SUMMARYThe field equations of three-dimensional elastostatics are transformed to boundary integral equations. The elastic body is divided into subregions, and the surface and interfaces are represented by quadrilateral and triangular elements with quadratic variation of geometry and linear, quadratic Oi cubic variation of displacement and traction with respect to intrinsic co-ordinates. The integral equation is discretized for each subregion, and a system of banded form obtained. For the integration of kernel-shape function products, Gaussian quadrature formulae are chosen according to upper bounds for error in terfns of derivatives of the integrands.

SUMMARYStraight and curved cracks are modelled by direct formulation boundary elements, of geometry defined by Hermitian cubic shape functions. Displacement and traction are interpolated by the Hermitian functions, supplemented by singular functions which multiply stress intensity factors corresponding to the dominant modes of crack opening in which displacement is proportional to the square root of distance I from the crack tip, and subdominant modes in which it is proportional to rl". The singular functions extend over many boundary elements on each crack face.A nodal collocation scheme is used, in which additional boundary integral equations are obtained by differentiation of the equation obtained from Betti's theorem. The hypersingular kernels of the equations so derived are integrated by consideration of trial displacement fields of subdomains lying to either side of the crack. Examples are shown of the analysis of buried and edge cracks, to demonstrate the effects of modelling subdominant modes and extending singular shape functions over many elements.KEY WORDS stress fracture boundary element

Special types of boundary elements are discussed which can be used for the modelling of surfaces which extend to infinity. The theoretical background and details of implementation are discussed. On test examples it is shown that the elements perform extremely well even for cases in which they are located close to the area of interest. A practical application of the use of the elements for the modelling of mining excavations is given.

The subject of this work is the development of a code to study the behaviour of stratified and jointed rock masses around underground excavations. The rock mass is divided into two types of regions, one which is supposed to exhibit linear elastic behaviour and which may extend to infinity, and the other which will include discontinuities that behave inelastically. The former has been simulated by a symmetric direct, boundary integral, plane strain, quadratic, orthotropic module, and the latter by quadratic plane strain, membrane and inelastic joint elements. The two modules are coupled in one program. Sequences of loading include static point, pressure, body and residual loads, construction and excavation sequences, and quasi-static earthquake load. The program is interactive, with graphics. A numerical example is presented to illustrate the method.

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