1,721,003 research outputs found
Non-reflecting boundary conditions and tensile instability in smooth particle hydrodynamics
Get PDFThis thesis aimed at the understanding and further development of
smoothed particle hydrodynamics (SPH). The first part described the
implementations of non-reflecting boundary conditions for elastic-
waves in SPH. The second part contains a stability analysis of the
semi-discrete SPH equations and a new method for stabilising basic
SPH in tension
Modelling of Damage in Orthotropic Materials: Including Strain-Softening Effects in Dynamic Problems
Get PDFDamage models are developed within the continuum damage mechanics framework
which allows the description of material degeneration with general constitutive
equations. The difficulty in the description of damage behaviour increases with
increasing complexity of the material behaviour. This is especially true when it comes
to composite materials which have an orthotropic material behaviour. The conventional
description of damage, i.e. the local continuum damage mechanics description, leads
to strain-softening behaviour which is characterised by a decline in stress with
simultaneously increasing strain.
Due to strain-softening the tangent stiffness becomes negative which forces the wave
speed to become imaginary in dynamic problems. Consequently the partial differential
equations governing the dynamic problem change from hyperbolic to elliptic and,
therefore, the initial boundary value problem no longer has a unique solution. Due to
this the physical meaning becomes unrealistic. Strain-softening is limited to an infinitely
small area in which waves are not able to propagate in a process called wave trapping.
A displacement discontinuity in an area of width zero (localisation zone) develops. The
strain becomes infinite in this zone and is accompanied with a zero stress. Areas
outside the softening zone are not able to interact with the strain-softening domain. As
a consequence the strain-softening domain acts similar to a free boundary at which
waves reflect. The implementation of local continua with strain-softening behaviour in
finite element codes leads to additional numerical problems. Strain-softening behaviour
manifests itself in the smallest area possible which is a single point in analytical
considerations. This area is defined by the element discretisation in finite element
codes. Therefore, strain-softening leads to a pronounced mesh sensitivity of results in
addition to mathematical and physical issues.
This work aims to find a solution which removes problems associated to strain-
softening. Its aim is to represent material behaviour due to damage realistically and
enable numerical results to convergence to a unique solution.
The strain-softening problem is the focus of this work. It was investigated using a 1D
wave propagation problem described by Bažant and Belytschko [1]. This simple
experiment allows for an easy comparison of analytical and numerical results and
therefore gives an insight into the problems connected to strain-softening.
Furthermore, regularisation methods, specifically nonlocal and viscous methods, were
investigated. Regularisation methods add additional terms to constitutive equations
which keep the initial boundary value problem well-posed and enable a unique solution
independent of the element discretisation. It was found that these methods are indeed
capable of regulating the softening problem; however, they add additional difficulties in
the description of material behaviour.
A new approach to the strain-softening issues, unique at this point of time, was
developed in this work which implements damage as an equivalent damage force. This
approach is able to keep the initial boundary value problem stable and converge to a
unique solution without adding additional terms in the constitutive equations, such as
regularisation methods. This new approach to strain-softening was implemented for an
isotropic material with scalar damage variable in DYNA3D successfully. Numerical
results converged to a unique solution and were physically reasonable. The concept of
an equivalent damage force was further developed to orthotropic material behaviour.
This made an advanced representation, using an 8th rank damage tensor, necessary.
The 8th rank damage tensor is able to represent anisotropic damage and it is also the
most general damage representation possible
Dynamic analysis and control system design of a deployable space robotic manipulator
Get PDFThis thesis presents a dynamic analysis and a control system for a flexible space
manipulator, the Deployable Robotic Manipulator or DRM, which has a
deployable/retractable link. The link extends (or retracts) from the containing slewing
link of the manipulator to change the DRM's length and hence its workspace. This
makes the system dynamics time varying and therefore any control strategy has to adapt
to this fact. The aim of the control system developed is to slew the manipulator through
a predetermined angle given a maximum angular acceleration, to reduce flexural
vibrations of the manipulator and to have a certain degree of robustness, all of this while
carrying a payload and while the length of the manipulator is changing. The control
system consists of a slewing motor that rotates the manipulator using the open-loop
assumed torque method and two reaction wheel actuators, one at the base and one at the
tip of the manipulator, which are driven by a closed-loop damping control law. Two
closed-loop control laws are developed, a linear control law and a Lyapunov based
control law. The linear control law is based on collocated output feedback. The
Lyapunov control law is developed for each of the actuators using Lyapunov stability
theory to produce vibration control that can achieve the objectives stated above for
different payloads, while the manipulator is rotating and deploying or retracting. The
response of the system is investigated by computer simulation for two-dimensional
vibrations of the deployable manipulator. Both the linear and Lyapunov based feedback
control laws are found to eliminate vibrations for a range of payloads, and to increase the
robustness of the slewing mechanism to deal with uncertain payload characteristics
Fracture toughness characterization of thin Ti/SiC composites
Get PDFTitanium based alloys reinforced uniaxially with silicon carbide fibres (Ti/SiC)
are advanced and innovative materials for aerospace vehicles. To avoid
potential problems, these new materials should be extensively tested and
analyzed before application.
