Finite Element Simulations

This paper presents a numerical analysis of a short circular hollow column using ABAQUS software. Circular hollow sections have high structural efficiency due to lack of major or minor axes. Such sections are also effective in areas with limited spaces.This paper provides an examination of their performance under axial loading using numerical analysis

In this paper high speed turning and milling models are considered and chip formation and cutting forces are investigated. For the simulation the Finite Element Modeling software Third Wave Systems AdvantEdge is employed and the cutting forces results as well as the morphology of the chip are compared with the results of experiments conducted with CNC machine tools. For the experimental work the principles for design of experiment were used in order to minimize the required amount of experiments and obtain useful results at the same time. All parameters and cutting conditions were chosen to be close to the common industrial ones, with the material of the workpiece being C45 steel and the tools being coated carbides. Although published work on FEM simulations on high speed machining exist, this paper provides validated 3D models that cover the cases of precision high speed turning and high speed milling. The validation of the numerical data with the experimental ones show a good agre...

Two original numerical techniques are developed for the finite element (FE) transient analysis of induction and permanent magnet motors operating in demanding aerospace applications. The first technique is the electromagnetic and thermal analysis weak coupling using a multiple slices 2D FE model. The advantage of the specific technique is the representation of complex actuator geometries including skewed magnets and winding ends, by using a low computational cost 2D model while taking into consideration temperature dependent material attributes. The second technique consists in the development of properly defined boundary conditions for the emulation of the cooling housing of actuators. Those boundary conditions are applied at the outer surface of the actuators in contact with the housing and eliminate the need of modeling complex 3D geometries of highly integrated actuator housings.

Engineering codes are a key method to guide designs to safe and reliable outcomes. Many such codes have prescribed calculations where the user provides specific inputs in a series of calculations, often using charts or tables, to get specific outputs. The design margins, units, and underlying theory are not always apparent. Engineering codes may not be suitable for reverse engineering an incident or providing a failure prediction. This article examines a criminal negligence case in which an initial forensic analysis incorrectly applied the ASME Pressure Vessel Code to use Finite Element Analysis (FEA) of a failed pressure vessel section. The flaws in the original analysis were revealed by applying reverse engineering using conventional stress calculations and understanding basic material science. This emphasizes the need to understand the underlying theories with both engineering codes and numerical modeling. Subsequent FEA provided an accurate analysis report that was successfully used in court. These same methods can be applied to many other engineering codes and standards. "Although most people do not realize it, standards and the methods used to assess conformity to standards are absolutely critical. They are essential components of our nation's technology infrastructure-vital to industry and commerce, crucial to the health and safety of Ameri-cans, and basic to the nation's economic performance 1 ."

A generalized macroscopic representation of electrical steels used in transformer manufacturing industry is developed. The proposed representation is specifically formulated for integration in the finite element method. Usage of the specific technique enables the accurate evaluation of electromagnetic field distribution of transformer cores under heavily saturated conditions. Advantages over conventional techniques include numerical stability, numerical accuracy, and reduction of iterations of the Newton–Raphson method.

The authors should be commended for presenting such an innovative approach to the estimation of the collapse potential in unsaturated soils. This is a pioneering work that sets the basis for further developments on the use of pressuremeter tests for the mechanical characterization of unsaturated soils in the framework of advanced constitutive models. This area has not been adequately investigated to date, mainly due to the lack of a methodology for pressuremeter tests in unsaturated soils and the complexity of constitutive models. The present discussion intends to offer the opportunity for a debate with the authors on some

Bogie is a unity that supports the construction of railway facilities monorail when running on the track. Bogie frame is a construction to support the carbody against imposition. The purpose of this analysis is to determine and ascertain the limits static strength numerical order before the prototype bogie frame through static testing or verification stage design. Stages in this research is the collection of data and bogie drawing APMS of PT.INKA Madiun, and then to identify the 3D CAD model of the structure of the bogie frame, then conducted to determine the boundary conditions for the imposition of simulated static load.Base on standard UIC-615 there are only two types of load that is vertical and transversal, the maximum value is 53 234 and 48 619 N. Result of static testing for static tests with exceptional load, the greatest deformation of 0.5 mm occurs on the balanced wheel, and a maximum stress of 175,97 MPa which lies in the foundation of anti-roll bar, due to transverse load occurring on the pedestal of the anti-roll bar is quite large. Safety factor value that occurs in the area of anti-roll bar is quite low, 1,39.The simulation results for the static testing workload (Static test to Simulate the main in-service load) obtained value of the lowest safety factor of 2.39 with a maximum stress value of 102.26 MPa and deformation of 0,339 mm at the time of load case 8.

