15 research outputs found
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Geometric modelling and shape optimisation of pharmaceutical tablets. Geometric modelling and shape optimisation of pharmaceutical tablets using partial differential equations.
Pharmaceutical tablets have been the most dominant form for drug delivery and they need to be strong enough to withstand external stresses due to packaging and loading conditions before use. The strength of the produced tablets, which is characterised by their compressibility and compactibility, is usually deter-mined through a physical prototype. This process is sometimes quite expensive and time consuming. Therefore, simulating this process before hand can over-come this problem. A technique for shape modelling of pharmaceutical tablets based on the use of Partial Differential Equations is presented in this thesis. The volume and the sur-face area of the generated parametric tablet in various shapes have been es-timated numerically. This work also presents an extended formulation of the PDE method to a higher dimensional space by increasing the number of pa-rameters responsible for describing the surface in order to generate a solid tab-let. The shape and size of the generated solid tablets can be changed by ex-ploiting the analytic expressions relating the coefficients associated with the PDE method.
The solution of the axisymmetric boundary value problem for a finite cylinder subject to a uniform axial load has been utilised in order to model a displace-ment component of a compressed PDE-based representation of a flat-faced round tablet. The simulation results, which are analysed using the Heckel model, show that the developed model is capable of predicting the compressibility of pharmaceutical powders since it fits the experimental data accurately. The opti-mal design of pharmaceutical tablets with particular volume and maximum strength has been obtained using an automatic design optimisation which is performed by combining the PDE method and a standard method for numerical optimisation
BĂ©zier surfaces with prescribed diagonals
The affine space of all tensor product BĂ©zier patches of degree n Ă n with prescribed
main diagonal curves is determined. First, the pair of BĂ©zier curves which can be
diagonals of a BĂ©zier patch is characterized. Besides prescribing the diagonal curves,
other related problems are considered, those where boundary curves or tangent planes
along boundary curves are also prescribed.Funding for open access charge: CRUE-Universitat Jaume
Sensitivity Analysis and Optimization of Aerodynamic Configurations With Blend Surfaces
A novel (geometrical) parametrization procedure using solutions to a suitably chosen fourth order partial differential equation is used to define a class of airplane configurations. Inclusive in this definition are surface grids, volume grids, and grid sensitivity. The general airplane configuration has wing, fuselage, vertical tail and horizontal tail. The design variables are incorporated into the boundary conditions, and the solution is expressed as a Fourier series. The fuselage has circular cross section, and the radius is an algebraic function of four design parameters and an independent computational variable. Volume grids are obtained through an application of the Control Point Form method. A graphic interface software is developed which dynamically changes the surface of the airplane configuration with the change in input design variable. The software is made user friendly and is targeted towards the initial conceptual development of any aerodynamic configurations. Grid sensitivity with respect to surface design parameters and aerodynamic sensitivity coefficients based on potential flow is obtained using an Automatic Differentiation precompiler software tool ADIFOR. Aerodynamic shape optimization of the complete aircraft with twenty four design variables is performed. Unstructured and structured volume grids and Euler solutions are obtained with standard software to demonstrate the feasibility of the new surface definition
Sensitivity Analysis and Optimization of Aerodynamic Configurations with Blend Surfaces
A novel (geometrical) parametrization procedure using solutions to a suitably chosen fourth order partial differential equation is used to define a class of airplane configurations. Inclusive in this definition are surface grids, volume grids, and grid sensitivity. The general airplane configuration has wing, fuselage, vertical tail and horizontal tail. The design variables are incorporated into the boundary conditions, and the solution is expressed as a Fourier series. The fuselage has circular cross section, and the radius is an algebraic function of four design parameters and an independent computational variable. Volume grids are obtained through an application of the Control Point Form method. A graphic interface software is developed which dynamically changes the surface of the airplane configuration with the change in input design variable. The software is made user friendly and is targeted towards the initial conceptual development of any aerodynamic configurations. Grid sensitivity with respect to surface design parameters and aerodynamic sensitivity coefficients based on potential flow is obtained using an Automatic Differentiation precompiler software tool ADIFOR. Aerodynamic shape optimization of the complete aircraft with twenty four design variables is performed. Unstructured and structured volume grids and Euler solutions are obtained with standard software to demonstrate the feasibility of the new surface definition
The geometric design of functional shapes
Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Ocean Engineering, 1997.Includes bibliographical references (p. 101-105).by Todd Robert Jackson.M.S
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Surface modelling for 2D imagery
Vector graphics provides powerful tools for drawing scalable 2D imagery. With
the rise of mobile computers, of different types of displays and image resolutions,
vector graphics is receiving an increasing amount of attention. However, vector
graphics is not the leading framework for creating and manipulating 2D imagery.
The reason for this reluctance of employing vector graphical frameworks is that it
is difficult to handle complex behaviour of colour across the 2D domain.
A challenging problem within vector graphics is to define smooth colour functions
across the image. In previous work, two approaches exist. The first approach,
known as diffusion curves, diffuses colours from a set of input curves and points.
The second approach, known as gradient meshes, defines smooth colour functions
from control meshes. These two approaches are incompatible: diffusion curves do
not support the local behaviour provided by gradient meshes and gradient meshes
do not support freeform curves as input. My research aims to narrow the gap between
diffusion curves and gradient meshes.
With this aim in mind, I propose solutions to create control meshes from freeform
curves. I demonstrate that these control meshes can be used to render a vector
primitive similar to diffusion curves using subdivision surfaces. With the use of
subdivision surfaces, instead of a diffusion process, colour gradients can be locally
controlled using colour-gradient curves associated with the input curves.
The advantage of local control is further explored in the setting of vector-centric
image processing. I demonstrate that a certain contrast enhancement profile, known
as the Cornsweet profile, can be modelled via surfaces in images. This approach
does not produce saturation artefacts related with previous filter-based methods.
Additionally, I demonstrate various approaches to artistic filtering, where the artist
locally models given artistic effects.
Gradient meshes are restricted to rectangular topology of the control meshes. I
argue that this restriction hinders the applicability of the approach and its potential
to be used with control meshes extracted from freeform curves. To this end, I
propose a mesh-based vector primitive that supports arbitrary manifold topology of
the mesh