579 research outputs found
Ionization dynamics in intense pulsed laser radiation. Effects of frequency chirping
Via a non-perturbative method we study the population dynamics and
photoelectron spectra of Cs atoms subject to intense chirped laser pulses, with
gaussian beams. We include above threshold ionization spectral peaks. The
frequency of the laser is near resonance with the 6s-7p transition. Dominant
couplings are included exactly, weaker ones accounted for perturbatively. We
calculate the relevant transition matrix elements, including spin-orbit
coupling. The pulse is taken to be a hyperbolic secant in time and the chirping
a hyperbolic tangent. This choice allows the equations of motions for the
probability amplitudes to be solved analytically as a series expansion in the
variable u=(tanh(pi t/tau)+1)/2, where tau is a measure of the pulse length. We
find that the chirping changes the ionization dynamics and the photoelectron
spectra noticeably, especially for longer pulses of the order of 10^4 a.u. The
peaks shift and change in height, and interference effects between the 7p
levels are enhanced or diminished according to the amount of chirping and its
sign. The integrated ionization probability is not strongly affected.Comment: Accepted by J. Phys. B; 18 pages, 17 figures. Latex, uses
ioplppt.sty, iopl10.sty and psfig.st
Femtosecond parabolic pulse shaping in normally dispersive optical fibers
Formation of parabolic pulses at femtosecond time scale by means of passive nonlinear reshaping in normally dispersive optical fibers is analyzed. Two approaches are examined and compared: the parabolic waveform formation in transient propagation regime and parabolic waveform formation in the steady-state propagation regime. It is found that both approaches could produce parabolic pulses as short as few hundred femtoseconds applying commercially available fibers, specially designed all-normal dispersion photonic crystal fiber and modern femtosecond lasers for pumping. The ranges of parameters providing parabolic pulse formation at the femtosecond time scale are found depending on the initial pulse duration, chirp and energy. Applicability of different fibers for femtosecond pulse shaping is analyzed. Recommendation for shortest parabolic pulse formation is made based on the analysis presented
CONTINUUM DAMAGE MODEL FOR NONLINEAR ANALYSIS OF MASONRY STRUCTURES
The present work focuses on the formulation of a Continuum Damage Mechanics
model for nonlinear analysis of masonry structural elements. The material is
studied at the macro-level, i.e. it is modelled as a homogeneous orthotropic
continuum.
The orthotropic behaviour is simulated by means of an original methodology,
which is based on nonlinear damage constitutive laws and on the concept of
mapped tensors from the anisotropic real space to the isotropic fictitious one. It is
based on establishing a one-to-one mapping relationship between the behaviour of
an anisotropic real material and that of an isotropic fictitious one. Therefore, the
problem is solved in the isotropic fictitious space and the results are transported to
the real field. The application of this idea to strain-based Continuum Damage
Models is rather innovative.
The proposed theory is a generalization of classical theories and allows us to use
the models and algorithms developed for isotropic materials. A first version of the
model makes use of an isotropic scalar damage model. The adoption of such a
simple constitutive model in the fictitious space, together with an appropriate definition of the mathematical transformation between the two spaces, provides a
damage model for orthotropic materials able to reproduce the overall nonlinear
behaviour, including stiffness degradation and strain-hardening/softening response.
The relationship between the two spaces is expressed in terms of a transformation
tensor which contains all the information concerning the real orthotropy of the
material. A major advantage of this working strategy lies in the possibility of
adjusting an arbitrary isotropic criterion to the particular behaviour of the
orthotropic material. Moreover, orthotropic elastic and inelastic behaviours can be
modelled in such a way that totally different mechanical responses can be predicted
along the material axes.