This research focuses on experimental fracture toughness study on 0.5 mm
thick Ti/SiC composite materials for aerospace applications. The fracture
toughness tests are mainly based on BS 7448 with some modifications for
transversely isotropic behaviour of the composite materials.
By loading on specimens in the direction perpendicular to the fibre axis, three
critical values of fracture toughness parameters characterizing fracture
resistance of material, plane strain fracture toughness [Plane strain fracture toughness
}, critical crack tip
opening displacement [Critical crack tip opening displacement
] and critical J-integral [Critical at the onset of brittle crack extension or pop-in when
Δa is less than 0.2 mm.
]are measured for two
kinds of titanium alloy specimens and three kinds of Ti/SiC composites
specimens.
The values of [Provisional value of Plane strain fracture toughness
] obtained from the fracture toughness tests are not valid [Plane strain fracture toughness
]
for these materials, since the thickness of specimens is insufficient to satisfy the
minimum thickness criterion; however, the results could be used as particular
critical fracture toughness parameter for 0.5 mm thick structures of the materials.
The valid values of [Critical J at the onset of brittle crack extension or pop-in when
Δa is less than 0.2 mm.
] and [Critical crack tip opening displacement
] could be used as fracture toughness
parameters for all thickness of structures of the materials. The results also show
that: fracture toughness of the titanium alloys decreases dramatically after being
unidirectional reinforced with SiC fibre, which is mainly triggered by poor
fibre/matrix bonding condition. Moreover, Ti-Al3-V2.5 reinforced with 25%
volume fraction SiC fibre performs better than the other two composites in
fracture resistance
Experimental and numerical investigation on the bird impact resistance of novel composite sandwich panels
Get PDFBird strikes represent a major hazard to the aerospace composite structures, due to their low impact resistance. Accurate selection and lay up of the materials in the composite structure can significantly improve the out of plane properties of the composites. However, application of the complex hybrid sandwich composites into bird strike proof structures was not investigated yet. Therefore, this work was focused on the soft body impact resistance of a novel composite design for aerospace applications. The investigation was divided into experimental and modelling parts.
In the beginning of this thesis, the numerical techniques for modelling of bird im¬pact and composite materials were studied. The theoretical background for the corresponding issue was provided, followed by the thorough validation of the exist¬ing numerical approaches.
A Smooth Particle Hydrodynamic (SPH) method was chosen for the modelling of the soft body. This modelling technique was validated against experimental data for the rotating fan blade. Three parametric studies of bird impacting fan blades revealed strong influence of the bird impact location and timing on the final deformed shape of the blade. Moreover, it was proved that the SPH is capable of reproducing the exact load on the structure and is appropriate technique for modelling bird strikes. [...cont.
Vibration analysis of compressor blade tip-rubbing
Get PDFThere has been a significant increase in air traffic volume, particularly over the past twenty years. In order to cope with this increase in demand, it has been necessary to increase the efficiency of aircraft engines. Over the years, this has been achieved by reducing the clearance between blade tips and the engine casing. As a consequence of the reduced clearance, tip-rubbing frequently occurs in the engine during operation.
The primary aim of this project is to address the vibrations involved in a tip-rubbing phenomenon when a blade of the Intermediate Pressure (IP) compressor in a Trent 900 engine interacts with the casing. Current trends towards blade optimisation tend to make the blade thinner and thus more flexible; therefore, it is very important to be able to successfully predict and prevent nonlinear response of a blade when tip-rubbing occurs. Current literature on the study of nonlinear vibration of a blade in a tip-rub event is limited; this project is understood to be the first to attempt an understanding of the issue.
In this thesis, analytical models are presented that predict the nonlinear responses of rotor-stator interactions. These are helpful in understanding nonlinear parameters that can have an effect on the system response. Simulations were started by determining the stresses in the blade due to centrifugal rotation. Resonant frequencies of the blade were determined by modal analysis. Finally, the tip-rubbing event was simulated. The results were used to output frequency response curves which were used to identify if the blades were behaving nonlinearly as a result of tip-rubbing.
The primary conclusion from this project is that tip-rubbing can excite nonlinear vibration in the compressor blades. However, the simulation results were affected adversely by hourglassing of the casing segments and should not be considered completely accurate
Hydrocode modelling of water impact
Get PDFThis thesis addresses the problem of hydrocode modelling of water impact. Two facets
that are of importance when numerically modelling the impact of metallic structures on
water are metal anisotropy and water behaviour during impact. In order to be able to
take account of these effects in a hydrocode simulation an SPH solver has been
incorporated into LLNL-DYNA3D. The treatment of contact in meshless methods has
been addressed through the development of a contact algorithm which does not require
the construction of surfaces. The interaction of finite elements and SPH particles is
accounted for by using a novel approach in treating the finite element nodes as particles
in the contact treatment. The same contact algorithm developed for the treatment of
contact in the SPH method has been used. In order to take account of metal anisotropy
a material model that takes account of anisotropy in the elastic and plastic regimes,
strain-rate dependency and non-linear behaviour at high pressures including spall failure
was developed.
