Academic literature on the topic 'Boundary Element Method (BEM) program'

This thesis describes the development of a coupled finite element — boundary element program for a microcomputer. The steps outlined in the thesis include the adaptation of a mainframe—based boundary element code for use on a microcomputer, the Verification of this program with sample problems, the development of an algorithm for coupling the Finite Element Method to the Boundary Element Method, the implementation of the coupling algorithm with finite element and boundary element codes, including the development of a Constant Strain Triangular finite element, and the Verification of the coupled program with sample problems. Conclusions are drawn from the results presented, and suggestions are made for future research in this area.<br>Master of Science

This research investigates effects of tensile stresses in liquids. Areas of application include bearing lubrication and polymer processing, in which liquids may be subjected to hydrostatic tension or large shear stresses. A primary thrust of this research is the development of a criterion for liquid failure, or cavitation, based upon the general state of stress in the liquid. A variable pressure, rotating inner cylinder, Couette viscometer has been designed and used to test a hypothesized cavitation criterion. The criterion, that cavitation will occur when a principal normal stress in a liquid becomes more tensile than some critical stress, is supported by the results of experiments with the viscometer for a Newtonian liquid. Based upon experimental observation of cavitation, a model for cavitation inception from crevice stabilized gas nuclei, and gaseous, as opposed to vaporous, cavitation is hypothesized. The cavitation inception model is investigated through numerical simulation, primarily using the boundary element method. Only Newtonian liquids are modeled, and, for simulation purposes, the model is reduced to two dimensions and the limit of negligible inertia is considered. The model includes contact line dynamics. Mass transport of dissolved gas through the liquid and in or out of the gas nucleus is considered. The numerical simulations provide important information about the probable nature of cavitation nucleation sites as well as conditions for cavitation inception. The cavitation criterion predicts cavitation in simple shear, which has implications for rheological measurements. It can cause apparent shear thinning and thixotropy. Additionally, there is evidence suggesting a possible link between shear cavitation and extrusion defects such as sharkskin. A variable pressure capillary tube viscometer was designed and constructed to investigate a hypothesized relationship between shear cavitation and extrusion defects. Results indicate that despite the occasional coincidence of occurrence of cavitation and sharkskin defects, cavitation cannot explain the onset of extrusion defects. If nuclei are removed, then liquids can withstand a negative hydrostatic pressure. A falling body viscometer has been constructed and used to investigate the effect of negative pressures on viscosity. It is found that current pressure viscosity models can be accurately extrapolated to experimentally achievable negative pressures.

The numerical simulation of elastic wave propagation in unbounded media is a topical issue. This need arises in a variety of real life engineering problems, from the modelling of railway- or machinery-induced vibrations to the analysis of seismic wave propagation and soil-structure interaction problems. Due to the complexity of the involved geometries and materials behavior, modelling such situations requires sophisticated numerical methods. The Boundary Element method (BEM) is a very effective approach for dynamical problems in spatially-extended regions (idealized as unbounded), especially since the advent of fast BEMs such as the Fast Multipole Method (FMM) used in this work. The BEM is based on a boundary integral formulation which requires the discretization of the only domain boundary (i.e. a surface in 3-D) and accounts implicitly for the radiation conditions at infinity. As a main disadvantage, the BEM leads a priori to a fully-populated and (using the collocation approach) non-symmetrical coefficient matrix, which make the traditional implementation of this method prohibitive for large problems (say O(106) boundary DoFs). Applied to the BEM, the Multi-Level Fast Multipole Method (ML-FMM) strongly lowers the complexity in computational work and memory that hinder the classical formulation, making the ML-FMBEM very competitive in modelling elastic wave propagation. The elastodynamic version of the Fast Multipole BEM (FMBEM), in a form enabling piecewise-homogeneous media, has for instance been successfully used to solve seismic wave propagation problems in a previous work (thesis dissertation of S. Chaillat, ENPC, 2008). This thesis aims at extending the capabilities of the existing frequency-domain elastodynamic FMBEM in two directions. Firstly, the time-harmonic elastodynamic ML-FMBEM formulation has been extended to the case of weakly dissipative viscoelastic media. Secondly, the FMBEM and the Finite Element Method (FEM) have been coupled to take advantage of the versatility of the FEM to model complex geometries and non-linearities while the FM-BEM accounts for wave propagation in the surrounding unbounded medium. In this thesis, we consider two strategies for coupling the FMBEM and the FEM to solve three-dimensional time-harmonic wave propagation problems in unbounded domains. The main idea is to separate one or more bounded subdomains (modelled by the FEM) from the complementary semi-infinite viscoelastic propagation medium (modelled by the FMBEM) through a non-overlapping domain decomposition. Two coupling strategies have been implemented and their performances assessed and compared on several examples

This work is devoted to the numerical analysis of saturated porous media, taking into account the damage phenomenon on the solid skeleton. The porous media is taken into poroelastic framework, in full-saturated condition, based on the Biot\'s Theory. A scalar damage model is assumed for this analysis. An implicit Boundary Element Method (BEM) formulation, based on time-independent fundamental solutions, is developed and implemented to couple the fluid flow and the elasto-damage problems. The integration over boundary elements is evaluated by using a numerical Gauss procedure. A semi-analytical scheme for the case of triangular domain cells is followed to carry out the relevant domain integrals. The non-linear system is solved by a Newton-Raphson procedure. Numerical examples are presented, in order to validate the implemented formulation and to illustrate its efficiency.<br>Este trabalho trata da análise numérica de meios porosos saturados, considerando danificação na matriz sólida. O meio poroso é admitido em regime poroelástico, em condição saturada, com base na teoria de Biot. Um modelo de dano escalar é empregado nesta análise. Uma formulação implícita do Método dos Elementos de Contorno (MEC), baseada em soluções fundamentais independentes do tempo, é desenvolvida e implementada de forma a acoplar os problemas de difusão de fluido e de elasto-dano. A integração sobre os elementos de contorno é feita através da quadratura de Gauss. Um esquema semi-analítico é aplicado sobre células triangulares para avaliar as integrais de domínio do problema. A solução do sistema não linear é obtida através de um procedimento do tipo Newton-Raphson. Apresentam-se exemplos numéricos a fim de validar a formulação implementada e demonstrar sua eficiência.