In this paper a robust three-dimensional (3D) finite element (FE) anisotropy model is introduced based on a particular scalar potential formulation. The specific 3D FE model is suitable for the accurate evaluation of the peak flux density distribution and no load loss of one-phase and three-phase wound core distribution transformers. The accuracy of the proposed 3D FE anisotropy model is validated by local flux density and no load loss measurements.

There have been numerous publications on unreinforced masonry construction in the literature; however, there is a lack of publications on the condition assessment of existing unreinforced masonry façades for disturbances due to nearby subway construction. To fill this gap, this paper presents a study in which a 5-story historical building with unreinforced masonry façade experiences inward and outward deformations perpendicular to the plane of wall due to nearby subway construction. The performance of the unreinforced masonry façade is examined under wind load combinations. For this, a finite-element (FE) model is built in ANSYS software to conduct a stress analysis of the brick façade. The results revealed that the tensile stresses exceeded the tensile stress limit at several locations; therefore, a structural remediation is required. A structural retrofit is proposed to tie the façade wall to the floor diaphragms with steel anchor rods at specific stories. Another FE model is built to represent the remedies proposed for stabilizing the façade wall. The results show that all stresses are within the limits, indicating that the structural solution for the remediation is appropriate. As a result of this study, the proposed remediation was implemented at the building, and the structure has been in good structural condition without any complaints, even after the subway construction was completed and the subway line was in operation.

The microstructure of dual phase steels can be compared with a composite composed of a matrix of ferrite reinforced by small islands of martensite. This assumption has been used in several attempts to model the mechanical properties of dual phase steels. However, recent measurements show that the properties of the ferrite phase change with distance from the martensite grains. These measurements showed that the grains of the ferrite phase are harder in the vicinity of martensite grains. As a consequence of this local hardening effect,the ferrite phase has to be considered as an inhomogeneous matrix in modeling dual phase steels. This experiment inspired the idea thatlocal hardening is caused by geometrically necessary dislocations. The idea is investigated experimentally and numerically in the presentanalysis, which for the first time leads to good agreement with experimental observations of the mechanical stress–strain behavior

Nowadays modern commercial simulation software provides acceptably faithful representation of reality, assuming the correctness of boundary conditions and reliability of data of processed composite material. In the case of non-standard plastics which include polyimide, we do not always have access to the target material and we do not have proper equipment to produce such products. Due to very interesting properties of the polyimide and its low popularity in use as an injection moulding material, the analysis of injection moulding of tooth plastic gear made from carbon fiber-polyimide composite was made. In this work the chosen material data, necessary for the numerical analysis, were presented. The impact analysis of main factors controlling the volumetric shrinkage during injection moulding processing was conducted. It was found that the greatest impact on the quality criterion is the melt temperature. To optimize control factors, the Taguchi orthogonal plans were used. In addition, the issue of polyimide properties, the possibility of its injection moulding and applications was discussed.

Die Planung und Ausführung von tiefen Baugruben in weichen Böden im innerstädtischen Bereich ist für alle Beteiligten eine große Herausforderung. In diesem Beitrag wird die Herstellung einer 8 m tiefen Baugrube mit unmittelbarer Nachbarbebauung in Konstanz vorgestellt. Hierzu werden umfangreiche Messergebnisse gezeigt, die im Rahmen der bei Baugruben in weichen Böden unverzichtbaren Beobachtungsmethode erfasst wurden, und mit den Ergebnissen einer numerischen Analyse unter Berücksichtigung der räumlichen und zeitabhängigen Effekte verglichen. Darüber hinaus werden die erforderlichen Nachweise für den Grenzzustand der Tragfähigkeit unter Berücksichtigung der komplexen Baugrund-Tragwerk-Interaktion präsentiert. Insbesondere wird ein modifizierter Ansatz zur Berechnung der Aufbruchsicherheit einer verankerten Baugrubensohle nach den Vorgaben des Eurocodes EC7-1 in Anlehnung an die Empfehlungen des Arbeitskreises „Baugruben“ der Deutschen Gesellschaft für Geotechnik vorgestellt.
Die Baugrube mit einem annähernd quadratischen Grundriss wurde im Jahr 2008 in weich-breiigem Seeton mit zwei Untergeschossen hergestellt. Als Verbauwand wurde eine eingepresste Spundwand verwendet, die in einer Höhe von –1,80 m durch einen oberen Aussteifungsring aus einer Gurtung mit diagonalen Ecksteifen und mit einer abschnittweise hergestellten Unterbetonsohle in einer Tiefe von –7,80 m ausgesteift wurde. Die räumlichen Einflüsse der Baugrund-Tragwerk-Interaktion, die für dieses Projekt durch den Einbau einer rautenförmigen oberen und unteren Aussteifung und den abschnittweisen Einbau der Betonsohle bestimmt wurden, konnten in einer zweidimensionalen numerischen Analyse mit Mobilisierungsfaktoren und unter Berücksichtigung der spannungspfadabhängigen Steifigkeit des Seetons zutreffend erfasst werden.
Dieses Ausführungsbeispiel einer tiefen Baugrube in weichen Böden verdeutlicht besonders die Wichtigkeit eines umfangreichen begleitenden Messprogramms im Hinblick auf die Anwendungsgrenzen der Finiten Elemente Methode bei Verwendung derzeit kommerziell verfügbarer höherwertigerer Stoffgesetze. In dem Beitrag wird darüber hinaus eine Methode zur Berücksichtigung der spannungspfadabhängigen Steifigkeit von weichen Böden vorgestellt.

