Journal
INTERNATIONAL JOURNAL OF PRESSURE VESSELS AND PIPING
Volume 192, Issue -, Pages -Publisher
ELSEVIER SCI LTD
DOI: 10.1016/j.ijpvp.2021.104402
Keywords
Elasticity; Analytical modelling; Functionally graded circular annulus
Ask authors/readers for more resources
This study proposes a semi-analytical technique for solving mixed boundary value problems in functionally graded circular annulus, utilizing two main steps to compute stress and displacement fields.
The present work proposes a semi-analytical technique for solution of mixed boundary value problem in functionally graded circular annulus wherein shear modulus varies radially in power-law form while Poisson's ratio is constant. The technique relies on two main steps. In the first step, corresponding to terms in periodic Fourier series applied individually as traction along the annulus surface, stress and displacement field in the annulus is computed harnessing Airy stress functions approach. In the second step, leveraging the strain-displacement relations in polar co-ordinates, mixed boundary conditions are rendered in terms of displacement all along the annulus surface. Assuming the unknown traction along the annulus surface in terms of periodic Fourier series with finite terms, the modified displacement boundary condition, family of solution from the first step and orthogonality of sine and cosine functions is used to generate a system of simultaneous linear equations for the series coefficients. Knowing the coefficients of periodic Fourier series, stress and displacement field can be computed everywhere in the annulus. The first step is digitized in terms of MAPLE functions, exhaustively validated through traction distribution comprising of normal, shear traction on part of the boundary and pair of equal and diametrically opposite point load along the boundary. The second step is corroborated through a problem where the inner surface is subjected to a specified traction distribution and mixed boundary conditions exist along the outer surface in the form of complete constraint along a part and traction-free condition elsewhere.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available