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Fourier series multiscale method, a concise and efficient analytical approachfor multiscale computation, will be developed out of this series of papers. Inthe fifth paper, the usual structural analysis of plates on an elasticfoundation is extended to a thorough multiscale analysis for a system of afourth order linear differential equation (for transverse displacement of theplate) and a second order linear differential equation (for the stressfunction), where general boundary conditions and a wide spectrum of modelparameters are prescribed. For this purpose, the solution function each isexpressed as a linear combination of the corner function, the two boundaryfunctions and the internal function, to ensure the series expression obtaineduniformly convergent and termwise differentiable up to fourth (or second)order. Meanwhile, the sum of the corner function and the internal functioncorresponds to the particular solution, and the two boundary functionscorrespond to the general solutions which satisfy the homogeneous form of theequation. With the corner function, the two boundary functions and the internalfunction selected specifically as polynomials, one-dimensional half-rangeFourier series along the y (or x)-direction, and two-dimensional half-rangeFourier series, the Fourier series multiscale solution of the bending problemof a Reissner plate on the Pasternak foundation is derived. And then theconvergence characteristics of the Fourier series multiscale solution areinvestigated with numerical examples, and the multiscale characteristics of thebending problem of a Reissner plate on the Pasternak foundation aredemonstrated for a wide spectrum of model parameters.

Fourier series (based) multiscale method for computational analysis in  science and engineering: V. Fourier series multiscale solution for elastic  bending of Reissner plates on Pasternak foundations