In questa tesi magistrale sono considerati i sistemi di ritenuta stradale costituiti da elementi prefabbricati in calcestruzzo armato, indicati comunemente come New Jersey.

Al contrario di quanto possa essere semplicisticamente supposto, questi sistemi di ritenuta, in funzione delle loro connessioni in direzione longitudinale fra i diversi moduli e in verticale fra i singoli moduli e il piano di appoggio, possono sviluppare comportamenti prestazionali altamente differenziati, in particolare per quanto riguarda la capacità di dissipare l’energia dovuta all’urto di veicoli. Il loro progetto e verifica prestazionale, oltre a necessarie prove sperimentali, può utilmente sfruttare le capacità di simulazione numerica proprie della meccanica computazionale.

Nello specifico, questo contributo vuole evidenziare:
a) l’importanza della concezione strutturale di questi sistemi di ritenuta sottolineandone i meccanismi elementari e il loro accoppiamento;
b) confrontare due diverse tipologie di connessioni, una sviluppata agli inizi degli Anni ’90 (TIPOLOGIA B), una successiva di uso corrente (TIPOLOGIA A);
c) valutare l’importanza del degrado per corrosione delle connessioni fra moduli sulle capacità prestazionali dell’intero sistema di ritenuta;
d) sottolineare l’utilità e l’importanza di simulazioni numeriche che permettano di prevedere il comportamento complessivo del sistema di ritenuta, ovvero di risalire alle cause di malfunzionamento dello stesso in un evento incidentale nei procedimenti di ingegneria forense

Proprio quest’ultima considerazione risulta, purtroppo, di attualità a seguito di recenti eventi che hanno funestato il traffico, primo fra tutti quello del luglio del 2013 sull’autostrada A16 Napoli-Canosa che ha visto un pullman precipitare dal viadotto di Acqualonga all’altezza di Monteforte Irpinio (AV), causando la morte di 40 persone.

A detailed study was carried out on crankshafts used in two wheeler made from C45 (EN 8/AISI 1042) steel. Undesirable noise was heard in crankshaft when the engine is in running. This was stated as failure of crankshaft. Material has been peeled off and seemed to be scraped at the central portion of the crankpin.  It was the bearing seating place where oil hole also provided. Under analysis the crankpin was identified as tempered. Chemical composition, micro-hardness and microstructure were studied and compared with the specified properties of the crankpin material. Reason for failure is identified as wear due to lower hardness, improper lubrication and high operating oil temperature.

In the finite-element solution of heat conduction problems with phase change, the singular behaviour of the specific heat near the phase-change point causes special problems. These problems can be overcome by lumping the thermal capacitance of the material at the nodes, to obtain a diagonal capacitance matrix. In this way the specific heat can be unambiguously calculated. The lumped-capacitance principle was combined with the explicit enthalpy method and Pham's three-level enthalpy method. Tests against freezing problems show that for Stefan problems both resulting methods are more accurate than previous three-level distributed capacitance methods.

In this paper, a novel model was proposed to reduce the weight of the rib of the engine mounting. The suggested
model is analyzed numerically and simulated using a computer program package (ANSYS 11) to perform the FEM
computations. In addition, two more models for the engine mounting part have been and built and applied to the same
boundary conditions as for the suggested model. The results of the stresses and deformations for the three models of the
engine mount were compared to each other. The proposed model of the engine mount had a superior performance over the
other the standard model in terms of weight reduction, whereas, 51.5% of the weight was reduced with the proposed model
maintaining an acceptable level of yield stress.

