Application of the boundary-integral equation method to three dimensional stress analysis

The boundary-integral equation method is based on a mathematical formulation which reduces the dimensionality of a problem by relating surface tractions to surface displacements. Discretization of the surface allows a direct and standard algebraic solution for the unknown surface data. The stresses at any point are then found by direct quadrature from the entirety of surface data. Because of the reduction of the dimension of the problem, the size of the algebraic problem is considerably smaller than for finite element models. Also, since only the surface is discretized the analyst is able to achieve considerably greater resolution of interior stresses than by finite element models.The paper reports on two direct comparisons of the boundary-integral equation and finite element methods: two dimensional crack problems and a bulky three dimensional problem representative of mine structures. Discussion of the results will include accuracy, storage requirements and computer time comparisons. The paper also discusses the utility of the boundary-integral method to model three dimensional elastic bodies with through and part-through cracks.