The aforementioned approach is then refined in order to account for different
behaviours of masonry in tension and compression. The aim of studying a real
material via an equivalent fictitious solid is achieved by means of the appropriate
definitions of two transformation tensors related to tensile or compressive states,
respectively. These important assumptions permit to consider two individual
damage criteria, according to different failure mechanisms, i.e. cracking and
crushing. The constitutive model adopted in the fictitious space makes use of two
scalar variables, which monitor the local damage under tension and compression,
respectively. Such a model, which is based on a stress tensor split into tensile and
compressive contributions that allows the model to contemplate orthotropic
induced damage, permits also to account for masonry unilateral effects. The
orthotropic nature of the Tension-Compression Damage Model adopted in the
fictitious space is demonstrated. This feature, both with the assumption of two
distinct damage criteria for tension and compression, does not permit to term the
fictitious space as “isotropic”. Therefore, the proposed formulation turns the
original concept of “mapping the real space into an isotropic fictitious one” into
the innovative and more general one of “mapping the real space into a favourable (or convenient) fictitious one”. Validation of the model is carried out by means of
comparisons with experimental results on different types of orthotropic masonry.
The model is fully formulated for the 2-dimensional case. However, it can be easily
extended to the 3-dimensional case. It provides high algorithmic efficiency, a
feature of primary importance when analyses of even large scale masonry
structures are carried out. To account for this requisite it adopts a strain-driven
formalism consistent with standard displacement-based finite element codes. The
implementation in finite element programs is straightforward.
Finally, a localized damage model for orthotropic materials is formulated. This is
achieved by means of the implementation of a crack tracking algorithm, which
forces the crack to develop along a single row of finite elements. Compared with
the smeared cracking approach, such an approach shows a better capacity to predict
realistic collapsing mechanisms. The resulting damage in the ultimate condition
appears localized in individual cracks. Moreover, the results do not suffer from
spurious mesh-size or mesh-bias dependence. The numerical tool is finally
validated via a finite element analysis of an in-plane loaded masonry shear wall
Behavior of Narrow Mechanically Stabilized Earth Walls with Secondary Reinforcement
Mechanically Stabilized Earth (MSE) walls have been used in past decades as an alternative, cost-effective, and performance solution to replace conventional retaining walls. AASHTO guidelines recommend a reinforcement length-to-height ratio of 0.7. However, this ratio is not applicable where there exist constraint conditions. FHWA guidelines recommend the minimum reinforcement length-to-height ratio of 0.3 for Narrow Mechanically Stabilized Earth (NMSE) walls in these cases. However, published guidelines have not sufficiently accounted for several parameters influencing NMSE performance and efficiency. Using finite element analysis (PLAXIS 2D), this study focuses on finding a relation between the length-to-height ratio and other parameters/components of the NMSE walls that influence the behavior and structure of NMSE walls. Moreover, length-to-height ratios from 0.3 to 0.5 were targeted, and effects of secondary reinforcement layers were applied. With a proposed reinforcement configuration, the lateral displacement can be reduced significantly and the amount of reinforcement material to be used
Advanced geotechnical characterisation to support driven pile design at chalk sites
Research is described that contributes to a major effort to improve current shortfalls in knowledge regarding pile driving, ageing, static and cyclic response under axial and lateral loading in chalk. More reliable design guidelines are needed urgently for offshore wind power, port, flood protection, high-speed rail and other applications. The ALPACA and ALPACA Plus joint industry projects aim to develop such new approaches through field testing at St Nicholas at Wade in Kent, UK. This Thesis describes the Author’s contributions.
The main area considered is the projects’ intensive site characterisation through high quality sampling, in-situ and advanced laboratory testing. However, the Thesis also contributes a substantial analysis of pile tests conducted by other industrial consortia on steel driven piles in chalk at other sites in France, Germany and the UK, considering a wider range of pile geometries, chalk types, sites’ corrosion chemistry and geographical locations, while also allowing the evaluation of existing procedures for calculating driving resistances and axial capacities. After reviewing the outcomes from these parallel test programmes, the Thesis moves to describe the stratigraphy, structure and mechanical properties of the low-to-medium density chalk encountered at the ALPACA piling site, in research that underpins the field experiments’ interpretation and is central to their representative modelling.