In this paper we displayed the problematic of modeling, analysis and simulating work process of specific tool used for punching and cutting operations on inner plate of the front car door. Basic principles of treating material with deformations are displayed, to easily understand operations that are performed during the work of the tool. Principles of geometric modeling, application of Boolean operations, parametrized individual standard parts and databases are very important factors for tool modeling. Beside modeling it is very important to calculate the specific parts based on standards which are used in car industry. After geometrical modeling of tool, simulation and work analysis have been performed to control the movement speed of the tool during production. Simulation also enables faster design process for the tool, increases work safety etc.

This paper presents a review of finite element analysis of stretch flanging process and its finite element
simulation, finite element formulation and finite element method (FEM) based parametric studies and their results. Stretch
flanging process is secondary sheet metal forming process which is widely used in conjunction with other sheet metal
forming process in sheet metal forming industry. It is used for making of automotive components and complex panels. In
past researchers had worked on the area of finite element analysis of stretch flanging process in terms of development of
FEM based computer programs and by using different commercial FEM software packages. It is observed that majority of
finite element simulation for stretch flanging processes have employed explicit dynamic FEM approach. It is also found
from FEM based parametric studies that geometrical parameters have greater influence upon the formability of stretch
flanging process as compared to material parameters. Besides this, it is also observed that for manufacturing of stretch
flange parts and components ferrous alloys were used in past, whereas aluminum alloys being used commonly in present
scenario for obtaining corrosion free and lightweight with increased strength parts. Hence, it is found that analysis based on
finite element method is a powerful, accurate and efficient technique for better designing of stretch flanging process.

Для более точной оценки прочности эксплуатируемых железобетонных конструкций необходимо использовать модели с дискретным расположением арматурных стержней с учетом реальных характеристик сцепления арматуры с бетоном, определяемых, как правило, экспериментальным путем. Одним из наиболее распространенных способов определения характеристик сцепления является вытягивание арматурного стержня из бетонного блока (pull-out test). Процесс разрушения связей сцепления арматуры с бетоном при выдергивании стержня из бетонного блока представляет собой сложный многостадийный процесс, сопровождающийся присутствием неоднородного и неупругого деформирования, нарушением адгезионных связей, возникновением и развитием трещин различной формы и ориентации, наличием изменяющихся зон контакта и трибологических явлений. В рамках данной работы выполнены экспериментальные исследования и произведено сравнение с результатами расчета с использованием различных моделей разрушения связей сцепления арматуры с бетоном в задаче о вытягивании стержневой профилированной арматуры из бетонного блока. В первой части статьи рассматриваются модели с учетом несплошности соединения, во второй – модели без явного учета несплошности.
The problem of pulling the reinforcing bar from the concrete block is urgent for the practice, as it represents the most widespread method of experimental evaluation of characteristics of reinforced-concrete bond behavior, which are necessary for an estimation of the strength and durability of reinforced concrete structures. Fracture process of bonds at pulling the rebar from the concrete is a complex multistep process, accompanied by the presence of inhomogeneous and inelastic deformation, a rupture of adhesive bonds, the initiation and propagation of cracks of different shape and orientation, the presence of contact and tribological phenomena. The nonlinear finite-element solutions of the problem of pulling the reinforcing bar from the concrete block have been obtained with using various models of bond behavior and concrete cracking. The comparison of obtained numerical results with experimental data has been presented and discussed. The first part of the article is devoted to the models taking into account the discontinuity of the connection, while the second part is concerned with the models without explicitly taking into account of discontinuities.

Excavations in soft soils in particular in urban environments with adjacent neighbouring buildings are always subjected to deformations that are not fully avoidable. The soil-structureinteraction of excavations in soft soils is dependent on many factors. A classification of these factors that influence the deformation behaviour depending on the degree of designer interference dealt with in chapter 2. The focus of this research work is to examine the uncontrollable factors that affect the deformation behaviour based on the above classification. The ground conditions, in general, and the material properties of the soft soils in particular, are responsible primarily for the deformation behaviour. For this reason, the material behaviour of soft soils has been scientifically studied using experimental and numeric methods taking into account characteristic stress conditions that arise during excavation. The factors that are under designer control, e.g. support system and its stiffness, the factors that are partially under designer control, such as the method and quality of support construction, and the construction period are also analysed taking into account the time and stress path dependent material behaviour of the soil.
The research work is organised in three core areas which are developed one up on the other. Using excavation model tests, a numerical parameter study of three idealized excavations, and stress path controlled element tests, the above mentioned factors are examined. The time and stress path dependent material behaviour can be generally analysed and validated using a numerical analysis of three practical case studies based on a method that considers the stress path dependent stiffness. This method is devolped and explained within this thesis. Two of the practical projects had been accompanied by the author in the framework of this research work during the construction phase and one starting from the design phase.

