A model of load-bearing layers and an approach for modeling the core of sandwich shells


Аuthors

Bakulin V. N.

Institute of Applied Mechanics of Russian Academy of Science, IAM RAS, 32a, Leninskii av., Moscow, В-334, GSP-1, 119991, Russia

e-mail: vbak@yandex.ru

Abstract

The article notes that due to their high flexural stiffness, weight efficiency, thermal protection, sound insulation, vibration absorption, and many other important characteristics, the use of sandwich shells in aviation, aerospace, and other modern technologies is highly relevant. 
Given the significant potential and promising applications of sandwich shells in modern engineering, theories and computational models for analyzing the stress-strain state of three-layer shells are being developed.
This article provides an overview of the theories and discusses the specifics of calculating the stress-strain state of three-layer shells. The main difference between models for studying sandwich structural elements and those for homogeneous elements lies in the aim to account as accurately as possible for the actual distribution of displacements and stresses across the thickness of the shell. In a precise formulation, the core must be treated as a three-dimensional body. However, solving the equations of three-dimensional elasticity theory presents significant mathematical challenges. This has led to the emergence and development of approximate models for calculating sandwich shells and plates, in which certain simplifications regarding the behavior of the core are applied. This article examines the historical development of theories and various assumptions used in calculating the stress-strain state in the core layer and the load-bearing layers of three-layer shells.
It has been noted that, despite its relevance, the problem of investigating the stress-strain state of irregular three-layer shells in general, including shells of double curvature, especially those with rectangular through  and non-through cutouts, has not been sufficiently studied due to the mathematical difficulties involved in solving such problems. This led to the need, in accordance with the approach proposed and developed by the author of this article, to employ the finite element method for constructing models for layer-by-layer analysis. 
An algorithm is presented for constructing a finite element model of moment-bearing layers in three-layer irregular shells of double curvature.
The results obtained using the constructed model of load-bearing layers were compared with known analytical and numerical solutions.
This paper briefly outlines an approach to constructing a finite-element model of the core layer and a model for the layer-by-layer analysis of the stress-strain state in the general case of irregular three-layer shells of double curvature, which allow for the important features of sandwich shells noted above and, based on these models, provide solutions to problems involving the stress-strain state of sandwich shells weakened by rectangular through-holes and non-through-holes in the in-plane direction.

Keywords:

sandwich doubly curved shell of revolution; core layer; skin-layers; stress and strain state; finite element model.

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