Finite Element Methods

We develop space-time adaptive and high-order methods for valuing American options using a partial differential equation (PDE) approach. The linear complementarity problem arising due to the free boundary is handled by a penalty method. Both finite difference and finite element methods are considered for the space discretization of the PDE, while classical finite differences, such as Crank-Nicolson, are used for the time discretization. The high-order discretization in space is based on an optimal finite element collocation method, the main computational requirements of which are the solution of one tridiagonal linear system at each time step, while the resulting errors at the gridpoints and midpoints of the space partition are fourth-order. To control the space error, we use adaptive gridpoint distribution based on an error equidistribution principle. A time stepsize selector is used to further increase the efficiency of the methods. Numerical examples show that our methods converge fast and provide highly accurate options prices, Greeks, and early exercise boundaries.

The seismic retrofitting of unsymmetric plan reinforced concrete (r.c.) framed buildings can be carried out by the insertion of damped braces (DBs), which are made of steel braces connecting two consecutive storeys and incorporating energy dissipating devices. Yet most of the proposals to mitigate the seismic response of asymmetric framed buildings by DBs rest on the hypothesis of elastic (linear) structural behaviour. The aim of the present work is to evaluate the effectiveness and reliability of a Displacement-Based Design procedure of hysteretic damped braces (HYDBs) based on the nonlinear behaviour of the frame members. An expression of the biaxial viscous damping equivalent to the hysteretic energy dissipated by the damped braced frame is assumed under bidirectional seismic loads, where corrective factors are adopted as a function of design parameters of the HYDBs. Moreover, the extended N2 method considered by Eurocode 8, which combines the nonlinear static analysis along the ...

Simulation of metal forming processes using the Finite Element Method (FEM) is a well-established procedure, being nowadays possible to develop alternative approaches, such as inverse methodologies, in solving complex problems. This study investigated the effect of orientation and pre-tension on stresses distribution numerically by software ANSYS 19 using the finite element method. The pre-tension is 55% from total strained in each rolling direction. The results show that the orientation has a significant effect on stresses distribution and stress value before and after pre-tension 55%. Although there is a regular distribution of stresses in three direction, but there is significant difference in the values of stresses in each of (0, 45, 90) degrees. The highest value of the stress is in the 0̊ to rolling direction, while the least value of the stress recorded in 45̊ to rolling direction. The pre-tension has a greater impact on stresses distribution and stress value. Although, there...

This paper investigates the stress distribution around a circular hole in a finite isotropic plate. The main problem in this analysis is how to apply the boundary conditions at the cutout boundary, which is represented in the Polar coordinate and at the plate outer edges, which is represented in the Cartesian coordinate. To solve this problem, the stress components are calculated from the solution of the Biharmonic equation in the Polar coordinate. The boundary conditions at the cutout edge are applied to the stress components which are written in the Polar coordinate. In order to apply the boundary conditions at the plate edges, a boundary integral which is obtained from the principle of virtual work is used. By substituting the displacement field and the stress components into the integral, the unknown constants are calculated. The variation of circumferential stress around the cutout is obtained for different hole sizes and different uniform and non-uniform loading conditions.

W artykule przedstawiono główne zasady symulacji numerycznej nieliniowych drgań samowzbudnych obrabiarek przy toczeniu w układnie wielomodalnym o dwóch stopniach swobody. Uwzględniono zarówno wychodzenie narzędzia z materiału obrabianego, jak i przenikanie się powierzchni przyłoŜenia z powierzchnią skrawania. Opracowane wzory i algorytmy zaimplementowano w uniwersalnym i łatwym do rozbudowania o kolejne stopnie swobody programie komputerowym w środowisku LabVIEW. Dokładność uzyskiwanych symulacji zweryfikowano przez porównanie ich wyników z otrzymywanymi analitycznie bez nieliniowości.

Ce travail présente une nouvelle intégrale appelée Mθv, découplant les modes de ruptures au cours du processus de propagation de la fissure due à un chargement en fluage dans un matériau viscoélastique orthotrope. La base de calcul issue d'un processus thermodynamique, et d'une combinaison des champs virtuels et réels est présentée. La prise en compte de l'intégrale dans le code de calcul aux éléments finis Castem et son couplage avec un processus viscoélastique incrémental est développée. Grâce à l'éprouvette ENS, l'évolution numérique du taux de restitution d'énergie en mode I, mode

