A Galerkin boundary element method for high frequency scattering by convex polygons

In this paper we consider the problem of time-harmonic acoustic scattering in two dimensions by convex polygons. Standard boundary or finite element methods for acoustic scattering problems have a computational cost that grows at least linearly as a function of the frequency of the incident wave. Here we present a novel Galerkin boundary element method, which uses an approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh, with smaller elements closer to the corners of the polygon. We prove that the best approximation from the approximation space requires a number of degrees of freedom to achieve a prescribed level of accuracy that grows only logarithmically as a function of the frequency. Numerical results demonstrate the same logarithmic dependence on the frequency for the Galerkin method solution. Our boundary element method is a discretization of a well-known second kind combined-layer-potential integral equation. We provide a proof that this equation and its adjoint are well-posed and equivalent to the boundary value problem in a Sobolev space setting for general Lipschitz domains.

A high frequency boundary element method for scattering by convex polygons with impedance boundary conditions

We consider scattering of a time harmonic incident plane wave by a convex polygon with piecewise constant impedance boundary conditions. Standard finite or boundary element methods require the number of degrees of freedom to grow at least linearly with respect to the frequency of the incident wave in order to maintain accuracy. Extending earlier work by Chandler-Wilde and Langdon for the sound soft problem, we propose a novel Galerkin boundary element method, with the approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh with smaller elements closer to the corners of the polygon. Theoretical analysis and numerical results suggest that the number of degrees of freedom required to achieve a prescribed level of accuracy grows only logarithmically with respect to the frequency of the incident wave.

Gradient recovery in adaptive finite-element methods for parabolic problems

We derive energy-norm a posteriori error bounds, using gradient recovery (ZZ) estimators to control the spatial error, for fully discrete schemes for the linear heat equation. This appears to be the �rst completely rigorous derivation of ZZ estimators for fully discrete schemes for evolution problems, without any restrictive assumption on the timestep size. An essential tool for the analysis is the elliptic reconstruction technique.Our theoretical results are backed with extensive numerical experimentation aimed at (a) testing the practical sharpness and asymptotic behaviour of the error estimator against the error, and (b) deriving an adaptive method based on our estimators. An extra novelty provided is an implementation of a coarsening error "preindicator", with a complete implementation guide in ALBERTA in the appendix.

NUMERICAL SIMULATION of THE BEHAVIOR of THE BEHAVIOR of REINFORCED CONCRETE BEAMS and COLUMNS BY FEM CAASTEM 2000 PROGRAM

The objective of this paper is the numerical study of the behavior of reinforced concrete beams and columns by non-linear numerical simulations. The numerical analysis is based on the finite element method implemented in CASTEM 2000. This program uses the constitutive elastoplastic perfect model for the steel, the Drucker-Prager model for the concrete and the Newton-Raphson for the solution of non-linear systems. This work concentrates on the determination of equilibrium curves to the beams and force-strain curves to the columns. The numeric responses are confronted with experimental results found in the literature in order to check there liability of the numerical analyses.

Influence of Crown Ferrule Heights and Dowel Material Selection on the Mechanical Behavior of Root-Filled Teeth: A Finite Element Analysis

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Methods Used for Assessing Stresses in Buccomaxillary Prostheses: Photoelasticity, Finite Element Technique, and Extensometry

The authors describe a literature revision on assessing stresses in buccomaxillary prostheses photoelasticity, finite element technique, and extensometry. They describe the techniques and the importance for use of each method in buccomaxillary prostheses with implants and the need of accomplishing more studies in this scarce literary area.

A finite element free convection model for the side wall heated cavity

This paper presents a finite element numerical solution of free convection in a cavity with side walls maintained at constant but different temperatures. The predictions from the model and the method of solution were validated by comparison with the 'bench mark' solution and Vahl Davis' results and good agreement was found. The present model was used to obtain additional results over a wide range of Rayleigh number (10(3)-10(6)) and L/H ratios varying from 0.1 to 1.0. The predicted stream function patterns, temperature and velocity profiles as well as the mean Nusselt number were presented and discussed. (C) 2000 Elsevier B.V. Ltd. All rights reserved.

A FEM approach to the equations of magneto-aerodynamics

In this work, a Finite Element Method treatment is outlined for the equations of Magnetoaerodynamics. In order to provide a good basis for numerical treatment of Magneto-aerodynamics, a full version of the complete equations is presented and FEM contribution matrices are deduced, as well as further terms of stabilization for the compressible flow case.