The experimental characterisation of the chalk identified aspects of behaviour that require careful attention when undertaking numerical analysis to model practical problems including the chalk’s marked sensitivity, brittleness, pressure dependency and anisotropy, as well as strain rate dependency. A clear hierarchy was found between profiles of peak strength with depth of Brazilian tension (BT), drained and undrained triaxial and direct simple shear (DSS) tests conducted from in-situ stress conditions. Highly instrumented triaxial tests revealed the chalk’s unusual effective stress paths, markedly brittle failure behaviour from small strains and the effects of consolidating to higher than in-situ stresses. The chalk’s structure, consisting of mainly sub-vertical joints, leads to varying properties dependent on specimen scale and in-situ stiffnesses falling significantly below equivalent laboratory measurements. The joints also promote stiffness anisotropy. Horizontal shear and Young’s modulus profiles fall well below the corresponding vertical trends. While vertical compressive strength and stiffness values are relatively insensitive to the applied effective stress levels, consolidation to higher pressures tends to close micro-fissures and reduces stiffness anisotropy. Additional laboratory research was incorporated that examined hypotheses regarding the role of corrosion in affecting the ALPACA pile field experiments, comprising mass loss and electrochemical experiments, as well as steel-chalk interface shear tests with different combinations of types of steel and chalk pore water chemistry. The corrosion reaction rates declined with time, were far faster with oxidizable steels when given access to air and faster still with saline water. The chalk’s dilation characteristics depended strongly on testing procedure, interface surface roughness, steel grade and the associated physiochemical interactions.
The contributions described proved vital to the interpretation and analysis of the time-dependent, axial and lateral, static and cyclic behaviour observed in the 41 piles driven and tested as part of the ALPACA and ALPACA Plus projects.Open Acces
An Assessment to Benchmark the Seismic Performance of a Code-Conforming Reinforced-Concrete Moment-Frame Building
This report describes a state-of-the-art performance-based earthquake engineering methodology
that is used to assess the seismic performance of a four-story reinforced concrete (RC) office
building that is generally representative of low-rise office buildings constructed in highly seismic
regions of California. This “benchmark” building is considered to be located at a site in the Los
Angeles basin, and it was designed with a ductile RC special moment-resisting frame as its
seismic lateral system that was designed according to modern building codes and standards. The
building’s performance is quantified in terms of structural behavior up to collapse, structural and
nonstructural damage and associated repair costs, and the risk of fatalities and their associated
economic costs. To account for different building configurations that may be designed in
practice to meet requirements of building size and use, eight structural design alternatives are
used in the performance assessments.
Our performance assessments account for important sources of uncertainty in the ground
motion hazard, the structural response, structural and nonstructural damage, repair costs, and
life-safety risk. The ground motion hazard characterization employs a site-specific probabilistic
seismic hazard analysis and the evaluation of controlling seismic sources (through
disaggregation) at seven ground motion levels (encompassing return periods ranging from 7 to
2475 years). Innovative procedures for ground motion selection and scaling are used to develop
acceleration time history suites corresponding to each of the seven ground motion levels.
Structural modeling utilizes both “fiber” models and “plastic hinge” models. Structural
modeling uncertainties are investigated through comparison of these two modeling approaches,
and through variations in structural component modeling parameters (stiffness, deformation
capacity, degradation, etc.). Structural and nonstructural damage (fragility) models are based on
a combination of test data, observations from post-earthquake reconnaissance, and expert
opinion. Structural damage and repair costs are modeled for the RC beams, columns, and slabcolumn connections. Damage and associated repair costs are considered for some nonstructural
building components, including wallboard partitions, interior paint, exterior glazing, ceilings,
sprinkler systems, and elevators. The risk of casualties and the associated economic costs are
evaluated based on the risk of structural collapse, combined with recent models on earthquake
fatalities in collapsed buildings and accepted economic modeling guidelines for the value of
human life in loss and cost-benefit studies.
The principal results of this work pertain to the building collapse risk, damage and repair
cost, and life-safety risk. These are discussed successively as follows.
