134 research outputs found
Analysis of the conditioning number of the plane wave approximation for the Helmholtz equation
No full textThe conditioning of the plane wave approximation finite element model for the Helmholtz equation is analysed when the number of the planar waves and the problem wave number are increased. It appears that conditioning for problems with low wave numbers is poorer than for high wave numbers and that it grows exponentially when the number of the approximating plane waves increases. It is shown that a reasonable choice of a reduced number of the approximating plane waves lead to good quality solutions.</p
Fundamental solutions for beams, plates, and shells under thermomechanical actions
No full textAs the engineering profession moves from prescriptive or “deemed-to-satisfy” approaches
towards design methodologies based on quantification of performance,
sophisticated modelling tools are increasingly needed, especially when complex combinations
of demand and capacity are encountered. Recourse is invariably made to
advanced computational tools to provide high fidelity solutions to large and complex
problems, such as the response of structural systems or components to thermomechanical
actions. Software packages based on the finite element method are most
commonly used for such analyses. There are some essential prerequisites to effective
use of advanced computational software for complex nonlinear problems, which
are often ignored, particularly in professional practice. These include a thorough
understanding of the underlying mechanics of the problem under consideration; a
good appreciation of the approximation methods for modelling the problem properly
(e.g. the choice between elements, continuum or structural, low or high order interpolation,
degree of mesh refinement necessary and so on); and perhaps most importantly
ensuring that the software is reliable and is able to reproduce established fundamental
solutions to an acceptable degree of accuracy.
This thesis attempts to address most of these issues but focusses primarily on the last
mentioned prerequisite and provides a range of novel and unprecedented fundamental
solutions for beams, plates, and shallow shells subject to moderate or extreme
thermomechanical loads such as those resulting from a fire. Geometric and material
nonlinearities are included in the proposed formulations along with the most
common idealised boundary conditions. Thermally induced deformations generate
large displacements and require the solutions to account for geometric nonlinearity,
while material nonlinearity arises from the degradation of the material at elevated
temperatures. In the context of structural performance under extreme thermal action
(such as fire), a finite element procedure is employed to analytically characterise
generic temperature distributions through the thickness of a structural component
arising from different types of fire exposure conditions including: a “short hot” fire
leading to a high compartment temperature over a relatively short duration; and a
“long cool” fire with lower compartment temperatures, but over a longer duration.
Results have shown that despite the larger area under the long cool fire time-temperature
curve, which traditionally represented the fire severity, the effect of the short hot fire
on the nonlinear responses of beams, plates, and shallow shells is more pronounced.
Also, the effect of temperature-dependent material properties is found to be more
pronounced during the short hot fire rather than the long cool fire. Comparison
studies have confirmed that while the current numerical and theoretical approaches
for analysing of thin plates and shells are often computationally intensive, the proposed
approach offers an adequate level of accuracy with a rapid convergence rate
for such structures. The solutions developed can be used to: verify software used
for modelling structural response to thermomechanical actions; help students and
professionals appreciate the fundamental mechanics better; provide relatively quick
solutions for component level analyses; and visualise internal load paths and stress
trajectories in complex structural components such as composite shells that can help
engineers develop deeper insights into the relevant mechanics. The formulations
developed are versatile and can be used for other applications such as laminated
composite or orthotropic shallow shells. A very significant by-product of developing
such fundamental solutions is their potential use in the development of highly accurate
hybrid elements for very efficient modelling of large problems. While this has not
been fully developed and implemented in the current work, the requisite theoretical
framework has been developed and reported in one of the appendices, which can be
used to develop such elements and implement on an appropriate software platform
A partition of unity FEM for time-dependent diffusion problems using multiple enrichment functions
No full textAn enriched partition of unity FEM is developed to solve time-dependent diffusion problems. In the present formulation, multiple exponential functions describing the spatial and temporal diffusion decay are embedded in the finite element approximation space. The resulting enrichment is in the form of a local asymptotic expansion. Unlike previous works in this area where the enrichment must be updated at each time step, here, the temporal decay in the solution is embedded in the asymptotic expansion. Thus, the system matrix that is evaluated at the first time step may be decomposed and retained for every next time step by just updating the right-hand side of the linear system of equations. The advantage is a significant saving in the computational effort where, previously, the linear system must be reevaluated and resolved at every time step. In comparison with the traditional finite element analysis with p-version refinements, the present approach is much simpler, more efficient, and yields more accurate solutions for a prescribed number of DoFs. Numerical results are presented for a transient diffusion equation with known analytical solution. The performance of the method is analyzed on two applications: the transient heat equation with a single source and the transient heat equation with multiple sources. The aim of such a method compared with the classical FEM is to solve time-dependent diffusion applications efficiently and with an appropriate level of accuracy
Time-independent hybrid enrichment for finite element solution of transient conduction–radiation in diffusive grey media
No full textWe investigate the effectiveness of the partition-of-unity finite element method for transient conduction–radiation problems in diffusive grey media. The governing equations consist of a semi-linear transient heat equation for the temperature ?eld and a stationary diffusion approximation to the radiation in grey media. The coupled equations are integrated in time using a semi-implicit method in the finite element framework. We show that for the considered problems, a combination of hyperbolic and exponential enrichment functions based on an approximation of the boundary layer leads to improved accuracy compared to the conventional finite element method. It is illustrated that this approach can be more effcient than using h adaptivity to increase the accuracy of the finite element method near the boundary walls. The performance of the proposed partition-of-unity method is analyzed on several test examples for transient conduction–radiation problems in two space dimensions
Two-dimensional numerical modelling of wave propagation in soil media
No full textWave propagation in soil media is encountered in many engineering applications. Given that
the soil is unbounded, any numerical model of finite size must include absorbing boundary conditions
implemented at the artificial boundaries of the domain to allow waves to radiate away to
infinity.