RESUME. Ce travail présente le développement d'une intégrale invariante permettant le découplage des modes de rupture dans un milieu viscoélastique et orthotrope. Il repose sur la base de l'intégrale M développée initialement par Chen pour des matériaux élastiques isotropes. Le découplage de mode est basé sur l'emploi de champs mécaniques virtuels empruntés aux développements analytiques des champs singuliers proposés par Shi qui permettent d'isoler les différents modes de rupture ne calculant que la part de taux de restitution d'énergie en mode d'ouverture et de cisaillement (le travail est limité, pour des raisons applicatives, à des problèmes plans). La généralisation à un milieu viscoélastique utilise les fondements thermodynamiques développés par Dubois et Petit qui ont permis de définir un taux de restitution d'énergie en prenant en compte un découplage total de l'énergie libre restituable et l'énergie dissipée due à la viscosité du matériau. Le calcul, intégré dans un code aux éléments finis, nécessite son couplage à une formulation incrémentale du comportement viscoélastique. Le travail proposé permet finalement d'étudier les phases d'amorçage et de propagation de fissure en prenant en compte la présence éventuelle d'une pression sur les lèvres de la fissure causée, par exemple, par un champ de contraintes thermiques ou hydriques induit par des phases de séchage et/ou d'humidification du bois. . The viscoelastic generalization uses a thermodynamic approach developed by Dubois and Petit by defining a energy release rate only taking into account a perfect uncoupling of free and viscous energies. This work is implemented in a finite element software and necessitates it integration with a viscoelastic incremental formulation. This work allows the study of the crack growth initiation and the crack propagation by taking into account crack lip pressure induced, for example, by thermical or hydric stress field during a dried or swelling process. MOTS-CLÉS : mécanique de la rupture, intégrales invariantes, viscoélasticité, orthotropie, éléments finis.

Mechanical loading causes material deformation, resulting in changes in mechanical properties due to microstructural alterations such as the multiplication of dislocations and evolution of grain morphology. Blast loading, a condition where materials deform at high strain rates, results in significant plastic deformation. This rapid deformation induces intense mechanical stresses, causing complex microstructural changes that influence the mechanical behavior and performance of the materials. Consequently, designing structures to withstand blast loading requires understanding the relationship between microstructure and property evolution. As the primary objective of this study, post-localized blast experiments have been conducted to elucidate the variability in microstructural response of Austenitic stainless steel (ASS) 316 L, characterized by its face-centered cubic crystal structure. Localized blast loads were applied to square test plates, 2 mm thick, with a circular exposed area of 106 mm in diameter. Quantitative mechanical property data from key zones within the deformed dome were determined through using a novel micro-tensile testing approach and nanoindentation tests. Electron backscatter diffraction (EBSD) in scanning electron microscopy (SEM) technique was employed to characterize the microstructural changes in the selected samples. The results revealed that blast loading induced complex mechanical and microstructural changes in ASS 316 L, including enhanced material strength, reduced ductility, and significant alterations in grain orientation and misorientation distributions. The materials underwent significant strain hardening due to the increased stress and deformation, resulting in a more resistant to plastic deformation and the greatest internal strain accumulations. Texture analysis underscored the influence of deformation geometry, with Goss and Copper emerging as predominant texture components.

A unit cell approach is adopted to numerically analyze the effect of plastic anisotropy on damage evolution in a microreinforced composite. The matrix material exhibit size effects and a visco-plastic anisotropic strain gradient plasticity model accounting for such size effects is adopted. A conventional cohesive law is extended such that both the average as well as the jump in plastic strain across the fiber-matrix interface are accounted for. Results are shown for both conventional isotropic and anisotropic materials as well as for higher order isotropic and anisotropic materials with and without debonding. Generally, the strain gradient enhanced material exhibits higher load carry capacity compared to the corresponding conventional material. A sudden stress drop occurs in the macroscopic stress-strain response curve due to fiber-matrix debonding and the results show that a change in yield stress, which is caused by plastic anisotropy, affects the overall composite failure strain.

