A Two-dimensional Boundary Element Method for Calculating Elastic Gravitational Stresses in Slopes

An electromagnetism module is under development in the commercial software LS-DYNA in order to perform coupled mechanical/thermal/electromagnetic simulations. The main part of the module is a so-called eddy current solver. This module allows us to introduce source electrical currents into solid conductors, and to compute the associated magnetic fields, electric fields, induced currents, Lorentz forces, Joule heating and so forth. The Maxwell equations are solved using a Finite Element Method (FEM) for the solid conductors coupled with a Boundary Element Method (BEM) for the surrounding air (or insulators). Both the FEM and the BEM are based on discrete differential forms (Nedelec-like elements). The use of the BEM for the air allows to handle complex 3D geometries with multiply connected conductors, very small air gaps, and motion of the conductors, due, in particular, to the electromagnetic forces. The variable of the BEM is a so-called surface current allowing the connection of the model to external current sources by simple dirichlet constraints, as well as direct computations of the self and mutual inductances of the system. In order to handle the large and dense BEM matrices, a domain decomposition is performed and low rank approximations are done on the off-diagonal blocks of the resulting block matrices. The diagonal blocks are used as an efficient preconditioner when solving the BEM part of the system. The singularities arising in the computation of the self and neighbor matrix elements of the Galerkin BEM are taken into account using a method based on Duffy transforms. The BEM method will be presented as well as benchmarks and real life application examples.

Finite Element Method (FEM1) is pervasively used in most of 3D product design analysis, in which Computer Aided Design (CAD) models need to be converted in to mesh models first and then enriched with some material features and boundary conditions data, etc. The interaction between CAD models and FEM models is intensive. Boundary Element Method (BEM) has been expected to be advantageous in large-scale problems in recent years owing to its reduction of the dimensionality and its reduced complexity in mesh generation. However, the BEM application has so far been limited to relatively small problems due to the memory and computational complexity for matrix buildup are O(N2). The fast multipole BEM (FMBEM) combined with BEM and fast multipole method (FMM) can overcome the defect of the traditional BEM, and provides an effective method to solve the large-scale problem. Combining GPU parallel computing with FMBEM can further improve its efficiency significantly. Based on the three-dimensional elastic mechanics problems, the parallelisms of the multipole moment (ME), multipole moment to multipole moment (M2M) translation, multipole moment to local expansion (M2L) translation, local expansion to local expansion (L2L) translation and near-field direct calculation were analyzed respectively according to the characteristics of the FMM, and the parallel strategies under CUDA were presented in this paper. Three main major parts are included herein: (1) FMBEM theory in 3D elastostatics, (2) the parallel FMBEM algorithm using CUDA, and (3) comparison the GPU parallel FMBEM with BEM, FEM and FMBEM respectively by engineering examples. Numerical example results show the 3D elastostatics GPU FMBEM not only can speed up the boundary element calculation process, but also save memory which can be effective to solve the large-scale engineering problems.

This paper addresses the challenges and advances made in the hydrodynamic design and design evaluation of ducted propellers. The application of new ducted propeller analysis tools is shown for the practical case of the design of controllable pitch propellers for hopper dredgers. Results of model tests and sea trials are compared with results of a state-of-the-art boundary element method (BEM) code that is used for the simulation of the unsteady cavitating flow around ducted propellers. The results of the BEM simulations are compared to more time consuming and comprehensive URANS sliding interface calculation results in which the flow including the unsteady flow around the rotating propeller is modelled in the RANS domain. Comparisons are made of pressure distributions and pressure side cavitation margins that are important in the propeller blade design. The details of the flow into the duct are discussed as well as its implications on the propeller blade design. The employed BEM method is proposed as the best practical next step in ducted propeller design given its reasonable calculation times. Based on the obtained results a new research initiative has been started to obtain better sea trial data from ducted propellers to improve and validate the ducted BEM method as well as the SI URANS method.

