final_quiz

# final_quiz - 2.081J/16.230J Plates and Shells Quiz Monday,...

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2.081J/16.230J Plates and Shells Quiz Monday, March 24 Problem 1 [Must be completed in the class.] A simply supported square elastic plate ( a × a ) is loaded by a transervese load q ( x, y ) . The origin of the coordinate system is at the center of the plate. The shape of the de ected plate was precisely measured and then ted by the following function: w x, y ¯)= w 0 ¡ 1 x ¯ 2 ¢¡ 1 y ¯ 2 ¢ where x y x ¯ = ; y ¯ = a/ 2 a/ 2 and w 0 is the central de ectioin of the plate w 0 = w (0 , 0) . a 0 1 x 1 0 x a 1 1 y y (a) Check if the kinematic boundary conditions are satis ed. (b) Calculate the components of the bending moment tensor M αβ and e f ec- tive shear force vector V α . (c) Check if the static boundary conditions are satis ed (both moments and e f ective shears). 1

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(d) Determine the magnitude and the distribution of the transverse loading q x, y ¯) that equilibrates the plate. (e)
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## This note was uploaded on 02/03/2012 for the course AERO 2.081J taught by Professor Tomaszwierzbicki during the Spring '07 term at MIT.

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final_quiz - 2.081J/16.230J Plates and Shells Quiz Monday,...

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