The developed simulation tool is validated against experimental data for the case of
water impact of rigid cylinders on water. Further validation is achieved by
demonstrating that the simulation tool can be used to analyse the crash behaviour of
subfloor designs on water. This was achieved by simulating the impact on water of a
structure representative of an aircraft subfloor. The effect of material anisotropy, skin
thickness and skin failure on the structural response was demonstrated.
A first step in extending the coupled FE-SPH modelling beyond fluid-structure
interaction problems has been the development and validation of an explicit time
integration ID Lagrangian kernel SPH code which in combination with an algorithm to
track crack propagation would make the simulation of dynamic brittle fracture problems
possible
Towards better understanding of the Smoothed Particle Hydrodynamic Method
Get PDFNumerous approaches have been proposed for solving partial differential equations; all these
methods have their own advantages and disadvantages depending on the problems being treated. In
recent years there has been much development of particle methods for mechanical problems.
Among these are the Smoothed Particle Hydrodynamics (SPH), Reproducing Kernel Particle
Method (RKPM), Element Free Galerkin (EFG) and Moving Least Squares (MLS) methods. This
development is motivated by the extension of their applications to mechanical and engineering
problems.
Since numerical experiments are one of the basic tools used in computational mechanics, in
physics, in biology etc, a robust spatial discretization would be a significant contribution towards
solutions of a number of problems. Even a well-defined stable and convergent formulation of a
continuous model does not guarantee a perfect numerical solution to the problem under
investigation.
Particle methods especially SPH and RKPM have advantages over meshed methods for problems,
in which large distortions and high discontinuities occur, such as high velocity impact,
fragmentation, hydrodynamic ram. These methods are also convenient for open problems. Recently,
SPH and its family have grown into a successful simulation tools and the extension of these
methods to initial boundary value problems requires further research in numerical fields.
In this thesis, several problem areas of the SPH formulation were examined. Firstly, a new approach based on ‘Hamilton’s variational principle’ is used to derive the equations of motion in the SPH form. Secondly, the application of a complex Von Neumann analysis to SPH method reveals the
existence of a number of physical mechanisms accountable for the stability of the method. Finally, the notion of the amplification matrix is used to detect how numerical errors propagate permits the identification of the mechanisms responsible for the delimitation of the domain of numerical stability.
By doing so, we were able to erect a link between the physics and the numerics that govern the SPH formulation
Development of a total Lagrangian SPH code for the simulation of solids under dynamioc loading
Get PDFThis thesis makes use of an alternative SPH formulation, the Total
Lagrangianf ormulation, to characterised ynamic eventsi n solids and to achieve
the proposed objectives outlined in Chapter 1. The structure is as follows:
Chapter 1, Introduction, describes the motivation for this research and
outlines the objectives and the structure of this thesis.
Chapter 2, SPH fundamentals, supplies the standard procedure to
generate particle equations and provides a comprehensive summary of gradient
approximation formulae in SPH. The discretised SPH form of the conservation
laws is included here.
Chapter 3, SPH drawbacks: describes the limitations of SPH such as
particle deficiency, consistency, zero energy modes, treatment of boundaries
and the tensile instability problem. A rigorous stability analysis of continua and
SPH particle equations is also presented in this chapter.
Chapter 4, Total Lagrangian SPH. Continuum Mechanics considerations
are discussed here; detailed derivations of SPH equations in a total Lagrangian
framework are given together with potential corrections to the total Lagrangian
SPH equations.
Chapter 5, Total Lagrangian SPH algorithms and their implementation
using FORTRAN. This chapter gives a brief introduction to explicit codes. It
also provides flow charts describing the Total Lagrangian algorithms and their
integration into the MCM code.
Chapter 6, Total Lagrangian SPH code validation. This chapter includes
problems of varying degrees of complexity. Examples are provided to illustrate
how the Total Lagrangian SPH code compares to a conventional collocational
SPH code. Cases are supplied for which the analytical solution is known, and
the results compared with the SPH approximations in order to show the accuracy of the approximation. Some examples are supplied which provide a
direct comparison between SPH and non linear FE results and SPH and
experimental results.
Chapter 7, Alternative formulation of SPH equations and improvements
to the standard MCM code: Various modifications to the standard SPH code are
presented. These modifications include the implementation of subroutines that
make use of an alternative approach to ensure the conservation of mass law is
met locally at every particle. The introduction of XSPH to achieve further
stabilisation of the code was also carried out and some examples are provided.
The theory behind an alternative form of the conservation of mass equation as
proposed by Belytschko [4] is explained and its implementation into the SPH
code is assessed through examples. Also, an alternative formulation of SPH
equations based on the general theory of mixed Lagrangian-Eulerian
formulations [35] is presented: these equations could serve as the foundation for
future research in this field.
Chapter 8, Conclusions are presented in this chapter.
A brief literature review is provided at the beginning of each chapter as a
means of introduction to the topic and a concise summary outlines the main
points discussed
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