It has long been accepted that cracking of hot-mix asphalt pavements is a major mode of premature failure. Many state agencies have verified that pavement cracking occurred not only in fatigue cracking, in which a crack initiates from the bottom of the asphalt layer, but also in other modes such as low-temperature cracking and the more recently identified top-down cracking. To improve current pavement designs and the cracking resistance of mixtures, it is necessary to understand the mechanisms associated with crack initiation and crack growth in hot-mix asphalt mixtures. However, the complexity of the problem and the lack of simple-to-use analysis tools have been obstacles to a better understanding of hot-mix asphalt fracture mechanics and the development of better hot-mix asphalt fracture models. Until today, the well-known finite element method has been the primary tool used for modeling cracks and their effects in mixtures and pavements. Unfortunately, it is both complex and numerically intensive for fracture mechanics applications. The displacement discontinuity boundary element method is presented, which is a numerical method that has been very successful in many other engineering fields, as a potential method for modeling cracking in hot-mix asphalt mixtures and pavements. A series of examples are provided to illustrate the effectiveness of the method in dealing with cracks, crack propagation, and visco-elasticity in hot-mix asphalt. It was concluded that the method was easy to use, resulted in accurate solutions, required minimal computation time, and significantly simplified the modeling of crack-related problems.

It has long been accepted that cracking of hot-mix asphalt (HMA) pavements is a major mode of premature failure. Many state departments of transportation have verified that pavement cracking occurred not only in fatigue cracking in which a crack initiates from the bottom of the asphalt layer but also in other modes such as low-temperature cracking and the more recently identified top-down cracking. Recent work at the University of Florida has led to the development of a crack growth law based on viscoelastic fracture mechanics that is capable of fully describing both initiation and propagation of cracks in asphalt mixtures. The model requires the determination of only four fundamental mixture parameters, which can be obtained from less than 1 h of testing using the Superpave® indirect tensile test (IDT). These parameters can account for microdamage, crack propagation, and healing for stated loading conditions, temperatures, and rest periods. The generalization of the HMA crack growth law needed for its successful implementation into a displacement discontinuity boundary element method is described. The resulting HMA boundary element approach is shown to predict the crack propagation of two coarse-graded mixtures under cyclic IDT loading conditions.

O presente trabalho considera o uso do Método dos Elementos de Contorno (MEC) na avaliação da carga de colapso de problemas em estado plano de deformação, usando o teorema estático da análise-limite. Essa análise envolve o modelo constitutivo rígido-plástico, onde uma formulação não-linear do MEC faz-se necessária. Análises não-lineares com o MEC normalmente requerem o uso de uma discretização auxiliar no domínio através de células internas. Para evitar essa discretização de domínio, o presente desenvolvimento baseia-se em uma nova formulação não-linear do MEC, recentemente desenvolvida por Noronha e Pereira, usando apenas discretização de contorno (interfaces entre subregiões da zona plastificada). Os resultados obtidos pela discretização com a nova formulação do MEC são comparados com os obtidos pelo MEC convencional e pelo Método dos Elementos Finitos (MEF). A comparação entre os diferentes resultados é feita com os valores da função de escoamento e com o valor obtido para a carga de ruptura.

In this article, a penny-shaped crack in the isotropic plane of three-dimensional transversely isotropic piezoelectric semiconductors is analyzed via the displacement discontinuity boundary element method. The general solutions are derived based on the generalized Almansi’s theorem and the operator theory. Green’s functions are derived using the Hankel transformation under uniformly distributed extended displacement discontinuities (including displacement discontinuities, potential discontinuity, and electron density discontinuity) on a penny-shaped crack in the isotropic plane of three-dimensional transversely isotropic piezoelectric semiconductors. Using the extended displacement discontinuity boundary element method, penny-shaped cracks in transversely isotropic plane of three-dimensional piezoelectric semiconductors are studied, and the stress, electric displacement, and electric current intensity factors under uniform mechanical-electric-current loads applied on the penny-shaped crack surface are calculated. The fracture behaviors of piezoelectric semiconductors are studied.

