Three dimensional elastostatics using the boundary element method

Nakagumba, Roberto Katumi (1979) Three dimensional elastostatics using the boundary element method. University of Southampton, Doctoral Thesis.

Abstract

This work uses the Kelvin, Mindlin and Boussinesq-Cerruti fundamental solutions within the framework of the Direct Boundary Element Method. The derivation of the boundary integral equations for finite bodies based on the Kelvin solution is reviewed and extended to incorporate the Mindlin and Boussinesq-Cerruti solutions and infinite regular regions. The method can be applied in general to solve three-dimensional linear elastic problems but it is particularly useful for structure-soil interaction analysis: the Kelvin solution is employed for finite regions (structure) and the Mindlin and Boussinesq-Cerruti for semi-infinite regions (soil). By doing so, the part of the ground surface which is free from traction does not necessarily need to be discretized.The integral equations are discretized by employing flat or curved triangles, and the displacements and tractions are assumed to have constant, linear or quadratic variations with respect to the homogeneous triangular coordinates. All surface integrals are carried out numerically by using the Hammer's method except those in the sense of Cauchy principal value which together with the coefficients of the free term are evaluated through rigid body considerations. The volume integrals are calculated numerically by dividing the domain into first order pentahedral or hexahedral cells. Since more integration points are needed near the singularity, elements and cells are subdivided into subelements and subcells. These subdivisions are implicitly performed by transforming the homogeneous coordinates associated with the subelements (subcells) into those associated with the element (cell).A program was developed for the constant flat triangular element; several examples involving finite bodies and foundations are presented.

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