Simplification of the calculation scheme for determining the stress state of non-thin cylindrical shells with a complex cross-sectional shape ellipticity
DOI:
https://doi.org/10.32347/2410-2547.2022.109.287-300Keywords:
corrugated ellipses, discrete Fourier series, linear theory of elasticity, stress state, non-thin cylindrical shells, orthotropic material, spatial model, simplification of the calculation schemeAbstract
An alternative to full-scale experiments is computer simulation, which allows studying a variety of states, phenomena, processes, etc. occurring in the environment.
Conducting a computational experiment is an integral part of the design phase of new structures and their elements. One of the important issues is the choice of research model, feasible calculation scheme and possibility of its simplification.
This research investigates orthotropic non-thin cylindrical shells with corrugated ellipses as cross sections, which has the two-parameter deviation of the cross-section shape from a circular one. Considered are shells, for which the cross-section curvature radius of the reference surface has the positive sign. The shells are subjected to internal pressure under conditions of simple support on the ends.The subject of the study is the stress state of shells and, as a consequence, the establishment of the relationship between the geometric parameters of the reference surface of the cross sections and the possibility of simplifying the calculation scheme (excluding from consideration the parameter characterizing ellipticity).The problem is solved using the spatial model of linear elasticity theory based on the method of approximation of functions by discrete Fourier series.For the class of considered shells, we find the limits of possible simplification of the calculation scheme during calculations on durability with use of the fourth theory of durability (the theory of the greatest specific potential energy), due to exclusion from consideration of the parameter, which characterizes ellipticity of corrugated cylindrical shells.The cross-sectional radius of curvature of the reference surface in the zone of greatest rigidity was chosen as a criterion for the possibility of using a simplified scheme. It is found that a simplified scheme can be used when the cross-section curvature radius of the reference surface of elliptical corrugated cylindrical shells in this section differs from that for circular corrugated shells by no more than 17%.
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