Stress-strain state of thick-walled anisotropic cylindrical shells under thermal power load, protected by the functionally graded material

Mykola Semenyuk,Volodymyr Trach,Andrii Podvornyi

doi:10.32347/2410-2547.2020.105.165-178

Mykola Semenyuk, Volodymyr Trach + Show 1 more

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https://doi.org/10.32347/2410-2547.2020.105.165-178

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Abstract

In the article the stress-strain state of thick-walled structurally anisotropic composite cylindrical shells under thermal power load, which are protected by a functionally graded material, are analysed. Based on the interrelations of the spatial theory of elasticity, a system of inhomogeneous differential equations in three-dimensional formulation, which describes the stress-strain state of thick-walled anisotropic cylindrical shells, was obtained. To reduce the dimensionality of this system, the Bubnov-Galerkin analytical method was used. Thus, the obtained one-dimensional system of twelve equations of normal Cauchy form was implemented using the numerical method of discrete orthogonalization. To represent the possibilities of the proposed approach, there were used stress-strain states of two, four and five-layered anisotropic cylindrical shells of fibrous composites, protected from temperature by a layer of transversely isotropic functionally graded material.

Highlights

Thin-walled structures made of composite materials are widely used in a variety of elements of up-to-date equipment
Traditional composite materials are not always able to be used in high temperatures, because their load-bearing capacity can be significantly reduced
Recently, a new class of composite materials known as functionally graded materials (FGMs) has emerged [16]

Summary

Introduction

Thin-walled structures made of composite materials are widely used in a variety of elements of up-to-date equipment. Heat-resistant ceramics can be used to protect thin-walled composites from temperatures, but it is well known that this material has brittle properties and does not bend and twist. A sufficiently detailed analysis of the stress-strain state of thinwalled and thick-walled cylindrical shells of both conventional composites and FGMs in the calculations of two-dimensional systems under the thermal power load [1, 3, 12, 15, 16, 17] is made. It is generally known that to calculate the stress-strain state of thick-walled cylindrical shells it should be applied an approach [2, 6, 7, 10, 11, 13], based on the use of equations of the spatial theory of elasticity and which allows you to correctly analyze changes of parameters such as stress-strain state of the construction by the thickness. The obtained solutions can serve as references in the calculations of stressstrain states of thinwalled structures of more complex geometry established, for example, when

Formulation of the problem

Research methodology

Results of the numerical calculations and their analysis

Findings

Conclusions