The Effect of Uniform Magnetic Field on Pressurized FG Cylindirical and Spherical Vessels

Abstract

The stress analysis of functionally graded thick hollow cylindrical and spherical pressure vessels under the effect of uniform magnetic field are examined. These pressure vessels are designed in such a way that the material properties and magnetic permeability are exponentially graded in radial direction, provided that the inner surface is pure metal and the outer surface is pure ceramic. The differential equations with variable coefficients obtained under these conditions are handled by both Complementary Functions Method and Pseudospectral Chebyshev Method. Benchmark solutions available in the literature for some special cases are used to confirm the results. The effects of different mixture and uniform magnetic field on stresses and displacement distribution are shown in graphical form.

Static Analysis of FG Beams via Complementary Functions Method

“…They built a FORTRAN code to predict the static response. The CFM is successfully applied previously in structural mechanics problems by [14][15][16][17][18][19][20] The main aim of this study is to suggest an accurate and effective numerical approach for the bending analysis of FG straight beams. The mechanical properties of the material are assumed to vary continuously in the thickness direction of the beam according to a power law form.…”

Numerical Methods in Calculating Eigenvalues: Case Studies in Stability of Euler Columns

“…[18] Uses CFM to study the effect of the Poisson ratio on stresses of heterogeneous pressure vessels. [19] Applied CFM while studying the effect of uniform magnetic field on pressurized FG cylindrical and spherical vessels. In the present paper application area of CFM method is extended by using it first time for solving Buckling stability problem and also comparing with Shooting Method.…”

“…On following the above mentioned numerical scheme single variable algebraic equations are generated for all Columns cases. From equation (1) , equation (2) & equation (18-20) ={1 0 1, 0 1 0, a 1 (1) a 2 (1) 1 } , = { c 1 , c 2 , c 3 }From equation(1), equation(6)& equation(18)(19)(20)…”

“…From equation(1), equation(8) & equation(18)(19)(20) 0 1, 0 1 0, a 1 (1) a 2 (1) 1 } , ={ c 1 , c 2 , c 3 } , = {0,0, δ}4. NUMERICAL RESULTS & DISCUSSIONIn order to establish a neutral medium for comparison; Secant method is applied as a root finding algorithmwhile Runge-kutta of 4 th order is used as numerical integrator for both methods.…”

“…, c m } For a non-trivial solution C ≠ 0, hence Det|A( )|=0(21)CFM provides an algebraic equation containing only a single variable and direct application of secant method as root finding algorithm on equation (21) will generate eigenvalue. On following the above mentioned numerical scheme single variable algebraic equations are generated for all Columns cases.From equation (1) , equation (2) & equation(18)(19)(20) From equation (1), equation (4) & equation(18)(19)(20)…”