On Analysis of Stress Concentration in Curvilinear Anisotropic Deformable Continuum Bodies

Subject Areas : Mechanical Engineering

Theddeus T Akano ¹ , Omotayo A Fakinlede ² , Patrick Shola Olayiwola ³

1 - Department of Systems Engineering, University of Lagos, Akoka, Lagos, Nigeria
2 - Department of Systems Engineering, University of Lagos, Akoka, Lagos, Nigeria
3 - Department of Mechanical and Biomedical Engineering, Bells University of Technology Ota, Ogun, Nigeria

Received: 2020-03-09 Accepted : 2020-05-09 Published : 2020-06-30

Keywords: Polar-orthotropy, Differential transform, Radial stress, Hoop stress, Curvilinear anisotropy,

Abstract :

In cylindrical continua, hoop stresses are induced due to the circumferential failure. This mainly happens when the cylinder is subjected to mechanical loads which vary in the circumferential directions. On the other hand, radial stress is stress in the direction of or opposite to the central axis of a cylindrical body. In the present study, the influence of curvilinear anisotropy on the radial and tangential stresses of the polar-orthotropic hollow cylinder is presented. The governing equations were derived to evaluate the radial and hoop stresses inside the material. A semi-analytical method through differential transform method (DTM) for the polar-orthotropic hollow cylinder is implemented in the solution. The findings, based on polar-orthotropy, of the effect of the radial and circumferential loads on the radial and hoop stresses of the growing cylinders, show elastic responses that assist in identifying some of the outstanding properties of the curvilinear anisotropic continuums. It is also revealed that the characteristic response of various wall thicknesses of the cylindrical segment is influenced by the fibre orientation, radial and tangential stresses. This work has shown that the curvilinear anisotropy momentously affects the radial and hoop stresses on the polar-orthotropic hollow cylinder.

References:

[1] Newnham R.E., 2005, Properties of Materials : Anisotropy, Symmetry, Structure, Oxford University Press.
[2] Humphrey J.D., 2003, Continuum biomechanics of soft biological tissues, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 459(2029): 3-46.
[3] Wang L., Song J., Ortiz C., Boyce M.C., 2009, Anisotropic design of a multilayered biological exoskeleton, Journal of Materials Research 24(12): 3477-3494.
[4] Tarn J.-Q., 2001, Exact solutions for functionally graded anisotropic cylinders subjected to thermal and mechanical loads, International Journal of Solids and Structures 38(46–47): 8189-8206.
[5] Gal D., Dvorkin J., 1995, Stresses in anisotropic cylinders, Mechanics Research Communications 2(2):109-113.
[6] Horgan C.O., Baxter S.C., 1996, Effects of curvilinear anisotropy on radially symmetric stresses in anisotropic linearly elastic solids, Journal of Elasticity 42(1): 31-48.
[7] Zhou J.K., 1986, Differential Transformation and its Applications for Electrical Circuits, Huazhong University Press, Wuhan, China.
[8] Ayaz F., 2004, Solutions of the system of differential equations by differential transform method, Applied Mathematics and Computation 147(2): 547-567.
[9] Arikoglu A., Ozkol I., 2006, Solution of differential-difference equations by using differential transform method, Applied Mathematics and Computation 181(1): 153-162.
[10] Liu H., Song Y., 2007, Differential transform method applied to high index differential–algebraic equations, Applied Mathematics and Computation 184(2): 748-753.
[11] Rashidifar M.A., Rashidifar A.A., 2013, Analysis of vibration of a pipeline supported on elastic soil using differential transform method, American Journal of Mechanical Engineering 1(4): 96-102.
[12] Mohamed M.A., 2010, Comparison differential transformation technique with adomian decomposition method for dispersive long-wave equations in (2+ 1)-dimensions, Applications and Applied Mathematics 5(1): 148-166.
[13] Jena S.K., Chakraverty S., 2019, Differential quadrature and differential transformation methods in buckling analysis of nanobeams, Curved and Layered Structures 6(1): 68-76.
[14] Shali S., Nagaraja S.R., Jafarali P., 2017,Vibration of non-uniform rod using Differential Transform Method, IOP Conference Series: Materials Science and Engineering 225(1): 12027.
[15] Kumar M., Reddy G.J., Kumar N.N., Bég O.A., 2019, Application of differential transform method to unsteady free convective heat transfer of a couple stress fluid over a stretching sheet, Heat Transfer Research 48(2): 582-600.
[16] Biazar J., Eslami M., 2011, Differential transform method for nonlinear fractional gas dynamics equation, International Journal of Physical Sciences 6(5): 1203-1206.
[17] Shit G.C., Mukherjee S., 2019, Differential transform method for unsteady magnetohydrodynamic nanofluid flow in the presence of thermal radiation, Journal of Nanofluids 8(5): 998-1009.
[18] Tari A., 2012, The differential transform method for solving the model describing biological species living together, Iranian Journal of Mathematical Sciences and Informatics 7(2): 63-74.
[19] Gökdoğan A., Merdan M., Yildirim A., 2012, The modified algorithm for the differential transform method to solution of Genesio systems, Communications in Nonlinear Science and Numerical Simulation 17(1): 45-51.
[20] Benhammouda B., Vazquez-Leal H., Hernandez-Martinez L., 2014, Modified differential transform method for solving the model of pollution for a system of lakes, Discrete Dynamics in Nature and Society 2014: 645726.
[21] Vasilenko A.T., Sudavtsova G.K., 2001, Elastic equilibrium of circumferentially inhomogeneous orthotropic cylindrical shells of arbitrary thickness, International Applied Mechanics 37(8): 1046-1054.