Stability of a reinforced non-circular cylindrical shell under combined bending moment and marginal transverse force

In the designs of modern aircraft, the shape of the fuselage of a non-circular cross-section is very often used. This is especially noticeable when designing large-capacity wide-body aircraft. Despite the fact that a large number of papers have been published on the study of the strength of such structures, nevertheless, the issues of strength and stability under nonlinear deformation remain unresolved. The latter is especially necessary for thin-walled aircraft fuselage structures, in which loss of skin stability is unacceptable. Methods for calculating the strength and stability of thin-walled structures, taking into account the nonlinearity of the initial stress-strain state, are currently insufficiently developed. Most studies on shell stability have been performed either by analytical methods or using well-known application software packages such as ANSYS and other, as a rule, in a linear formulation and under the separate action of external loads. In addition, there are no studies in the literature on non-circular shells with geometric parameters close to the dimensions of modern wide-body aircraft. Therefore, the development of reliable and effective methods for calculating shells, as well as the results of their stability testing, is undoubtedly an urgent task. In this paper, the problem of strength and stability of non-circular cylindrical shells under arbitrary non-axisymmetric loading is solved by finite element methods and Newton–Kantorovich linearization. The stability of a reinforced non-circular cylindrical shell under combined bending moment and transverse force loading is investigated. In contrast to well-known studies, this work considered discretely reinforced stringer sets and frames and thinner shells (the ratio of the shell radius to the thickness of the order of 1,500), for which the influence of nonlinearity is more significant. In the presented work, the influence of the nonlinearity of deformation and the ovality of the contour of the shell cross-section on critical loads due to the loss of shell stability is investigated. The curves of interaction of critical external loads, as well as the forms of loss of stability, are treated.
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