Question

# The deflection w of a clamped circular membrane of radius r d subjected to pressure Pis given by (small deformation theory)$w ( r ) = \frac { P r _ { d } ^ { 4 } } { 64 K } \left[ 1 - \left( \frac { r } { r _ { d } } \right) ^ { 2 } \right] ^ { 2 }$where r is the radial coordinate, and $K = \frac { E t ^ { 3 } } { 12 \left( 1 - v ^ { 2 } \right) }$ , where E, t, and u are the elastic modulus, thickness, and Poisson's ratio of the membrane, respectively. Consider a membrane with P = 15 psi, $r_d$ = 15 in., E = 18 x 10$^6$ psi, t = 0.08 in., and $v$ = 0.3 . Make a surface plot of the membrane.

Solution

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Make a surface plot of the given function.

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