Hydraulique des sols 20 3 Contraintes dans les sols 28 4 Tassement et consolidation des sols 45 5 Résistance au cisaillement des sols 56 6 Etude de la portance des fondations superficielles à partir d'essais de laboratoire 70 7 Poussée et butée des terres 81 Références bibliographiques Cours Mecanique des sol 2 Khaled MEFTAH Khaled MEFTAH CHAPITRE 1 LES SOLS : Structure -Identification et Classification 1-Eléments constitutifs d'un sol Un sol est un mélange : d'éléments solides : Provienant de la désagrégation mécanique et/ou chimique d'une roche mère. On distingue les minéraux non argileux (∅>2µm et ayant le même comportement que la roche mère : Sols pulvérulents), les minéraux argileux ( kaolinite, illite et montmorillonite) et le sols organiques (vases et tourbes) d'eau : Existe sous plusieurs formes (eau de constitution, interfeuillets, liée et libre). de gaz : Contenu dans les vides,c'est l'air pour un sol sec ou mélange d'air et de vapeur d'eau pour un sol humide. 2-Paramètres de définition des sols 2-1 Modèle élémentaire d'un sol Un sol étant composé de grains solides, d'eau et d'air , on peut rassembler chaque phase en un volume partiel unique de section unit. Les notations suivantes sont utilisées : Volumes Poids Va Air Wa=0 Vw Eau Ww Vs Grains solides Ws Cours Mecanique des sol 7 Khaled MEFTAH 3. Identification des sols Pour caractériser un sol, il faut déterminer les paramètres de nature et les paramètres d'état. Les paramètres de nature indiquent les caracteristiques intrinsèques du sol. IIs ne varient pas au cours du temps (poids volumique des grains solides, granularité, argilosité, limites d'Atterberg, teneur en matières organiques,…). Les paramètres d'état sont fonction de l'état du sol et caractérisent le comporetement du sol sous l'effet d'un chargement donné (teneur en eau, indice des vides, porosité, Equivalent de sable,...). Nous regroupons dans ce paragraphe les essais géotechniques de laboratoire classiques qui permettent de caractériser un sol. solides s γ Sa détermination se fait à l'aide d'un pycnomètre. Une masse de sol sec m s est introduite dans un pycnomètre conteneant de l'eau distillée. Aprés avoir éliminé toutes les bulles d'air, on mesure le volume d'eau déplacé par les grains solides v s . N.B : Pour les sols (à part les sols organiques) : 26 kN/m 3 ≤ γ S ≤ 28 kN/m 3 3.2 Les essais granulométriques Ils permettent d'obtenir la répartition en pourcentage des grains solides selon leurs dimensions. Deux types d'essais sont envisageables selon le sol à tester : -Par tamisage (par voie humide ou sèche) pour les élements de diamétre ∅ ≥ 80µm. -Par sédimentométrie pour les élements de diamétre ∅ < 80µm. Les résultats sont traduits sous forme d'une courbe granulométrique, tracee dans des axes semi-logarithmiques, à partir de laquelle on peut déterminer : -Le coéfficient d'uniformité de Hazen : 10 60 d d u C = -Le coéfficient de courbure : 2 60 10 30 xd d d c C = N.B : d i : diamètre correspondant à i% de pourcentage de tamisat cumulé. Fig 1.1 :Exepmle de détermination des di : -d 10 =0.17 d 30 = 0.58 -d 60 = 1.80 Cours Mecanique des sol 9 Khaled MEFTAH 3.3 Essais sur sols pulvérulents Le comportement de ces sols dépend des paramètres qui caractérisent le squelette solide, à savoir les dimensions des grains et l'indice des vides. Les essais les plus courants sont : a) Equivalent de sable (ES%) : Permet de caractériser la propreté des sables et le type de sol analysé. . Tableau 1.1 : Caractérisation des sols à partir de la valeur de E.S ES Type de sol 0 20 40 100 Argile pure Sol plastique Sol non plastique Sable pur et propre b) Densité relative (ou indice de densité) : Permet de caractériser la compacité d'un sol grénu et son aptitude à supporter des charges. min max max *Eléments de mécanique des sols : François schlosser

Dissertation for the degree of Doctor of Science in Technology to be presented with due permission of the Department of Electrical and Communications Engineering for public examination and debate in Auditorium S4 at Helsinki University of Technology (Espoo, Finland) on the 14th ...

This study investigates the impact of various element and concrete material models on the finite element analysis (FEA) of reinforced concrete (RC) structures. A comparative evaluation was conducted using 1D, 2D, and 3D finite element models. The research includes the numerical modeling of an experimentally tested RC beam with different finite element and concrete material models. The modeling process was carried out using DIANA FEA software, and the results were compared with experimental data. Furthermore, a parametric analysis was carried out to evaluate the impact of mesh size. Although mesh size varies depending on the element type and geometric properties, the study provides valuable insights for selecting appropriate mesh refinement in similar analyses. The results indicate that the most accurate element model is the 3D model, while the Eurocode concrete model exhibited the best agreement with experimental results. However, other concrete models also demonstrated reasonable accuracy. It was concluded that selecting the smallest feasible mesh size, within the constraints of computational efficiency and analysis requirements, leads to improved numerical accuracy.

The finite element technique is used widely for researchers and manufacturers to design and simulate electrical systems in general and electrical machines such as shunt reactors (SRs) and transformers in particular. Many papers have recently applied several methods to analyze magnetic fields, copper losses and joule power losses in the shunt reactors (SRs). In this research, the finite element technique with coupling to global quantities is proposed to investigate the voltage and current distributions in the windings, and compute the distribution of magnetic field in the air gap and along the air core of the SR, as well as copper and core losses. The developed method is directly applied to the practical SR of 91 MVAr and a rated voltage of 500 kV. The finite element method (FEM)-simulated results are validated with experimental results to ensure accuracy and reliability. This facilitate designing the reactor.

The three-dimensional structures of the primary Al3Sc particles in an Al-2Sc master alloy were studied by synchrotron X-ray microtomography, scanning and transmission electron microscopy. The Al3Sc phases were found to be a single cube and a cluster of cubes. The surface area, equivalent diameter of the Al3Sc cubes increased with the increasing of cube volume, but the specific surface area decreases. The primary Al3Sc cubes and Al-matrix have the same crystal orientation, indicating that the Al3Sc phases are the heterogeneous nucleation sites for Al. The experimental results show that {\alpha}-Al2O3 are the possible nucleation sites for the Al3Sc cubes.

We propose a method to solve large sparse linear systems directly on a parallel processing environment consisting of a cluster of workstations. The sparse coe cient matrix represented as a graph is rst partitioned into n regions of approximately equal number of nodes using centered heuristic to form a dense matrix. The sparse linear system is then solved using pipelined Gaussian elimination

Abstract: A two dimensional instationary analysis of the conjugate optical-thermal fields induced in a multilayer thin film structure by a moving Gaussian laser source is carried out numerically in order to compare back and front laser treatment processes. The work-piece is considered semi-infinite along the motion direction and different thicknesses of the thin film are considered. Thermal and optical nonlinearity is induced during transient heating, since the response of weakly absorbing thin films depends on temperature. The heat source can ...

