Determination of Stresses Caused by Infinitely Long Line Loads on Semi-Infinite Elastic Soils Using Fourier Transform Method

Onah, HN; Osadebe, NN; Ike, Charles Chinwuba; Nwoji, CU

doi:10.4314/njt.v35i4.6

Cited by 3 publications

(8 citation statements)

References 4 publications

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“…Onah et al [12] applied the Fourier transform method to the determination of stresses induced by infinitely long line loads on semi-infinite, homogeneous elastic soil. Airy's stress potential functions of the Cartesian coordinates system were used to express the governing equations of plane strain elasticity for a semiinfinite homogeneous soil as a biharmonic problem; which was solved using exponential Fourier transform technique.…”

Section: Introduction / Axisymmetric Elasticity Problems Of Semi-infimentioning

confidence: 99%

General Solutions for Axisymmetric Elasticity Problems of Elastic Half Space using Hankel Transform Method

Ike¹

2018

IJET

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In this work, the Hankel transform method was used to obtain general solutions for stress and displacement fields in semi-infinite linear elastic, isotropic soil under axisymmetric load. Hankel transformation of the governing equations in a stress-based formulation was used to find the Love stress function. Hankel transforms were also applied to the stress and displacement fields to obtain general solutions for the stresses and displacements. The general solutions obtained were used to solve the particular axisymmetric elasticity problem of Boussinesq. The solutions obtained were exactly the same as the solutions obtained by Boussinesq who solved the problem using Boussinesq stress potential functions.

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Section: Introduction / Axisymmetric Elasticity Problems Of Semi-infimentioning

confidence: 99%

General Solutions for Axisymmetric Elasticity Problems of Elastic Half Space using Hankel Transform Method

Ike¹

2018

IJET

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“…Elasticity problems of semi-infinite soil media under boundary loads have been studied by Onah et al [9]; Ike et al [10]; Nwoji et al [11]; Ike et al [12]; Onah et al [13]; Nwoji et al [14] and Onah et al [15].…”

Section: Introductionmentioning

confidence: 99%

Hankel Tranform Method for Solving Axisymmetric Elasticity Problems of Circular Foundation on Semi-infinite Soils

Ike¹

2018

IJET

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The Hankel transform method was implemented in this paper to obtain general solutions for stress and displacement fields in homogeneous, isotropic linear elastic, semi-infinite soil subject to uniformly distributed axisymmetric load distribution over a circular area on the surface. The work adopted a stress based formulation. Hankel transformation of the biharmonic stress compatibility equation was done to obtain bounded stress functions for the elastic half space problem. Hankel transformations were also applied to the Love expression to obtain the stresses and displacements in Hankel transform space. Enforcement of boundary conditions yielded the unknown constants of the stress functions for the particular problem considered. Inversion of the Hankel transform expressions for the stresses and displacements yielded the general expressions for stresses and displacements for the semiinfinite linear elastic soil under uniformly distributed load over a circular area on the surface. The solutions obtained were identical with solutions in literature obtained using Boussinesq stress functions.

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“…The field equations for plane strain elasticity are: the strain displacement relations [11][12][13], the stress-strain equations, and the differential equations of equilibrium. The straindisplacement relations are given by:…”

Section: Field Equations Of 2d Elasticitymentioning

confidence: 99%

“…Otherwise, when the soil mass occupies a two dimensional region of space which is of semi-infinite extent, the problems become elastic half-plane problems [11][12][13]. Problems of the mathematical theory of elasticity are formulated using the differential equations of equilibrium, the generalised Hooke's stressstrain laws and the geometric (kinematic) relations together with the deformation and traction boundary conditions [5][6][7][8][9][10][11][12][13]. The governing equations for such problems are usually complicated when heterogeneity and anisotropy are considered.…”

Section: Introductionmentioning

confidence: 99%

“…Stress-based methods for formulation of elasticity problems entail the simultaneous formulation of the governing equations involving the differential equations of equilibrium, the stressstrain relations and the kinematic relations such that the stresses are the primary unknown variables. This achieves a reduction in the number of governing equations from fifteen to six for three dimensional problems [5][6][7][8][9][10][11][12][13]. Similarly, the displacement based method involve a reformulation of the governing equations to have the three displacement components as the primary unknowns.…”

Section: Introductionmentioning

confidence: 99%

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Fourier Integral Transformation Method for Solving Two Dimensional Elasticity Problems in Plane Strain Using Love Stress Functions

Ike¹

2021

MMEP

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The Fourier integral method was used in this work to determine the stress fields in a two dimensional (2D) elastic soil mass of semi-infinite extent subject to line and strip loads of uniform intensity acting on the boundary. The two dimensional plane strain problem was formulated using stress-based method. The Fourier integral was used to transform the biharmonic stress compatibility equation to a fourth order linear ordinary differential equation (ODE) in terms of the stress function. The ODE was solved subject to the boundedness condition to obtain the bounded stress function. Cartesian stress components were obtained using the Love stress functions. Application of the stress boundary conditions for the case of line load of uniform intensity and the cases of uniformly distributed load on a strip of finite width gave the respective unknown constants of the Love stress functions; and hence the complete determination of the Cartesian stress components for the two cases considered. Inversion of the Fourier integral expressions obtained for the normal and shear stresses in the Fourier parameter gave respective expressions for the normal and shear stress fields for line and finite strip loads of finite width in the physical domain variables. The results obtained agreed with the results from previous studies which used displacement based methods.

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Determination of Stresses Caused by Infinitely Long Line Loads on Semi-Infinite Elastic Soils Using Fourier Transform Method

Cited by 3 publications

References 4 publications

General Solutions for Axisymmetric Elasticity Problems of Elastic Half Space using Hankel Transform Method

General Solutions for Axisymmetric Elasticity Problems of Elastic Half Space using Hankel Transform Method

Hankel Tranform Method for Solving Axisymmetric Elasticity Problems of Circular Foundation on Semi-infinite Soils

Fourier Integral Transformation Method for Solving Two Dimensional Elasticity Problems in Plane Strain Using Love Stress Functions

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