3D mixed boundary elements for elastostatic deformation field analysis
Résumé
A 3D Boundary Elements Method (BEM) combining the Direct and Displacement Discontinuity (DD) methods is developed for the analysis of elastic deformation fields. It can incorporate realistic surface topographies, pressurized reservoirs of any shape, tensile cracks and shear fractures. For accurate representation of geometries, boundaries are discretized with triangular elements. The Direct method, based on Betti's reciprocal theorem and the solution of Kelvin's problem, is the only BEM for which stresses do not become infinite at corners and edges. Therefore, linear planar elements with nodes at the apex shared between adjoining elements have been used for accurate and fast modeling of surface topographies and reservoirs. The DD method, based on the analytical solution to the problem of a single DD, is suitable for modeling fractures. With this method, use of constant planar elements is numerically less costly. A modified row-sum elimination method has been developed to permit discretization of surface topographies with linear elements using the Direct method. The Mixed BEM, herein proposed, is tested on a horizontal pressurized fracture of circular shape embedded in an elastic half-space. This example demonstrates the importance of a proper discretization for improving solution time and accuracy. Finally, intersection between elements of different types is discussed.
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