Strain-stress state analysis of multilayer composite spherical shells based on the refined theory


DOI: 10.34759/trd-2020-114-07

Аuthors

Firsanov V. V.1*, Pham V. T.1**, Tran N. D.2***

1. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia
2. Le Quy Don Technical University, 236, Hoang Quoc Viet, Ha Noi, Viet Nam

*e-mail: k906@mai.ru
**e-mail: pvthien88@gmail.com
***e-mail: ngocdoanmai@gmail.com

Abstract

Nowadays, due to such advantages as high strength and low density, multilayer composite shells are widely used in various fields of mechanical engineering, including aerospace engineering. Theoretical and experimental studies have shown that when determining the stress condition of plates and shells, especially in the areas of joints (flanged, welded), local and rapidly changing load, as well as those made of non-homogeneous materials, the classical theory is not in line with the practice.

For multilayer composite shells, reliable determination of normal and shear stresses corresponding to lateral deformations represents an urgent issue. This article presents an option of the refined theory of the strain-stress state calculation of spherical shells made of layered composite materials. When creating mathematical model of the shell, the three-dimensional equations of linear elasticity are used. Components of the required displacements are being approximated by polynomials at a coordinate normal to the middle surface of the shell by the two degrees higher than the classical Kirchhoff–Love theory. A system of differential equations of equilibrium and corresponding boundary conditions have been obtained using the Lagrange variation principle. The formulated boundary value problem is being solved by successive application of finite difference and matrix sweep methods. The calculations were performed using a computer program.

A multilayer composite shell, rigidly pinched at two edges was considered as calculation example. The numerical results of the calculation of dimensionless shells deflection under the action of symmetric and asymmetric loads are practically identical to the published results of researchers, employing the other methods, which confirms the validity of the proposed refined theory.

The thickness impact on the stress condition of the shell is being studied. The article presents the graphs of the continuous stress distribution over the thickness of the shell are presented, which is of great importance for the composite materials. It has been established that lateral, normal and tangential stresses of significant value occurred in the edge zone of the multilayer shells. The authors recommend employing the proposed refined theory for their determining.

Keywords:

spherical shell, layered composite material, variant of the refined theory, Lagrange variation principle, finite difference method, matrix sweep method, shell deflection, lateral normal stresses

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