Finite element analysis of warpage in laminated aluminium alloy plates for machining of primary aeronautic parts

The aim of this paper consists in presenting a method of simulating the warpage in 7xxx series aluminium alloy plates. To perform this simulation finite element software MSC.Patran and MSC.Marc were used. Another result of this analysis will be the influence on material residual stresses induced on the raw material during the rolling process upon the warpage of primary aeronautic parts, fabricated through machining (milling) at Embraer. The method used to determinate the aluminium plate residual stress was Layer Removal Test. The numerical algorithm Modified Flavenot Method was used to convert layer removal and beam deflection in stress level. With such information about the level and profile of residual stresses become possible, during the step that anticipate the manufacturing to incorporate these values in the finite-element approach for modelling warpage parts. Based on that warpage parameter surely the products are manufactured with low relative vulnerability propitiating competitiveness and price. © 2007 American Institute of Physics.

Three-dimensional finite element analysis of stress distribution in retention screws of different crown-implant ratios

The retaining screw of the implant-supported dental prosthesis is the weakest point of the crown/implant system. Furthermore, crown height is another important factor that may increase the lever arm. Therefore, the aim of this study was to assess the stress distribution in implant prosthetic screws with different heights of the clinical crown of the prosthesis using the method of three-dimensional finite element analysis. Three models were created with implants (3.75 mm × 10 mm) and crowns (heights of 10, 12.5 and 15 mm). The results were visualised by means of von Mises stress maps that increased the crown heights. The screw structure exhibited higher levels of stresses in the oblique load. The oblique loading resulted in higher stress concentration when compared with the axial loading. It is concluded that the increase of the crown was damaging to the stress distribution on the screw, mainly in oblique loading. © 2013 Taylor & Francis.

Nonlinear formulation based on FEM, Mazars damage criterion and Fick's law applied to failure assessment of reinforced concrete structures subjected to chloride ingress and reinforcements corrosion

Structural durability is an important design criterion, which must be assessed for every type of structure. In this regard, especial attention must be addressed to the durability of reinforced concrete (RC) structures. When RC structures are located in aggressive environments, its durability is strongly reduced by physical/chemical/mechanical processes that trigger the corrosion of reinforcements. Among these processes, the diffusion of chlorides is recognized as one of major responsible of corrosion phenomenon start. To accurate modelling the corrosion of reinforcements and to assess the durability of RC structures, a mechanical model that accounts realistically for both concrete and steel mechanical behaviour must be considered. In this context, this study presents a numerical nonlinear formulation based on the finite element method applied to structural analysis of RC structures subjected to chloride penetration and reinforcements corrosion. The physical nonlinearity of concrete is described by Mazars damage model whereas for reinforcements elastoplastic criteria are adopted. The steel loss along time due to corrosion is modelled using an empirical approach presented in literature and the chloride concentration growth along structural cover is represented by Fick's law. The proposed model is applied to analysis of bended structures. The results obtained by the proposed numerical approach are compared to responses available in literature in order to illustrate the evolution of structural resistant load after corrosion start. (C) 2014 Elsevier Ltd. All rights reserved.

Finite element evaluation of three methods of stable fixation of condyle base fractures

The surgical treatment of mandibular condyle fractures currently offers several possibilities for stable internal fixation. In this study, a finite element model evaluation was performed of three different methods for osteosynthesis of low subcondylar fractures: (1) two four-hole straight plates, (2) one seven-hole lambda plate, and (3) one four-hole trapezoidal plate. The finite element model evaluation considered a load applied to the first molar on the contralateral side to the fracture. Results showed that, although the three methods are capable of withstanding functional loading, the lambda plate displayed a more homogeneous stress distribution for both osteosynthesis material and bone and may be a better method when single-plate fixation is the option.

