Let a simply supported rectangular plate be subjected to load p(x, y)given in the form of...

Let a simply supported rectangular plate be subjected to load p(x, y)given in the form of a double trigonometric series

Let the displacement w(x, y)be represented in terms of a double trigonometric series

This double-series method was used by Navier (the Navier method; see Timoshenko and Woinowsky-Krieger, 1959) in a lecture presented to the French Academy in 1820.

a. Show that

---

b. For the case p (x, y)= p0, show by the method of Fourier series that

---

c. and hence that

---

d. and that the maximum deflection is given by