Effective Model of Load-Bearing Layers for Layer-by-Layer Analysis of the Stress-Strain State of Three-Layer Cylindrical
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ctive Model of Load-Bearing Layers for Layer-by-Layer Analysis of the Stress-Strain State of Three-Layer Cylindrical Irregular Shells of Revolution V. N. Bakulin Institute of Applied Mechanics of the Russian Academy of Sciences, Moscow, 125040 Russia e-mail: [email protected] Received January 17, 2020; revised January 27, 2020; accepted January 28, 2020
Abstract—The use of effective approximations that increase the rate of convergence of numerical results when constructing a finite element model of bearing layers for a more accurate layer-by-layer analysis of the stress-strain state of three-layer irregular cylindrical shells is considered. It is believed that the carrier layers are sufficiently thin and rigid, and two-dimensional finite elements of natural curvature, constructed on the basis of the classical theory of moment shells, are used to simulate the stress-strain state. It is assumed that the aggregate layer can be modeled in thickness by the required number of three-dimensional finite elements, which allows one to take into account the change in geometric and physical-mechanical characteristics, as well as the parameters of the stress-strain state, not only along the meridional and circumferential coordinates, but also along the thickness of the shell and the aggregate layer. The finite element approximations considered allow one to reduce the order of systems of equations, i.e. to reduce the dimensionality of the problems being solved in comparison with the traditionally used approximations, which is especially important for layer-by-layer analysis of layered-heterogeneous structures. The high convergence rate of the numerical results obtained using the considered finite element model of the bearing layers is confirmed by a comparison with other known finite elements. Keywords: irregular three-layer shells of revolution, bearing layers, stress-strain state, layer-by-layer analysis, finite element approximations, finite element model DOI: 10.3103/S0025654420030048
1. INTRODUCTION To increase the specific rigidness of the structures of modern rocket and aviation equipment, the use of shells of a layered-heterogeneous structure, including three-layer cylindrical irregular shells of rotation, is growing [1–4]. Models for the analysis of the stress-strain state (SSS) of the structures of modern technology, characterized by many design features and complex types of loads, should allow the calculation to be performed with a high degree of accuracy and detail. From an analysis of works devoted to studies of the stress-strain state of layered-inhomogeneous shells, it follows that the problems for a limited range of types of loading and conditions for fixing the layers are mainly considered, and it should be noted that models are common that often do not satisfy the requirements for the degree of detail of SSS calculations bearing layers and filler layers and not allowing analysis with the necessary accuracy in the general case of irregular orthotropic layered shells, taking into account features such as the inhomoge
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