The frame of the standard dump truck supports all types of complicated loads coming from the road and freight
being loaded. So, the intensity and the strength of the frame play a big role in the truck's design. A frame of 6 wheels,
standard dump truck has been studied and analyzed using ANSYS package software. The static intensity of the frame has
been analyzed when exposed to pure bending and torsion stress, within two cases. First case is when the rear wheels zigzag
gets over block (only one side of the chassis steps the block), and the second case is when both wheels gets over the block.
Finite element model of a stress analysis of the vehicle chassis has been built using three dimension hyper elastic elements
for the modeling. The results show important differences between the two case studies, especially in the torsion and
deformations results obtained from the chassis model. Also, vibration modes have been analyzed during the loading
conditions. The more damping ratio used, the more stabilizing of the stresses with respect to time.

Post-print of "SM Mirfalah-Nasiri, A Basti, R Hashemi (2016) Forming limit curves analysis of aluminum alloy considering the through-thickness normal stress, anisotropic yield functions and strain rate, Abstract Based on three anisotropic yield criterions including Karafillis-Boyce (K-B), Yld96 and Yld2011, directional normalized uniaxial yield stresses, directional r-value and forming limit curve (FLC) for AA3104-H19 aluminum alloy under plane stress condition are numerically investigated in this article. Moreover, considering through-thickness normal stress effect the forming limit diagram (FLD), stress-based forming limit diagram (FLSD) and extended forming limit stress diagram (XFLSD) is also studied theoretically based on Yld2011 yield criterion and modified Marciniak-Kuczynski (M-K) model. The nonlinear equations set are solved employing Newton-Raphson numerical method to calculate limiting strains. The anisotropic plastic behavior and FLC of AA3104-H19 predicted by Yld2011 yield criterion is in good agreement with experimental data and is more accurate than those of K-B and Yld96 yield functions. In addition, according to FLD, the formability of sheet metal increases by applying the through-thickness normal stress. The effects of strain rate at quasi-static condition and temperature are theoretically investigated on the FLD of AA3104 sheets. The positive temperature sensitivity and negative strain rate sensitivity are observed of FLD of AA3104 alloy.

In the current paper, numerical results of cylindrical cup drawing of aluminum-lithium sheets using the commercial software abaqus/explicit are presented. This software permits investigating physical models of real procedures putting singular emphasis on geometrical non-linearities produced by large deformations, material properties and complex conditions. Numerical simulation using finite element methods (fem) offers the ability of analysing the feasibility of a process, allowing the benefit of saving time and reducing costs by comparison with traditional methods. The 2090 t3 aluminum-lithium alloy was studied with the focus on the influencing plastic anisotropy that affect the final predicted part. The results illustrate that anisotropy influence the thickness variation, and a comparison between anisotropic and isotropic yield was discussed.

The aim of this thesis is to design and analyse an optimal lightweight chassis for the GUtech Shell Eco Marathon Team (GSET) prototype vehicle 2016. Considering the fact that increased weight has a detrimental effect on fuel economy, this thesis aims to aid the weight reduction objective set by GSET through designing a chassis that is lighter and stiffer than the previous year’s chassis. The overall proportions of the vehicle are also reduced by packaging the rear end in a more compact manner. Chassis design concepts are introduced and different composite materials are analysed. The newly designed composite chassis is modelled in Solidworks and then simulated in ANSYS Workbench Mechanical coupled with ANSYS Composite PrepPost using finite element analysis (FEA). Several possible loading scenarios are taken into consideration and then simulated in order to achieve the optimum compromise between low weight and adequate stiffness.

A sandwich panel structure utilising nomex and carbon fibre reinforced polymers (CFRP) is researched instead of a solely carbon fibre approach. The effect of increasing the sandwich core thickness is analysed using FEA. Furthermore an attempt to implement the engine as a chassis member is looked at with the final composite chassis design weighing in at less than half as much as the previous year’s aluminium chassis. A 55% weight reduction is achieved without compromising on stiffness and in the final chapter fabrication recommendations are provided that would be helpful for the next generation of GSET to fabricate the composite chassis in the University workshop.