In this paper, flow of slightly rarefied compressible nitrogen in microchannels has been investigated numerically for low values of Reynolds and Mach numbers. The 2D governing equations were solved using Finite Element Method with first-order slip boundary conditions (Comsol Multiphysics software). A validation was performed by comparing with similar configuration from the literature. It was found that our model can accurately predict the pressure driven flow in microchannels. Several interesting findings are reported about the Relative pressure, longitudinal velocity, Mach number, effect of gas rarefaction and flow rate.

Transmit-arrays (TAs) are a popular cost-effective solution for high-gain antennas at millimeter waves (mmW). The design of these antennas relies on the fine tuning of the subwavelength unit-cells that compose the aperture. The intricacy of the unit-cells increases as new features are implemented, such as dual-band operation and wide-angle beam steering, making this antenna even more computationally challenging. In this work, a high gain (25 dBi @ 20 GHz and 28 dBi @ 30 GHz) multiscale Ka dual-band TA for beam-steering applications is analyzed using a massively parallel implementation on multicores clusters of the Finite Element Tearing and Interconnecting method, with a two Lagrange Multiplier (FETI-2LM) technique. The main contribution of this work is the implementation of 3D non-periodic grids with sub-domains of different scales, that is suitable for proper modelling of different regions of the antenna (horn feed, lens cells, air region). An automatic batch file procedure is proposed for the TA meshing, allowing the limited set of constitutive unit-cells of the TA to be meshed separately. Additionally, we are using a block-Krylov strategy to efficiently capture the TA beam-steering capability, without restarting from scratch the interface problem for each feed position. Since other Finite Element Method (FEM) results were not accessible due the size of the problem, the FETI-2LM numerical results provided in this work are compared with other MultiLevel Fast Multipole Method (MLFMM) and Transmission Line Modeling Method (TLM) of CST Microwave Studio solvers, as well as with the measured results of the corresponding Ka dual-band prototype. The computational infrastructure has been used only a fraction of its capacity. Therefore, a much higher gain design (40 dBi) can be assessed, opening a new realm of applicability of TAs in the space segment usually occupied by reflector-based solutions.

The effective electric resistivity of conductive thermoplastics manufactured by filament extrusion methods is determined by both the material constituents and the printing parameters. The former determines the multifunctional nature of the composite, whereas the latter dictates the mesostructural characteristics such as filament adhesion and void distribution. This work provides a multi-scale computational framework to evaluate the thermo-electro-mechanical behaviour of printed conductive polymers. A full-field homogenisation model first provides the influence of material and mesostructural features (i.e., filament orientations, voids and adhesion between filaments). Then, a macroscopic continuum model elucidates the effects of thermo-electro-mechanical mixed boundary conditions. The in-silico multi-scale methodology is validated with extensive original multi-physical experiments and a functional application consisting of an electro-heatable printing cartridge. Overall, this work establishes the foundations to virtually break the gap between mesoscopic and macroscopic multifunctional responses in conductive components manufactured by additive manufacturing techniques.

Prediction of hydrogen embrittlement requires a robust modelling approach and this will foster the safe adoption of hydrogen as a clean energy vector. A generalised computational model for hydrogen embrittlement is here presented, based on a phase field description of fracture. In combination with Part I of this work, which describes the process of hydrogen uptake and transport, this allows simulating a wide range of hydrogen transport and embrittlement phenomena. The material toughness is defined as a function of the hydrogen content and both elastic and elastic-plastic material behaviour are incorporated, enabling to capture both ductile and brittle fractures, and the transition from one to the other. The accumulation of hydrogen near a crack tip and subsequent embrittlement is numerically evaluated in a single-edge cracked plate, a boundary layer model and a 3D vessel case study, demonstrating the potential of the framework. Emphasis is placed on the numerical implementation, which is carried out in the finite element package COMSOL Multiphysics, and the models are made freely available.

Hydrogen threatens the structural integrity of metals and thus predicting hydrogen-material interactions is key to unlocking the role of hydrogen in the energy transition. Quantifying the interplay between material deformation and hydrogen diffusion ahead of cracks and other stress concentrators is key to the prediction and prevention of hydrogen-assisted failures. In this work, a generalised theoretical and computational framework is presented that for the first time encompasses: (i) stress-assisted diffusion, (ii) hydrogen trapping due to multiple trap types, rigorously accounting for the rate of creation of dislocation trap sites, (iii) hydrogen transport through dislocations, (iv) equilibrium (Oriani) and non-equilibrium (McNabb-Foster) trapping kinetics, (v) hydrogen-induced softening, and (vi) hydrogen uptake, considering the role of hydrostatic stresses and local electrochemistry. Particular emphasis is placed on the numerical implementation in COMSOL Multiphysics, releasing the relevant models and discussing stability, discretisation and solver details. Each of the elements of the framework is independently benchmarked against results from the literature and implications for the prediction of hydrogenassisted fractures are discussed. The second part of this work (Part II) shows how these crack tip predictions can be combined with crack growth simulations.

