DETERMINATION OF STRESSES CAUSED BY INFINITELY LONG LINE LOADS ON SEMI-INFINITE ELASTIC SOILS USING FOURIER TRANSFORM METHOD
DOI:
https://doi.org/10.4314/njt.354.1164Keywords:
Fourier transform method, Airy’s stress function, plane strain elasticity, line load, biharmonic problemsAbstract
In this work, the Fourier transform method has been applied to the determination of stresses induced by infinitely long line loads on semi-infinite homogeneous elastic soils. Airy’s stress functions of the Cartesian coordinates system were used to express the governing equations of plane strain elasticity for a semi-infinite homogeneous soil as a biharmonic problem. The fourth order partial differential equation was then solved by an exponential Fourier transform technique, with respect to the space valuable x where -¥£x£¥; and the resulting solutions made subject to the stress – boundary conditions. The stresses obtained were found to be exactly identical with solutions obtained by integrating Boussinesq’s solutions for a point load which are available in the technical literature. The stresses determined in the present study were also exactly identical with the Flamant’s solution for the same problem; obtained by assuming a stress function in terms of the cylindrical coordinates.
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