A 2D finite element analysis for the numerical prediction of capacity curve of unreinforced masonry (URM) walls is conducted. The studied model is based on the fiber finite element approach. The emphasis of this paper will be on the errors obtained from fiber finite element analysis of URM structures under pushover analysis. The masonry material is modeled by different constitutive stress-strain model in compression and tension. OpenSees software is employed to analysis the URM walls. Comparison of numerical predictions with experimental data, it is shown that the fiber model employed in OpenSees cannot properly predict the behavior of URM walls with balance between accuracy and low computational efforts. Additionally, the finite element analyses results show appropriate predictions of some experimental data when the real tensile strength of masonry material is changed. Hence, from the viewpoint of this result, it is concluded that obtained results from fiber finite element analyses employed in OpenSees are unreliable because the exact behavior of masonry material is different from the adopted masonry material models used in modeling process.

Even though, the transformer is the most efficient of electrical machines, with efficiencies typically in the high 90s, it is possible to reduce transformer costs and losses by using composite magnetic cores. This paper presents a new composite magnetic core that can be used effectively for manufacturing single–phase and three–phase wound core distribution transformers. The new composite wound core concept is based on experimental evidence concerning the flux density non–uniformity of conventional single–phase and three–phase magnetic wound cores and the losses and magnetization properties of conventional and high permeability Si–Fe grain–oriented steels. A systematic experimental losses and flux distribution analysis of single phase and three–phase magnetic wound cores is undertaken as well as finite element (FE) analysis considering the bulk anisotropic characteristics of laminated wound cores.

The manuscript presents advanced coupled analysis: Maxwell 3D, Transient Thermal and Fluent CFD, at the time of a rated current occurring on the main busbars in the low-voltage switchgear. The simulations were procured in order to aid the design process of such enclosures. The analysis presented the rated current flow in the switchgear busbars, which allowed determining their temperature values. The main assumption of the simulation was measurements of temperature rise during rated current conditions. Simulating such conditions is a valuable asset in order to design better solutions for energy distribution gear. The simulation model was a precise representation of the actual prototype of the switchgear. Simulations results were validated by experimental research. The heat dissipation in busbars and switchgear housing through air convection was presented. The temperature distribution for the insulators in the rail bridge made of fireproof material was considered: halogen-free polyest...

Nowadays modern commercial simulation software provides acceptably faithful representation of reality, assuming the correctness of boundary conditions and reliability of data of processed composite material. In the case of non-standard plastics which include polyimide, we do not always have access to the target material and we do not have proper equipment to produce such products. Due to very interesting properties of the polyimide and its low popularity in use as an injection moulding material, the analysis of injection moulding of tooth plastic gear made from carbon fiber-polyimide composite was made. In this work the chosen material data, necessary for the numerical analysis, were presented. The impact analysis of main factors controlling the volumetric shrinkage during injection moulding processing was conducted. It was found that the greatest impact on the quality criterion is the melt temperature. To optimize control factors, the Taguchi orthogonal plans were used. In addition, the issue of polyimide properties, the possibility of its injection moulding and applications was discussed.

Design of machine foundation involves the prediction of vibration magnitude. Very slight (of the order of a hundredth of a centimeter) vibration magnitude may cause harm to function of the machine and may even terrify people or threaten the safety of surrounding structures so the codes and manufacturers of the machines limit the amplitudes of the vibrations of machine foundation to certain values depending on their
frequencies and types. In most designs the interaction of nearby machine foundations is ignored, with the assumption of being far apart to minimize their cross effects. With no reliable analysis of machine foundation interaction, ignorance of interaction may lead to unsatisfactory results.
In this research the cross interaction of machine foundations is investigated using the finite element method (FEM). The soil is modeled as visco-elastic half space. The complex response method is adopted and the analysis is implemented in the frequency domain. A model of two square footings using three dimensional finite elements, loaded with vertical harmonic forces is analyzed to study the following factors:
1. The effect of loading parameters (angular velocity, amplitude and phase difference) and spacing on the interaction of surface footings.
2. The effect of the footing embedment for the case of embedded-surface footings and the case of  embedded-embedded footings. The loading parameters are also considered for the two cases.
3. The effect of the soil depth to the underlain rock stratum on the interaction of adjacent footings.
4. The use of trenches to reduce the effect of adjacent footings' interaction.