When accounting for uncertainties in structural modeling and record-to-record variability
(i.e., conditional on a specified ground shaking intensity), the structural collapse probabilities of
the various designs range from 2% to 7% for earthquake ground motions that have a 2%
probability of exceedance in 50 years (2475 years return period). When integrated with the
ground motion hazard for the southern California site, the collapse probabilities result in mean
annual frequencies of collapse in the range of [0.4 to 1.4]x10
-4
for the various benchmark
building designs. In the development of these results, we made the following observations that
are expected to be broadly applicable:
(1) The ground motions selected for performance simulations must consider spectral
shape (e.g., through use of the epsilon parameter) and should appropriately account for
correlations between motions in both horizontal directions;
(2) Lower-bound component models, which are commonly used in performance-based
assessment procedures such as FEMA 356, can significantly bias collapse analysis results; it is
more appropriate to use median component behavior, including all aspects of the component
model (strength, stiffness, deformation capacity, cyclic deterioration, etc.);
(3) Structural modeling uncertainties related to component deformation capacity and
post-peak degrading stiffness can impact the variability of calculated collapse probabilities and
mean annual rates to a similar degree as record-to-record variability of ground motions.
Therefore, including the effects of such structural modeling uncertainties significantly increases
the mean annual collapse rates. We found this increase to be roughly four to eight times relative
to rates evaluated for the median structural model;
(4) Nonlinear response analyses revealed at least six distinct collapse mechanisms, the
most common of which was a story mechanism in the third story (differing from the multi-story
mechanism predicted by nonlinear static pushover analysis);
(5) Soil-foundation-structure interaction effects did not significantly affect the structural
response, which was expected given the relatively flexible superstructure and stiff soils.
The potential for financial loss is considerable. Overall, the calculated expected annual
losses (EAL) are in the range of 97,000 for the various code-conforming benchmark
building designs, or roughly 1% of the replacement cost of the building (3.5M, the fatality rate translates to an EAL due to
fatalities of 5,600 for the code-conforming designs, and 66,000, the monetary value associated with life loss is small,
suggesting that the governing factor in this respect will be the maximum permissible life-safety
risk deemed by the public (or its representative government) to be appropriate for buildings.
Although the focus of this report is on one specific building, it can be used as a reference
for other types of structures. This report is organized in such a way that the individual core
chapters (4, 5, and 6) can be read independently. Chapter 1 provides background on the
performance-based earthquake engineering (PBEE) approach. Chapter 2 presents the
implementation of the PBEE methodology of the PEER framework, as applied to the benchmark
building. Chapter 3 sets the stage for the choices of location and basic structural design. The subsequent core chapters focus on the hazard analysis (Chapter 4), the structural analysis
(Chapter 5), and the damage and loss analyses (Chapter 6). Although the report is self-contained,
readers interested in additional details can find them in the appendices
Triangular Recurrences, Generalized Eulerian Numbers, and Related Number Triangles
Many combinatorial and other number triangles are solutions of recurrences of
the Graham-Knuth-Patashnik (GKP) type. Such triangles and their defining
recurrences are investigated analytically. They are acted on by a
transformation group generated by two involutions: a left-right reflection and
an upper binomial transformation, acting row-wise. The group also acts on the
bivariate exponential generating function (EGF) of the triangle. By the method
of characteristics, the EGF of any GKP triangle has an implicit representation
in terms of the Gauss hypergeometric function. There are several parametric
cases when this EGF can be obtained in closed form. One is when the triangle
elements are the generalized Stirling numbers of Hsu and Shiue. Another is when
they are generalized Eulerian numbers of a newly defined kind. These numbers
are related to the Hsu-Shiue ones by an upper binomial transformation, and can
be viewed as coefficients of connection between polynomial bases, in a manner
that generalizes the classical Worpitzky identity. Many identities involving
these generalized Eulerian numbers and related generalized Narayana numbers are
derived, including closed-form evaluations in combinatorially significant
cases.Comment: 62 pages, final version, accepted by Advances in Applied Mathematic
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