Finite element analysis of bonded model Class I 'restorations' after shrinkage

Objectives. The C-Factor has been used widely to rationalize the changes in shrinkage stress occurring at the tooth/resin-composite interfaces. Experimentally, such stresses have been measured in a uniaxial direction between opposed parallel walls. The situation of adjoining cavity walls has been neglected. The aim was to investigate the hypothesis that: within stylized model rectangular cavities of constant volume and wall thickness, the interfacial shrinkage-stress at the adjoining cavity walls increases steadily as the C-Factor increases. Methods. Eight 3D-FEM restored Class I 'rectangular cavity' models were created by MSC.PATRAN/MSC.Marc, r2-2005 and subjected to 1% of shrinkage, while maintaining constant both the volume (20 mm(3)) and the wall thickness (2 mm), but varying the C-Factor (1.9-13.5). An adhesive contact between the composite and the teeth was incorporated. Polymerization shrinkage was simulated by analogy with thermal contraction. Principal stresses and strains were calculated. Peak values of maximum principal (MP) and maximum shear (MS) stresses from the different walls were displayed graphically as a function of C-Factor. The stress-peak association with C-Factor was evaluated by the Pearson correlation between the stress peak and the C-Factor. Results. The hypothesis was rejected: there was no clear increase of stress-peaks with C-Factor. The stress-peaks particularly expressed as MP and MS varied only slightly with increasing C-Factor. Lower stress-peaks were present at the pulpal floor in comparison to the stress at the axial walls. In general, MP and MS were similar when the axial wall dimensions were similar. The Pearson coefficient only expressed associations for the maximum principal stress at the ZX wall and the Z axis. Significance. Increase of the C-Factor did not lead to increase of the calculated stress-peaks in model rectangular Class I cavity walls. (C) 2011 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

Finite element models of coseismic deformation due to the 2009 L'Aquila (Italy) and 2008 Wenchuan(China) earthquakes

The topic of my Ph.D. thesis is the finite element modeling of coseismic deformation imaged by DInSAR and GPS data. I developed a method to calculate synthetic Green functions with finite element models (FEMs) and then use linear inversion methods to determine the slip distribution on the fault plane. The method is applied to the 2009 L’Aquila Earthquake (Italy) and to the 2008 Wenchuan earthquake (China). I focus on the influence of rheological features of the earth's crust by implementing seismic tomographic data and the influence of topography by implementing Digital Elevation Models (DEM) layers on the FEMs. Results for the L’Aquila earthquake highlight the non-negligible influence of the medium structure: homogeneous and heterogeneous models show discrepancies up to 20% in the fault slip distribution values. Furthermore, in the heterogeneous models a new area of slip appears above the hypocenter. Regarding the 2008 Wenchuan earthquake, the very steep topographic relief of Longmen Shan Range is implemented in my FE model. A large number of DEM layers corresponding to East China is used to achieve the complete coverage of the FE model. My objective was to explore the influence of the topography on the retrieved coseismic slip distribution. The inversion results reveals significant differences between the flat and topographic model. Thus, the flat models frequently adopted are inappropriate to represent the earth surface topographic features and especially in the case of the 2008 Wenchuan earthquake.

Mixed finite-element methods for elliptic convection-dominated problems arising in semiconductor physics

In this work we develop and analyze an adaptive numerical scheme for simulating a class of macroscopic semiconductor models. At first the numerical modelling of semiconductors is reviewed in order to classify the Energy-Transport models for semiconductors that are later simulated in 2D. In this class of models the flow of charged particles, that are negatively charged electrons and so-called holes, which are quasi-particles of positive charge, as well as their energy distributions are described by a coupled system of nonlinear partial differential equations. A considerable difficulty in simulating these convection-dominated equations is posed by the nonlinear coupling as well as due to the fact that the local phenomena such as "hot electron effects" are only partially assessable through the given data. The primary variables that are used in the simulations are the particle density and the particle energy density. The user of these simulations is mostly interested in the current flow through parts of the domain boundary - the contacts. The numerical method considered here utilizes mixed finite-elements as trial functions for the discrete solution. The continuous discretization of the normal fluxes is the most important property of this discretization from the users perspective. It will be proven that under certain assumptions on the triangulation the particle density remains positive in the iterative solution algorithm. Connected to this result an a priori error estimate for the discrete solution of linear convection-diffusion equations is derived. The local charge transport phenomena will be resolved by an adaptive algorithm, which is based on a posteriori error estimators. At that stage a comparison of different estimations is performed. Additionally a method to effectively estimate the error in local quantities derived from the solution, so-called "functional outputs", is developed by transferring the dual weighted residual method to mixed finite elements. For a model problem we present how this method can deliver promising results even when standard error estimator fail completely to reduce the error in an iterative mesh refinement process.