Dimensionless curves have been developed for a mass ratio of 5.0 to account for the interaction of machine footings. The results show the importance of the interaction to get a satisfactory serviceability of machine foundation. The study also shows the effect of the loading characteristics, spacing, depth of compressible layer on the dynamic behaviour of adjacent footings. The following results were obtained:
1. The vibrations of surface footings may double in magnitude due to the interaction in case of applying forces with equal angular frequencies.
2. The load-vibration relation is linear in case of equal angular frequencies and non-linear for other cases.
3. The maximum out-of-phase vibration amplitudes are greater than the in-phase vibration amplitudes by a slight difference.
4. The vertical and the rocking vibrations are no longer uncoupled when considering the dynamic interaction of adjacent footing.
5. The embedment of the footings reduces the vibration if the two footings are equally embedded and may increase the vibration for the case of surface-embedded footings.
6. The vibration amplitudes decrease for cases of shallow depths of soil underlain by rock. In the same time, the dynamic response of the footings is not affected by the angular speed of the applied dynamic forces.
7. Trenches can be used to reduce the effect of machine foundation interaction with width greater than O.lB, depth greater than 2B and length greater than 3B, where B is the footing width.

From the results of this study, the interaction of machine foundations must be considered in design. Vibration reduction methods such as embedment and trenches, are investigated to obtain the optimum values of the parameters of each method.

Structures are normal or special; these are precious part and are promptly associated with living as well as non living things. Sometimes minute fault inside the structure might affect whole body and it would lead to collapse the structure which might create a significant loss of property and human beings too. So, increased awareness of structural Health Monitoring Techniques (SHM) gives an idea and remedies for the concerned defect due to aging, deterioration and fault during construction. Previous day's people used just a visual inspection for defect detection but extreme and worst damage in infrastructure leads to invent new technologies for the recognition of new methods on Structural Health

This book is dedicated to the use of the finite elements method for the approximation of equations having partial derivatives. It resumes part of the curriculum leading to the certificate in “Numerical Methods forMechanics” taught by the author since the past twelve years as part of the graduate studies in Mechanics at the University of Pierre and Marie Curie (Paris VI).
Numerical Analysis has undergone a spectacular development during these past forty years. It is most probably related to the boom in InformationTechnologywhich has literally invaded the planet and provided, de facto, calculation capacities undreamt
of up to now.
This mathematical knowledge field – Numerical Analysis – may be characterised as the “mathematic of mathematics” in the same line of thought as that of a “police of polices”.
Indeed, as soon as a mathematical technology cannot be applied within the industrial applications due to operational inadequacy, numerical analysis takes over and finds the solution by identifying the best adapted approximation process.
From there on, all other mathematical branches may be used to “force a passage” and to estimate a solution by often combining shrewdness and lucidity within a stringent mathematical framework.
Numerical analysis is best and most often applied to the approximation of equations having partial derivatives as a major support to the modelling of real systems.
Whether it be applications in physics or in mechanics, in economy, marketing or in the field of finance, the phenomenological translation of the system under study often leads to the resolution of equations having partial derivatives.
This justifies the invention of numerous methods to solve such equations. The finite elements method, the finite volumes method, the singularity or integral method, the spectral methods and the variational finite differences method are some of the most popular methods.
However, the finite elements are those that definitely and drastically changed the world of numerical approximation of equations having partial derivatives. Having an exceptional flexibility, the finite elements undoubtedly constitute the approximation method that is mostly used in solving mathematical models in engineering sciences.
Considering the mathematical technicality required to apply finite elements, many authors specialised in numerical analysis, including Pierre Arnaud Raviart (8), presented the subject at higher level university teaching reserved to students who possess the mathematical prerequisites, particularly in function analysis, essential for the theoretical initiation to the finite elements method.
Other student populations who have followed a curriculum not specialised in mathematics – specially graduate and postgraduate students in Physics or in Mechanics and the Graduate Engineering Schools who are users of the mathematical tool at different degrees – may get recourse to Daniel Euvrard’s (5) book which was written in the 90’s and that offers a version of a course adapted to students who are unfamiliar with the tools for functional analysis.
The superiority of those two manuals reflects the quality of the teachings of Numerical
Analysis by Pierre Arnaud Raviart and subsequently by Daniel Euvrard at the Training and Research Unit in Mechanics of the Pierre and Marie Curie University.
As far as this piece of work is concerned, its necessity and its core content have been greatly influenced by the strong interaction between components of the author’s teaching activities in mechanics, at graduate level, consisting of Numerical Methods applied to Mechanics and to the mechanics of deformable solids at the Pierre and Marie Curie University.
Indeed, the author was motivated by the will to pursue the initiative set by the two authors mentioned above by contributing to a new balance between a selective specialist reading and one dedicated to “operational aspects while skimming over the mathematical aspects”, as stated by Daniel Euvrard ([5], p.198).
The author’s training and awareness on all topics dealing with numerical analysis was greatly influenced by Professor Gérard Tronel, a specially active and passionate member of the team teaching numerical analysis at the Jacques Louis Lions laboratory of the Pierre and Marie Curie University (Paris VI).
The author benefited from Professor Tronel’s significant educational methods and experience as a student and, later, as a colleague and friend, in bringing about the new balance offered in this book.
The author’s warm thanks are conveyed to him for his contribution.
Graduate students in Mechanics of the Pierre and Marie Curie University are the ones who have followed this novel presentation within the framework of unidimensional applications of the resistance of materials.
The present work takes up these examples again and extends them to other applications.
Having identified targeted tools for functional analysis, as exposed without any demonstration, the problems dealing with the existence, uniqueness and regularity of weak solutions and their equivalence with strong solutions have been examined through the display and use of the result of this identification.
Following this perspective, the present work is composed of a Summary of Courses on finite elements in addition to Daniel Euvrard’s [5] work, and of various solutions demonstrating these techniques of functional analysis while, at the same time, tackling the construction of nodal equations characteristic of numerical implementation of the finite elements method.
Moreover, a special emphasis has been laid on the presentation of the application of assembly techniques illustrated in the problems related to the Resistance of Materials.
The author seizes this opportunity to pay tribute to the memory of Claude Kammoun who initiated him to these techniques within the framework of Resistance of Materials.
Finally, this work would never have been published without Benoît Goyeau and Cédric Croizet’s proofreading of the different examination subjects at graduate level Mechanics that constitute a major part of this book. The author conveys his sincere thanks to both of them also to Dr. Arnaud Chauvière for his efficient advices in Latex Programmation.