In heavy-duty material handling equipment, major concern is optimum utilization of material for equipment construction without sacrificing the design parameters. To understand this aspect and also to validate the design, as this kind of equipment are vital part of any manufacturing industry, finite element analysis is one of the best method that can be used extensively. This paper work provides a modeling of the structural strength of a crane bridge, in operation for 15 years in the continuous casting department of a steel plant. Due to the importance of the cranes bridge within the technological processes in which they are involved, either from the point of view of steel consumption or functionality, their resistance calculation, during the design phase and after a certain operation period, constitutes a permanent field of investigation which aims a faithful schematization to be used in further modeling, appropriate for our target. Modeling will be done with the aid of a COSMOS/M s...

Miniaturised tensile tests coupled with in-situ scanning electron microscopy are used to deduce the grain boundary properties of a nickel-based superalloy at 750 C. This allows the damage initiation, evolution and failure processes to be observed directly. The significant variation in ductility e consistent with the limited number of grain boundaries being present e is rationalised using a crystal plasticity approach calibrated by experiments on single crystals loaded along the <001>, <011>, and <111> directions. Quantitative strength and toughness values for the grain boundaries are estimated using a cohesive zone method. The modelling approach is used to determine an approximation of the size of the representative volume element (RVE) needed for volume-averaged behaviour.

This paper presents the details of the development, evaluation process, and results of linear and nonlinear time-invariant models used to represent the frequency response of inductive high-voltage instrument transformers. The study encompasses both sinusoidal and distorted quasi-sinusoidal test waveform conditions, focusing on harmonic voltage amplitude and phase-angle measurements up to 10 kHz. A linear time-invariant model was derived using a higher-order transfer-function estimation technique that minimized the least-squares error between the measured frequency response of the transformer and the estimated transfer function across harmonic orders ranging from 50 Hz to 10 kHz. Acknowledging the limited validity of the linear time-invariant model under multi-tone distorted waveform conditions, a nonlinear timeinvariant model employing a simplified Volterra series was introduced to represent the instrument transformer frequency response under multi-tone distorted waveform scenarios. The accuracy of both models was rigorously assessed using the experimental frequency responses obtained through sinusoidal lowvoltage-frequency sweep signals and multi-tone-distorted high-voltage waveforms. This study contributes to a comprehensive understanding of the behaviour of instrument transformers at high frequencies under different input voltage conditions, providing valuable insights into the accuracy of high-frequency harmonic measurements up to 10 kHz. INDEX TERMS Frequency domain analysis, frequency response, high-voltage techniques, instrument transformers, nonlinear systems, power quality, power system harmonics, transfer functions.

Fatigue life prediction of a welded structure is a complex phenomenon due to the nature of fatigue and the welding process. Additionally, Finite Element Method (FEM) results are extremely sensitive to the size of elements. Therefore, it is difficult to adopt a method to estimate the fatigue life, especially for welded structures. Besides, mesh size independence is a critical issue to perform fatigue life prediction methods that eliminates the need for excessive element numbers in the mesh. This paper investigates the Master S-N Curve Approach (MCA) using the output parameters of the mesh insensitive Structural Stress Method (SSM). MCA based on SSM employs structural stresses recovered from nodal forces and nodal moments. To recover these inputs, FEM model should be established properly. Thus, boundary conditions and applied loads were prepared for the model according to the BS EN 13749:2021. The submodeling technique in ANSYS software was used to analyze the bogie structure. To justify the mesh independence for the model, different mesh sizes were tested. In a specific range for shell bodies, SSM was shown to provide sufficient mesh independence feature. Furthermore, MCA was compared with Hot Spot Stress Method and Nominal Stress Method based on their fatigue life estimations.

We revisit the cell-based smoothed finite element method (SFEM) for quadrilateral elements and extend it to arbitrary polygons and polyhedrons in 2D and 3D, respectively. We highlight the similarity between the SFEM and the virtual element method (VEM). Based on the VEM, we propose a new stabilization approach to the SFEM when applied to arbitrary polygons and polyhedrons. The accuracy and the convergence properties of the SFEM are studied with a few benchmark problems in 2D and 3D linear elasticity. Later, the SFEM is combined with the scaled boundary finite element method to problems involving singularity within the framework of the linear elastic fracture mechanics in 2D.

For the model Poisson problem we propose a method combining the discontinuous Galerkin method with a mixed formulation. In the method independent and fully discontinuous basis functions are used both for the scalar unknown and its flux. The continuity requirement is imposed by Nitsche's technique . In the implementation the flux is eliminated by local condensing. We show that the method is stable and optimally convergent for all positive values of the stability parameter. We also perform an a posteriori error analysis. The theoretical results are verified by numerical computations.