In this work, a finite element model is developed under plane strain conditions to simulate
the effects of harmonic loading induced waves. The soil can be homogeneous or multi-layered
where the soil properties are linear elastic. It may overlay rigid bedrock or half-space. It may
also incorporate various discontinuities such as foundations, wave barriers, embankments, tunnels
or any other structure.
For the case of soil media over rigid bedrock, lateral wave radiation is ensured through the implementation
of the consistent transmitting boundaries, using the Thin Layer Method (TLM),
which allow replacing the two semi-infinite media, on the left and right of a central domain of
interest, by equivalent nodal forces simulating their effect. Those are deduced from an eigenvalue
problem formulated in the two semi-infinite lateral media.
In the case of soil media over half-space, the Thin Layer Method is combined to the Paraxial
Boundary Conditions to allow the incoming waves to radiate away to infinity laterally and
in-depth. The performance of this coupled model is enhanced by incorporating a buffer layer
between the soil medium and the underlain half-space.
For extensive analyses, the eigenvalue problem related to the TLM may become computationally
demanding, especially for soil media with multi-wavelength depths. As the TLM involves
thin sub-layers, in comparison to the wavelength, the size of the eigenvalue problem increases
with increasing depth. A modified version of the TLM is proposed in this work to reduce the
computational effort of the related eigenvalue problem.
This dissertation work led to the development of a Fortran computer code capable of simulating
wave propagation in two-dimensional soil media models with either structured or unstructured
triangular mesh grids. This latter option allows considering soil-structure problems with geometrical
complexities, different soil layering configurations and various loading conditions.
The pre- and post-processing as well as the analysis stages are all user friendly and easy
Conception et réalisation d’un Robot mobile télécommandé à base de la PCDUINO V3
No full text51 f. : ill. ; 30 cm. (+ CD-Rom)Résumé Un robot mobile est un système mécanique, électronique et informatique agissant physiquement sur son environnement en vue d'atteindre un objectif qui lui a été assigné. Cette machine est polyvalente et capable de s'adapter à certaines variations de ses conditions de fonctionnement. Elle est dotée de fonctions de perception, de décision et d'action. Ainsi, le robot devrait être capable d'effectuer des tâches diverses, de plusieurs manières, et accomplir correctement sa tâche, même s'il rencontre de nouvelles situations inattendues. Ce projet concerne la conception, la réalisation et la commande d'un robot mobile à chenille à l'aide des cartes électroniques" Arduino et pcDuino"
Subsea pipes under high-mass low-velocity impacts
No full textSubsea steel pipes are often used to form networks for transporting oil and gas over large distances. Such pipes can potentially be subjected to actions characterised by high loading rates and intensities stemming from accidental loads caused by high-mass low-velocity impacts. In order to ensure that such networks can continue to operate after being subjected to such extreme loading conditions, it is essential that the behaviour of the pipes is characterised by a certain level of resilience. The short duration and high intensity that often characterises impact loads can potentially result in large strain-rates being exhibited within the pipes. To study the effects of the loading-rate on the material behaviour of steel and identify the causes that trigger the experimentally observed shift in specimen behaviour with increasing loading rates compared to that established under equivalent static testing, a review of the relevant experimental evidence is carried out. A review reveals that the specimen behaviour is significantly affected by the developing inertia forces and the interaction with the experimental setup. This suggests that the available test data describes structural rather than material behaviour, thus raising concerns regarding the validity of current practices to employ such data for the development of constitutive models capable of predicting material behaviour under high loading rates.