For the derivation of the axial resistance of driven sheet piles empirical calculation procedures are given in the recommendations of the working groups "Ufereinfassungen" (EAU, 2004) and "Baugruben" (EAB, 2006), which does not always lead to consistent results. Hence, sev-eral static and dynamic load tests on driven sheet piles were evaluated using statistical meth-ods and the resulting characteristic axial resistance are verified on the basis of the approach of the working group "Pfähle" (EA-Pfähle, 2007). The examined load tests had been carried out in North Germany, hence the resulting characteristic axial resistance of driven sheet piles are first presented as preliminary result for North German underground conditions and compared with the present empiric calculation procedures. Further investigations on axial resistance of driven sheet piles, especially the consideration of restraining effects in dependence on the cross section of the sheet pile profile, are running at the present at the University of Kassel.

The role of composite box bridges in the interchanges of modern highway systems has become more and more popular for functional, economic and artistic considerations. This type of structure, guides to an efficient transverse load distribution due to excellent torsional stiffness of the part. Further utilities and services can be readily provided within the boxes. In this thesis as a first approach a study of the effect of shear connector's numbers and distribution on the behaviour of composite box girder bridges is submitted. Additionally, several finite element models are developed to assessed against the results acquired from a field test. A number of factors are considered, and confirmed through available experimental results, especially full shear connections, which are obviously essential in composite box girder. A good representative for shear connectors of suitable finite element type is considered. Preparatory results signalize that number of shear studs can be obviously reduced to facilitate adoption of a new arrangement in design of composite box girder bridges with full makeup. The parametric investigations are performed along with the composite box girder model to appraise the effects of several important parameters on the behaviour of the girder. The outcomes from this study would enable bridge engineers to design composite box girder bridges more reliably and economically. Referable to the complexity of the three-dimensional interaction between shear connector and concrete, there is little success in numerical modelling of the push-out test in literature. A three-dimensional finite element model with multiple elements was counseled to simulate shear connector based on static loading. The interaction between the steel connector and concrete will cause the main significance of the global behaviour of the structural element. The geometry and material nonlinearities of headed stud, steel beam were included in the finite element model. Contact regions between the concrete and steel elements are simulated using surface to surface and embodiment techniques. Shear capacity for studs are obtained and results compared with various codes of practices such as EC4, AISC and BS and BS5950. The proposed model was used to estimate the load-slip curve and to analyse important phenomena of the mechanical behaviour of connectors that are usually difficult to evaluate through tests.
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