E F HG PI RQ SI RT VU 4W YX %4a Hb cW ed fd fW 5g ha HQ 4i qp rF Hd ts ¦u wv xW eQ wy cW Y 2 D " ¢ 1 ) % Bd e gf xh % "d cf xi jd e k ml e d e gf xh n ol qp jl qd ¢ l 2r sf x ¢i g "t e l u @v f xw e "d zy Yf )l {d v er e h 2 ¨d "f v "d e r " B ¡ l qd r d e l % v r !f h v ¢ n ep Ph e ¢ v mr " } "h }r r v %l qd n xl ¢ Y£ )¤ ¥ e¦ o § } V x }h d " g " ¢ "h ed @ ¢ "d f n l s }l qd g " n ¢ "d f n l ! jl ml s n V ¢f n " © y ¨ }ª Ry ¨« $ j¬ 4l q j ew e r !d zr ! xl el { ®r Bd e gf xh }l ª " v " l q gf xh H¬ 4 x° ± x² e ´³ x± xµ 1 "°e ´³ x± B ¶ ² °• g5¹ º q» {¼ "½ ¹ º c¾ V¿ À» {Á àsÄ Å AE Ç ÉÈ zÊ HË sÌ ÎÍ %Ê Ï È zÈ ÎÐ Ñ Ñ xË sÌ ÎÒ tÓ {Ô YÇ ÉÕ kÑ xÏ Ì tÒ Ö "× kÒ ÎAE Ó Ø VÐ Ù ¡Ï ÚÕ ÜÛ Ï ÚÑ Ç ÉÒ RÏ ÚÝ wÏ Õ Ô AÞ ßË sÖ Ç ÉÝ ÉÇ ÉÒ m× %à Ì tË !á sÌ RÏ ÚÙ ãâ fä "AE Ó {Ý ÉÝ ÉÈ å Þ Ï ÚÒ tAE Ó qÙ ¡Ï Ò ÎÇ Éae Ï Ý Þ ßË Ô BÓ {Ý ÉÇ çÕ Bá hÏ ÚÕ Ô zè VÕ Ï Ý É× "È tÇ ÉÈ é ä xae {Ç ÉÓ {Õ "Ò tÇ ëê ae 4Û HË sÙ Ñ Ð Ò tÇ ÉÕ á !ì @Ë í jÒ ÎAE Ó 4Û HË sÙ Ù zÇ îÈ ÎÈ tÇ ÉË sÕ 2Ë í Ò tAE Ó 4ï Ð BÌ tË sÑ xÓ Ï ÚÕ Û HË !Ù zÙ 2Ð Õ Ç ÉÒ tÇ ÉÓ {È ð gÛ HË !Õ "Ò tÌ RÏ Úae {Ò ¤ñ òï }ó ô Û HØ ¤ó ´õ wÛ HÅ wö ÷ ø !ù sú !û sü {ý

Flows involving waves and free-surfaces occur in several problems in hydrodynamics, such as sloshing in tanks, waves breaking in ships and motions of offshore platforms. The computation of such wave problems is challenging since the water/air interface (or free-surface) commonly present merging, fragmentation and cusps, leading to the use of interface capturing Arbitrary Lagrangian-Eulerian (ALE) approaches. In such methods the interface between the two fluids is captured by the use of a marking function which is transported in a flow field. In this work we simulate these problems with a 3D incompressible SUPG/PSPG parallel edge-based finite element flow solver associated to the Volume-of-Fluid (VOF) method [1]. The hyperbolic equation for the transport of the marking function is also solved by a fully implicit parallel edge-based SUPG finite element formulation. Global mass conservation is enforced adding or removing mass proportionally to the absolute value of the normal velocity ...

Cardiovascular disease has become a major healthcare problem. To tackle this along with bypass surgery, the use of the Cardiovascular Stent is considered promising and effective. In this study, we aim to find the effectiveness of stent deployments and their influence on haemodynamics post their deployment. For the study we have reconstructed single unit of two commercially available stent designs: PS Stent and Bx Velocity Stent using COMSOL. Five different commercially used stent materials (SS-316L, PT-Cr alloy, Co-Cr alloy, Nitinol and Tantalum) were considered. Also three different stent strut geometries (rectangular, square and circular) were analyzed to study the heamodynamics post stent deployment and eventually find out the risk of restenosis.

Convolving the output of Discontinuous Galerkin (DG) computations using spline filters can improve both smoothness and accuracy of the output. At domain boundaries, these filters have to be one-sided for non-periodic boundary conditions. Recently, position-dependent smoothness-increasing accuracy-preserving (PSIAC) filters were shown to be a superset of the topof-the-line one-sided RLKV and SRV filters. Since PSIAC filters can be formulated symbolically, convolution with PSIAC filters reduces to a sequences of small inner products with local DG output and hence provides a more stable and efficient implementation. The paper focuses on the remarkable fact that, for the canonical hyperbolic test equation, new piecewise constant PSIAC filters of small support outperform the top-of-the-line boundary filters in the literature. Numerical experiments show that these least-degree filters reduce the error at the boundaries to less than the error even of the symmetric filters of the same support that are applied in the interior. Due to their simplicity, and since this least degree filter has an exact symbolic form, convolution is stable as well as efficient; and derivatives of the convolved output are easy to compute.