The boundary element method for elasticity problems with concentrated loads based on displacement singular elements

In the past several decades, many papers have been published on fluid–structure coupled calculations to analyse the hydro-elastic response of flexible (composite) propellers. The flow is usually modelled either by the Navier–Stokes equations or as a potential flow, by assuming an irrotational flow. Phenomena as separation of the flow, flow transition, boundary layer build-up and vorticity dynamics are not captured in a non-viscous potential flow. Nevertheless, potential flow based methods have been shown to be powerful methods to resolve the hydrodynamics of propellers. With the upcoming interest in flexible (composite) propellers, a valid question is what the consequences of the potential flow simplifications are with regard to the coupled fluid–structure analyses of these types of propellers. This question has been addressed in the following way: calculations and experiments were conducted for uniform flows only, with a propeller geometry that challenges the potential flow model due to its sensitivity to leading edge vortex separation. Calculations were performed on the undeformed propeller geometry with a Reynolds-averaged-Navier–Stokes (RANS) solver and a boundary element method (BEM). These calculations show some typical differences between the RANS and BEM results. The flexible propeller responses were predicted by coupled calculations between BEM and finite element method (FEM) and RANS and FEM. The applied methodologies are briefly described. Results obtained from both calculation methods have been compared to experimental results obtained from blade deformation measurements in a cavitation tunnel. The results show that, even for the extreme cases, promising results have been obtained with the BEM-FEM coupling. The BEM-FEM calculated responses are consistent with the RANS-FEM results.

In general, internal cells are required to solve elastoplastic problems using a conventional boundary element method (BEM). However, in this case, the merit of BEM, which is ease of data preparation, is lost. Triple-reciprocity BEM can be used to solve two-dimensional elastoplasticity problems with a small plastic deformation. It has been shown that three-dimensional elastoplastic problems can be solved, without the use of internal cells, by the triple-reciprocity BEM and initial strain method. In this study, an initial stress formulation is adopted and the initial stress distribution is interpolated using boundary integral equations. A new computer program was developed and applied to solving several problems.

روستای هاونان در 15کیلومتری جنوب غرب بیرجند و در دامنه شمالی رشته‌کوه باقران واقع شده و تاریخ اولین حرکت اصلی لغزش در منطقه در سال 1364 و تاریخ آخرین حرکت اصلی در سال 1385 است. در این مقاله پهنه‌بندی حساسیت به لغزش و تحلیل پارامترهای فیزیکی- هیدرولوژیکی و تکتونیکی به‌منظور شناسایی بیشتر وضعیت شکل‌گیری توده‌های لغزشی منطقه و تحلیل پایداری دامنه‌ها به کمک مدل فرآیندی SINMAP انجام‌شده است. این مدل نشان می‌دهد بخش اندکی از پهنه لغزشی هاونان در محدوده رطوبتی اشباع قرار می‌گیرد و کمتر از 30 درصد آن دارای حساسیت متوسط تا بالا به لغزش است؛ لذا بایستی در این محدوده به دنبال علل خارجی تأثیرگذار در پدیداری لغزش بود. محدوده هاونان متأثر از سه سری گسل اصلی با روندهای مختلف می‌باشد و در اثر تقاطع این سه سری گسل، واحدهای سنگی (اسپیلیت ها، پریدوتیت ها و گابروها) به‌صورت بلوک‌های گسلی کشیده درآمده و در اثر ادامه فرآیند برش، این بلوک‌ها متحمل تغییر شکل، جابجایی و چرخش شده‌اند. ترکیب سنگ‌شناسی (قرارگیری اسپیلیت بر روی سرپانتینیت) و وجود دو سری شکستگی به‌موازات گسل‌های هاونان و مزار مهم‌ترین عوامل ناپایداری هستند. علاوه بر این برخاستگی رشته‌کوه باقران باعث افزایش تدریجی نشیب دامنه و رخداد زمین‌لرزه‌ای ادواری نیز موجب تشدید لغزش می‌گردد.

