Browsing by Subject "Boundary element method"

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    Static and Dynamic Boundary Element Methods for Layered Pavement Systems
    (1997-12) Birgisson, B.; Crouch, S.L.; Newcomb, D.E.
    The main objective of this report is to present two numerical computer models that compute the static and the transient displacements and stresses in pavement systems consisting of one or more distinct layers of material. Both models are based on the boundary element method, which is described in detail in the attachment. The static model is capable of predicting the static solution, which is sometimes also the steady-state distribution of stresses and displacements anywhere within a layered pavement system. The dynamic model is capable of representing the propagation of displacement and stress waves across the interfaces separating the layers and includes the wave scattering effects of reflection and refraction from these interfaces. The transient displacements and stresses tend towards the static or steady-state solution as time tends to infinity, thus complimenting the solution obtained with the static boundary element method. Both of these methods are validated through a comparison with existing analytical and numerical solutions in the literature. Finally, both the static and dynamic computer models are applied to typical three layered rigid pavement configurations and loads to provide examples of the potential usefulness of these methods in developing appropriate guidelines for transient loading conditions.
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    Three-dimensional boundary element analysis of fractured rock
    (2016-03) Nikolskiy, Dmitry
    Understanding the mechanisms of rock fracture is of key importance to the mining and petroleum industries. Rock masses feature complicated geometry and structure including joints, heterogeneities of different scales (e.g. grains, pores, macroscopic inhomogeneities, etc.) and may be subject to various effects of injected fluid pressure, temperature gradient, etc. Therefore, comprehensive three-dimensional computational models that would allow to adequately treat complex behavior of a rock mass are required. Among the industrial applications of such models are the quantification of safety of underground workings and simulation of hydraulic fracturing. The dissertation presents a new Boundary Element Method-based technique for analysis of a three-dimensional elastic medium containing multiple cracks and/or openings of arbitrary shapes. The technique employs planar triangular elements to discretize the boundaries and quadratic polynomials to approximate the boundary unknowns, with two options of the arrangement of the nodal points on the elements. The novel features of the technique include the following: • the use of complex variable formalism involving various combinations of the geometrical parameters and the elastic fields, e.g. components of tractions and displacement discontinuities in the plane of the considered element; • analytical integration with the use of Cauchy-Pompeiu formula to reduce the surface integrals to the contour ones; • “limit after integration" approach, i.e. enforcing the boundary conditions after the discretization and analytical handling of the internal fields, by allowing the field point to reach the boundaries. The method can still capture the behavior of stress field near the crack fronts (tips) although no special approximating functions (tip asypmtotics) are used. The solutions of some benchmark problems are provided to demonstrate the capabilities of the proposed method.