Convolving the output of Discontinuous Galerkin (DG) computations with symmetric Smoothness-Increasing Accuracy-Conserving (SIAC) filters can improve both smoothness and accuracy. To extend convolution to the boundaries, several one-sided spline filters have recently been developed. We interpret these filters as instances of a general class of position-dependent spline filters that we abbreviate as PSIAC filters. These filters may have a non-uniform knot sequence and may leave out some B-splines of the sequence. For general position-dependent filters, we prove that rational knot sequences result in rational filter coefficients. We derive symbolic expressions for prototype knot sequences, typically integer sequences that may include repeated entries and corresponding B-splines, some of which may be skipped. Filters for shifted or scaled knot sequences are easily derived from these prototype filters so that a single filter can be re-used in different locations and at different scales. Moreover, the convolution itself reduces to executing a single dot product making it more stable and efficient than the existing approaches based on numerical integration. The construction is demonstrated for several established and one new boundary filter.

In recent years, energy storage systems rise in importance associated with increase market share of renewable energy sources in energy production. One of the best option to remove disadvantages of renewable energy sources, originating from it characteristics is to use energy storage systems. Nowadays, there are various storage systems and needed to be developed further. In this study, compressed air storage systems which are mechanical storage system were introduced and a small scale compressed air storage system was designed. In this design, it is aimed to compress and expand air isothermally using liquid pistons. Information about designed system performance was obtained by a mathematical model. Numerical analyses were applied in order to determine the air pressure and other air properties during the compression process in liquid pistons. For numerical analyses, commercial packaged software which is based on finite volume method was used. The system was designed, manufactured and tested under laboratory conditions. It is found that, the most important parameter that effect the performance during compression and expansion processes in the system is the liquid piston speed. System performance can be improved by using variable piston speeds. It is seen that, compression and expansion efficiencies can be enhanced by changing the liquid piston geometry. The compression performance of the energy storage system for different conditions was investigated experimentally. It is seen that designed and manufactured system can be operated with renewable energy sources and other storage applications.

If the modeling approach for strain localization with softening does not contain a material length-scale parameter, the numerical simulation suffers from the excessive mesh dependence. This paper presented the extended finite element (XFEM) method combined with new integral type nonlocal model for numerical simulation of strain localization with softening. The XFEM method was employed for simulation of high strain gradient in the localization band. The governing differential equations were regularized by nonlocal continuum theory, including the material length-scale parameter. For nonlocal plasticity, element size has a critical effect on the solution. Sufficiently refined meshes are required for an accurate solution without mesh dependency. It was shown that an extended finite element method can be applied to the problem to decrease the required mesh density close to the localization band. A new method based on the local bifurcation theory was proposed for the initiation and growth criterion of the strain localization interface. When using this method, the softening zone initiation locus did not need to be known in advance. Finally, several numerical examples were used to demonstrate the efficiency of the mixed XFEM-integral type nonlocal model in shear band localization modeling without mesh dependency.

Localization phenomena, as e.g. shear bands, is a narrow zone of local concentrations of plastic strains. Classical continuum theory does not include material length scale parameters and is inadequate when localization phenomena occur. Therefore, numerical results based on classical continuum theory strongly depend on the mesh size of the finite element discretization. The present study explored the application of an extended finite element model in the nonlocal continuum mechanics of fluid-saturated material for numerical simulation of shear band localization. In the present paper, a new relation was proposed to calculate the stress rate based on the integral-type nonlocal model. It was shown that the inclusion of fluid viscosity and nonlocal plasticity for saturated cases leads to a regularization of the shear band problem. The goal of the present paper was to propose a new numerical method for reduction of computational effort and mesh dependency. For nonlocal plasticity, element...

Local adaptivity and mesh refinement are key to the efficient simulation of wave phenomena in heterogeneous media or complex geometry. Locally refined meshes, however, dictate a small time-step everywhere with a crippling effect on any explicit time-marching method. In [18] a leap-frog (LF) based explicit local time-stepping (LTS) method was proposed, which overcomes the severe bottleneck due to a few small elements by taking small time-steps in the locally refined region and larger steps elsewhere. Here optimal convergence rates are rigorously proved for the fully-discrete LTS-LF method when combined with a standard conforming finite element method (FEM) in space. Numerical results further illustrate the usefulness of the LTS-LF Galerkin FEM in the presence of corner singularities.

La subdivision de l&#39;element parent en sous-cellules d&#39;integration utilisee dans le cadre de la methode X-FEM convient difficilement a l&#39;etude de la propagation d&#39;une fissure dans un milieu plastifie. Il est alors notamment necessaire de realiser la projection des variables internes aux points d&#39;integration des sous-elements. Cette contribution etend au cas de la plasticite une methode d&#39;integration utilisant les formules de quadrature de Gauss standards, initialement developpee dans le cadre de l&#39;elasticite lineaire. La methode proposee se limite aux cas des interfaces et des elements lineaires.

Nous présentons une implémentation X-FEM capable de représenter des conditions de contact et frottement pour des surfaces de failles dans des bassins sédimentaires. Ces failles constituant des réseaux avec intersections, nous définissons un enrichissement du champ de déplacement qui représente les jonctions entres ces surfaces de discontinuité. Pour satisfaire la condition LBB sur l'espace des inconnues de contact par rapport aux inconnues de déplacement, nous proposons d'utiliser une interpolation P 0 sur les jonctions. Un cas d'application d'un bassin sédimentaire démontre la robustesse de la méthode. Mots clés -X-FEM, contact, frottement, LBB, failles.

