Plates - Navier solution

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As mentioned, this method can be used on a plate with pinned edges. The boundary conditions can then be formulated as:

w = 0 and w,nn = 0 (or Mn = 0) on all edges.

The method consists of a Fourier serial development of an arbitrary load like this:


where the load factor pmn fo each m,n can be taken from tables or calculated by standard Fourier coefficient calculations, expressed as:


We can now express the displacement function as as a Fourier series:


where each load contribution


have its own displacement expressed as


Cmn is given by the equation


And the displacement then becomes


When the displacement w(x,y) is known, inner moment, shear forces and stresses can be calculated. This calculation method has quick convergence for load distributions that covers the entire plate. And the method is well suited for solution on computers.