A numerical study is carried out investigating the behaviour exhibited by steel pipes under impact loading, accompanied by a limited number of drop-weight tests. The numerical predictions, which are validated against relevant test data reveal that number of parameters associated with the characteristics of the impacting object, the geometry and the support conditions of the pipes, the level of axial loading as well as the level of internal and external pressure imposed onto the walls of the pipes can significantly affect, often detrimentally, the exhibited behaviour under impact loading. Existing assessment methods employed in practice for predicting the level of damage sustained by pipes during impact do not accurately consider the effect of the above parameters. As a result questions rise concerning their ability to realistically predict the level of damage sustained by such pipes under impact. The numerical predictions are presented in the form of simple diagrams quantifying the individual and combined effect of the above parameters on the level of damage sustained by the pipes when subjected to impact. The latter predictions can potentially form the basis for the development of more advanced analysis methods suitable for practice and leading to the development of more effective design solutions capable of safeguarding the intended level of resilience required to characterise the behaviour of subsea pipes. Finally, it is shown that the use of coatings, constructed from reinforced concrete or engineered cementitious composites, can potentially further reduce the level of damage sustained by pipes due to impact loading, however, further – more detailed – studies are required in order to accurately quantify these benefits
Identification of major ion chemistry and associated hydrogeochemical processes in the groundwater environment in Bangladesh
No full textDetailed hydrogeochemical investigations were carried out in four areas selected from south to north of Bangladesh such as, Lakshmipur District in the southern part, Faridpur and Nawabganj Districts in the central part and North Bengal in the northern part of the country with the main objective to detect and delineate the major hydrogeochemical processes that are responsible for groundwater chemistry in Bangladesh. The study approach includes geochemical analysis, graphical plots and analysis of the hydrochemical data to assess the geochemical evaluation of aquifer system based on the ionic constituents, water types, hydrochemical processes etc. Derived Gibbs diagrams reveal that the overall hydrogeochemical environment of the study areas is controlled by the rock water interaction dominance. Further analyses with Piper diagrams show that the hydrogeochemical facies in Lakshmipur and Faridpur is mostly Ca–Mg–HCO3 type, though other type waters (Na–HCO3, Na–Cl and Mg–Cl) also observed in Lakshmipur and the hydrogeochemical facies in Nawabganj and North Bengal is mostly Ca–HCO3 type though other type waters (Na–HCO3, Na–Cl and Ca–Cl) also observed in North Bengal. In addition, various relationships related to carbonate dissolution and silicate weathering process support that in all four areas silicate weathering is dominating. The cation exchange process controls the concentration of ions and confirms that Ca, Mg and Na concentrations in groundwater are derived from aquifer minerals. The concentrations of sulfate in the groundwater are very low throughout the study areas indicating sulfate reduction. All of these results suggest that weathering and dissolution of silicate minerals, cation exchange processes, rock-water interaction, sulfate reduction etc. are responsible for the groundwater chemistry in Bangladesh regardless of different geologic formation. Thus, the present study and analysis techniques can be useful as an effective tool in groundwater aquifer system evaluation
Enriched finite elements for the solution of hyperbolic PDEs
No full textThis doctoral research endeavors to reduce the computational cost involved in the
solution of initial boundary value problems for the hyperbolic partial differential
equation, with special functions used to enrich the solution basis for highly oscillatory solutions. The motivation for enrichment functions is derived from the fact that
the typical solutions of the hyperbolic partial differential equations are wave-like in
nature. To this end, the nodal coefficients of the standard finite element method
are decomposed into plane waves of variable amplitudes. These plane waves form
the basis for the proposed enrichment method, that are used for interpolating the
solution over the elements, and thus allow for a coarse computational mesh without
jeopardizing the numerical accuracy.
In this research, the time dependant wave problem is established into a semi-discrete
finite element formulation. Both implicit as well as explicit discretization schemes
are employed for temporal integration. In either approach, the assembled system
matrix needs to be inverted only at the first time step. This inverted matrix is
then reused in the subsequent time steps to update the numerical solution with
evolution of time. The implicit approach provides unconditional stability, whereas
the explicit scheme allows lumping the mass matrix into blocks that are cheaper
to invert as opposed to the consistent mass matrix. These methods are validated
with several numerical examples. A comparison of the performances of the implicit
and the explicit schemes, in conjunction with the enriched finite element basis, is
presented. Numerical results are also compared to gauge the performance of the enriched approach against the standard polynomial based finite element approaches.
Industrially relevant numerical examples are also studied to illustrate the utility of
the numerical methods developed through this research
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