In this paper, Rayleigh wave equation has been solved numerically for finding an approximate solution by Successive approximation method and Finite difference method. Example showed that Successive approximation method is much faster and effective for this kind of problems than Finite difference method.

Designers are continuously challenged to manage complexity in embodiment designprocesses, in the context of integrated product and materials design. In order to manage complexity in design processes, a systematic strategy to embodiment design-process generation and selection is presented in this paper. The strategy is based on a value-ofinformation-based Process Performance Indicator. The approach is particularly well-suited for integrated product and materials design, and all other scenarios where knowledge of a truthful design-process and bounds of error are not available in the entire design space. The proposed strategy is applied to designing embodiment design-processes for multifunctional blast resistant panels. It is shown that the proposed strategy based on the Process Performance Indicator is useful in assessing the performance of embodiment designprocesses particularly when knowledge of prediction accuracy or its error bounds is not known throughout the whole design space. B in-plane spacing of webs of square honeycomb core BRP blast resistant panel d i + , d i deviation variables for goals in cDSP cDSP compromise decision support problem h c , h f , h b thickness of core webs and face sheets, respectively δ, ∆δ deflection of back face, variance in deflection of back face c ε

The Ernst-Mach-Institute (EMI) of the Fraunhofer-Society is dealing with a wide spectrum of subjects in the fields of applied physics, mechanical and civil engineering. The EMI department for numerical simulation supports the institute and the external customers with the high-performance software applications in the fields of compressible flows, structural dynamics, electro dynamics and multi-disciplinary couplings of these applications. A majority of the in-house codes is written in FORTRAN 95 for efficiency reasons. Nevertheless, potential benefits of object-oriented programming in C++ are recognized. Performance studies for numerical simulations in terms of explicit finite element methods have shown that FORTRAN provides much better efficiency than C++. Here we analyze the factors contributing to the code performance for the explicit finite volume scheme and present pro and contras of possible C++ solutions.

We have developed a new algorithm for the inversion of magnetotelluric (MT) data. The developed algorithm is built to be fast, versatile, and accurate. A fast inversion algorithm has to include a fast forward-modeling routine. To achieve that, a hybrid approach consisting of finite-difference (FD) and finite-element (FE) methods is used to benefit from the speed of the FD method and the flexibility to add topographic features of the FE method. To reduce the number of cells, and thus reducing the size of the system to be solved in the forward and pseudoforward solutions, different meshes for various groups of frequencies are used. Then, these are mapped onto the inversion mesh by a mesh-decoupling technique to further accelerate the inversion. To build a versatile inversion algorithm, the capability of using different data types is implemented. In addition to the impedance tensor and the magnetic transfer function, the algorithm also computes the phase tensor and phase vector, which ...

The analysis of travelling waves in elastic waveguides with complex cross-sections, such as train rails, can only conveniently be performed numerically. The semi-analytical finite element (SAFE) method has become a popular tool for performing such analyses. This paper employs a hybrid SAFE-3D method to investigate the scattering of guided waves interacting with discontinuities, such as welds, in continuous welded train rails. The aim of the analysis is to predict transmission and reflection coefficients for a given incident wave and known discontinuity parameters. This characterisation is useful for predicting the long-range transmission characteristics of transducers in NDT and monitoring systems, such as the rail break alarm system developed by the Institute for Maritime Technology (IMT) and the Council for Scientific and Industrial Research (CSIR). The numerical model can also be used to estimate welded sections properties from experimental measurements using a scanning laser vibrometer.

The preservation of cultural heritage and the seismic resilience of historic buildings are crucial for maintaining social identity, particularly in earthquake-prone regions. This study focuses on the modeling of Sırçalı Kumbet, a Seljuk monument built in the 14th century in Kayseri province, located in the Central Anatolia region of Turkey, using survey drawings and analysis using the finite element method (FEM) to evaluate its seismic performance. The analysis indicates that linear elastic calculation methods can serve as an initial approach for evaluating such geometrically complex structures. The findings demonstrate that Sırçalı Kumbet exhibits substantial structural rigidity, reducing deformation and enhancing resistance to material fatigue during seismic events. Displacement and stress analyses under G+EQx and G+EQy loading conditions reveal that tensile and compressive stresses remain within acceptable limits, with localized exceedances occurring at specific points, such as cavity corners and wall bases. While these localized stresses are manageable, they highlight areas that require continuous monitoring and potential reinforcement to ensure long-term stability. Additionally, the study suggests that the integration of regular maintenance and targeted reinforcement measures can further improve the monument's durability and minimize potential damage. This research underscores the essential role of the FEM in bridging the gap between cultural heritage conservation and seismic resilience. It provides a methodological framework for integrating architectural, restoration, and engineering expertise into comprehensive conservation strategies. Future studies should expand this approach to include various building types and material properties to enhance the development of preservation strategies.