Civil Engineering and Architecture Vol. 9(3), pp. 559 - 583
DOI: 10.13189/cea.2021.090301
Reprint (PDF) (819Kb)

Trefftz Displacement Potential Function Method for Solving Elastic Half-Space Problems

Charles Chinwuba Ike ^1,*, Benjamin Okwudili Mama ², Hyginus Nwankwo Onah ², Clifford Ugochukwu Nwoji ^2
1 Department of Civil Engineering, Enugu State University of Science and Technology, Enugu State, Nigeria
² Department of Civil Engineering, University of Nigeria, Nsukka, Enugu State, Nigeria

ABSTRACT

The elastic half-space problem has been solved previously using Boussinesq, Papkovich, Love, and Green and Zerna, potential function methods. In this work, the Trefftz displacement potential function method is used to obtain the stress and displacement fields in an elastic half-space subjected to boundary loads. Point load and various distributed loads are considered. The problem is presented using displacement formulation as Navier–Lamé equations. It is proved that the Trefftz functions are solutions of the Navier–Lamé displacement equations. Strain fields are derived in terms of the Trefftz function using the strain-displacement relations. The stress fields are similarly derived. The Trefftz function for the case of a point load acting at the origin of the elastic half-space is derived using the double exponential Fourier transformation technique. Stress equilibrium boundary conditions are used to fully determine the Trefftz function. Stress and displacement fields for the point load are then determined. The solutions to stress and displacement fields for point load are then used as Green functions to obtain stress and displacement fields for uniformly distributed load over a finite line, circular area and rectangular area. It is found that the solutions obtained for the stress and displacement fields in the elastic half-space due to point and distributed loads are identical with previously obtained expressions, thus validating this work.

KEYWORDS
Trefftz Displacement Potential Function Method, Elastic Half-Space Problem, Stress Fields, Displacement Fields, Boussinesq Problem

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Charles Chinwuba Ike , Benjamin Okwudili Mama , Hyginus Nwankwo Onah , Clifford Ugochukwu Nwoji , "Trefftz Displacement Potential Function Method for Solving Elastic Half-Space Problems," Civil Engineering and Architecture, Vol. 9, No. 3, pp. 559 - 583, 2021. DOI: 10.13189/cea.2021.090301.

(b). APA Format:
Charles Chinwuba Ike , Benjamin Okwudili Mama , Hyginus Nwankwo Onah , Clifford Ugochukwu Nwoji (2021). Trefftz Displacement Potential Function Method for Solving Elastic Half-Space Problems. Civil Engineering and Architecture, 9(3), 559 - 583. DOI: 10.13189/cea.2021.090301.