Vol. 14, No. 4, 2019

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Plane strain polar elasticity of fibre-reinforced functionally graded materials and structures

Konstantinos P. Soldatos, Metin Aydogdu and Ufuk Gul

Vol. 14 (2019), No. 4, 497–535
Abstract

This study investigates the flexural response of a linearly elastic rectangular strip reinforced in a functionally graded manner by a single family of straight fibres resistant in bending. Fibre bending resistance is associated with the thickness of fibres which, in turn, is considered measurable through use of some intrinsic material length parameter involved in the definition of a corresponding elastic modulus. Solution of the relevant set of governing differential equations is achieved computationally, with the use of a well-established semianalytical mathematical method. A connection of this solution with its homogeneous fibre-reinforced material counterpart enables the corresponding homogeneous fibrous composite to be regarded as a source of a set of equivalent functionally graded structures, each one of which is formed through inhomogeneous redistribution of the same volume of fibres within the same matrix material. A subsequent stress and couple-stress analysis provides details of the manner in which the flexural response of the polar structural component of interest is affected by certain types of inhomogeneous fibre distribution.

Keywords
cylindrical bending, elastic beams, elastic plates, fibre bending stiffness, fibre-reinforced structures, functionally graded structures, plane strain elasticity, polar elasticity
Milestones
Received: 20 February 2019
Revised: 11 September 2019
Accepted: 30 September 2019
Published: 13 December 2019
Authors
Konstantinos P. Soldatos
University of Nottingham
School of Mathematical Sciences
University Park
Nottingham
NG7 2RD
United Kingdom
Metin Aydogdu
Mechanical Engineering
Trakya University
22030 Edirne
Turkey
Ufuk Gul
Mechanical Engineering
Trakya University
22030 Edirne
Turkey