Question

#4. A simply supported rectangular plate is under the action of hydrostatic pressure expressed by p = poxa, where constant po represents the load intensity along the x = a edge. Determine, using Navier's approach and retaining the first term of the series solution, the equation for the resulting deflection shown below. Po 8 p , TX. ty mn

Answer 1

Navier solution for rectangular plate Subject to hydrostatic pressure. For any kind of loading the equation is given by Q = f (x, y) For this purpose we represent the function F (x, y) in the form of double trigonometric series F (x, y) = sigma_ m = 1^infinity sigma_ n = 1^infinity alpha_mn sin m pi x/a sin n pi y/b To calculate any particular coefficient alpha m^1 n^1 Multiply both equation by sin n^1 pi y/b. dy Integrated from O to b Integral_0^b sin n pi y/b sin n^1 pi y/b dy = 0 when n = n^1 Integral_0^b sin n pi y/b sin n^1 pi y/b dy = b/2 when n = n^1 We find in this way Integral_0^b f (x, y) sin n^1 pi y/b dy = b/2