In classical plate theory, for a circular plate with radius a and thickness A, the governing...

 

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In classical plate theory, for a circular plate with radius a and thickness A, the governing equation can be written as d 1 2² - (+) (+)- dra r dr (1) where w is the vertical deflection, P is the applied uniform pressure, and D is the flexural rigidity which is given by Eh³ 12 (1-1 In the above equation, E is the modulus of elasticity, and is the Poisson's ratio. D= -2²) 1. Find the general solution of the plate equation (Eq. (1)). 2. For a circular plate with clamped (fixed) edges, the boundary conditions are 1) at r = 0, 2) at r = a, 3) at r = a, 1) at r = 0, dw dr du dr W=0 2) at r = a, 3) at r = a, = 0 = <=0 Using these boundary conditions, find the vertical deflection expression. Then, for P = 500 kPa, E= 200 GPa, v=0.29, h = 10 mm, and a 250 mm plot the deflection of the circular plate. 3. For a circular plate with simply supported edges, the boundary conditions are dw dr w=0 -D (w"+w) = 0 <=0 (2) Using these boundary conditions, find the vertical deflection expression. Then, for P = 500 kPa, E= 200 GPa, v= 0.29, h = 10 mm, and a 250 mm plot the deflection of the circular plate. 0.1 (b) In classical plate theory, for a circular plate with radius a and thickness A, the governing equation can be written as d 1 2² - (+) (+)- dra r dr (1) where w is the vertical deflection, P is the applied uniform pressure, and D is the flexural rigidity which is given by Eh³ 12 (1-1 In the above equation, E is the modulus of elasticity, and is the Poisson's ratio. D= -2²) 1. Find the general solution of the plate equation (Eq. (1)). 2. For a circular plate with clamped (fixed) edges, the boundary conditions are 1) at r = 0, 2) at r = a, 3) at r = a, 1) at r = 0, dw dr du dr W=0 2) at r = a, 3) at r = a, = 0 = <=0 Using these boundary conditions, find the vertical deflection expression. Then, for P = 500 kPa, E= 200 GPa, v=0.29, h = 10 mm, and a 250 mm plot the deflection of the circular plate. 3. For a circular plate with simply supported edges, the boundary conditions are dw dr w=0 -D (w"+w) = 0 <=0 (2) Using these boundary conditions, find the vertical deflection expression. Then, for P = 500 kPa, E= 200 GPa, v= 0.29, h = 10 mm, and a 250 mm plot the deflection of the circular plate. 0.1 (b)