells with two curved holes and develop a numerical technique to solve them. We will present specific numerical results on the inelastic deformation of a conical shell with two circular holes under high uniform internal pressure.

Stress concentration in the region of a rec tangular hole on the side surface of a nonlinearly elastic orthotropic conical shell

“…вими отворами при дії статичних навантажень [7,8]. Чисельні дослідження проведені з використанням методу скінченних елементів (МСЕ).…”

“…Вирази для компонент мембранної ε ( ) ij і згинної μ ( ) ij деформацій представимо у векторній формі згідно з теорією непологих оболонок, в якій виконуються гіпотези Кірхго фа-Лява [2,8]:…”

“…Методом додаткових напружень вихідна фізично нелінійна задача (13) зводиться до послідовності лінійно-пружних задач, які розв'язуються модифікованим МСЕ. Особливість запропонованого варіанту МСЕ полягає в тому, що вектор кутів повороту ϕ  не визначається за допомогою формул (2) для ϕ l і ϑ ϕ , як це прийнято в традиційному МСЕ для тонких оболонок, а апроксимується біквадратичним поліномом серендипового типу з виконанням гіпотез Кірхгофа-Лява у вузлах скінченного елемента (СЕ) [8,12].…”