  Fourier series multiscale method, a concise and efficient analytical approach
for multiscale computation, will be developed out of this series of papers. In
the fifth paper, the usual structural analysis of plates on an elastic
foundation is extended to a thorough multiscale analysis for a system of a
fourth order linear differential equation (for transverse displacement of the
plate) and a second order linear differential equation (for the stress
function), where general boundary conditions and a wide spectrum of model
parameters are prescribed. For this purpose, the solution function each is
expressed as a linear combination of the corner function, the two boundary
functions and the internal function, to ensure the series expression obtained
uniformly convergent and termwise differentiable up to fourth (or second)
order. Meanwhile, the sum of the corner function and the internal function
corresponds to the particular solution, and the two boundary functions
correspond to the general solutions which satisfy the homogeneous form of the
equation. With the corner function, the two boundary functions and the internal
function selected specifically as polynomials, one-dimensional half-range
Fourier series along the y (or x)-direction, and two-dimensional half-range
Fourier series, the Fourier series multiscale solution of the bending problem
of a Reissner plate on the Pasternak foundation is derived. And then the
convergence characteristics of the Fourier series multiscale solution are
investigated with numerical examples, and the multiscale characteristics of the
bending problem of a Reissner plate on the Pasternak foundation are
demonstrated for a wide spectrum of model parameters.
