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Vol.21, Special Issue, 2021, pp. S83–S88 |
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FROBENIUS SERIES SOLUTION FOR FUNCTIONALLY GRADED MATERIAL WITH EXPONENTIALLY VARIABLE THICKNESS AND MODULI M. Sahni1*, R. Sahni2, N. Patel3, M. Kumar4 1) Department of Mathematics, School of Technology, Pandit Deendayal Petroleum University, Gandhinagar, Gujarat, INDIA 2) Department of Physical Sciences, Institute of Advanced Research, Gandhinagar, Gujarat, INDIA 3) Department of Mathematics, Adani Institute of Infrastructure Engineering, Ahmedabad, Gujarat, INDIA 4) Department of Mathematics, Graphic Era (Deemed to be University), Dehradun, Uttarakhand, INDIA *email: manojsahani117@gmail.com
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Abstract In this paper, a Frobenius series solution is obtained for a functionally graded non-rotating cylinder following the exponential law variation in material properties across radii. The plane strain condition is considered in which the strain along the axial direction is taken as zero. The expressions are obtained for stresses - radial and circumferential. The strains are also obtained for functionally graded material considering the problem as axi-symmetric. The expressions for the homogeneous case are obtained by making the material index zero. Graphs are plotted for stresses, strains, and displacements for the homogeneous case and are numerically discussed. The results are obtained under internal pressure in which the external pressure is kept as zero. It is seen that the radial stress is compressive at the internal radii and moves towards zero at the outer radii. The circumferential stress is tensile and is maximum at the internal radii and minimum at the outer radii. Keywords: power series method, elastic moduli, thick-walled cylinder, internal pressure |
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