A plasticity model with yield limit degradation is implemented in a boundary element program to study the fracture behavior of quasi-brittle materials. A special integration method is applied to deal with the singular integrations encountered in the volume integrals over internal cells. Strain-softening damage localizations are investigated. It is found that the damage tends to localize into a zone of one cell wide which leads to an incorrect result when different cell meshes are used in the analysis. Some sort of localization limiter has to be incorporated into the analysis in order to achieve meaningful results. INTRODUCTION In the simulation of fracture behavior of quasi-brittle materials such as concrete or ceramics, it is essential to take into account the evolution of a relative large fracture process zone forms in front of the crack tip. The process zone consists of hundreds of microcracks and its overall behavior can generally be simulated either by discrete-cracking models such as the fictitious crack model [4, 5] or smeared-cracking models such as strain-softening damage models [2, 3]. In this paper the fracture process zone is simulated by a plasticity model with yield limit degradation. When the stresses near the crack tip reach the yield surface, the yield surface will contract rather than expand. This results in a decrease in stresses during an increase in strains, i.e., a strain softening. The decrease in stresses simulates a material damage caused by mainly the formation of microcracks. Difficulty has been encountered in the finite element analysis involving strain-softening behavior. As different meshes are used in an analysis, Transactions on Modelling and Simulation vol 2, © 1993 WIT Press, www.witpress.com, ISSN 1743-355X 304 Boundary Elements different results are obtained. The results are not objective with respect to finite element meshes. Also, the energy dissipation of a structure at failure decreases with the refinement of the finite element mesh. It implies that the structure will fail at near zero energy dissipation when a very fine mesh is used. This is in contradiction with the reality. All these problems are considered due to damage localization [1,2,3]. In this paper, the plasticity model with yield limit degradation is incorporated into a boundary element program to study the damage localization problems. Many publications on the boundary element analysis of elastoplastic problems [7-14] have been seen since the first paper on the problem published in 1971 by Swedlow and Cruse [6]. However, the literature on the study of damage localization problems using boundary element approach is rarely seen. The initial stress boundary element method is applied to deal with the nonlinear damage problems, For localization problems, damage tends to localize into a small region of the body, and thus the internal cells required for integration purposes are needed only in a small region rather than the entire body. A special semi-analytical integration method for triangular cell is used to carry out the volume integration over the cell that contains a singular node. A rectangular panel with three different cell meshes are analyzed. It is shown that the results are not objective to the cell meshes even though all other conditions are kept the same. BOUNDARY ELEMENT FORMULATION FOR ELASTOPLASTIC ANALYSIS For elastoplastic problems based on small strain theory, the basic equations in incremental form are as follows: The governing equations are da^ + db* = 0 (1) with boundary conditions du;(x) = (x) x e I (2) cR (x) x e I I + T^T and total strain increment de^ = de^ 4de^= (du + dUjJ/2 (3) where de^ and de^ are elastic and plastic strain increments. T is the boundary of body 0 under consideration, da^ ,db; ,du;, dr; are the stress, body force (per unit volume), displacement, and traction increment respectively. du ± and df j are prescribed displacements and tractions on boundary I and r%. Transactions on Modelling and Simulation vol 2, © 1993 WIT Press, www.witpress.com, ISSN 1743-355X Boundary Elements 305 The yield criterion is F(a%,k)= f(a$ <Kk) = 0 (4) where F and f are yield functions, $ is a work hardening function, and k is the work hardening parameter. The constitutive equations are de'u) = d<^ do, = DV^U (5) where D^= &pvl(l-2v)] 6fo + M<Wji + W

An analytical method for solving gravity-induced stresses in slope

Revisit of the equivalence of the displacement discontinuity method and boundary element method for solving crack problems

Revisit of a degenerate scale: A semi-circular disc