U-splines are a novel approach to the construction of a spline basis for representing smooth objects in Computer-Aided Design (CAD) and Computer-Aided Engineering (CAE). A spline is a piecewise-defined function that satisfies continuity constraints between adjacent cells in a mesh. U-splines differ from existing spline constructions, such as Non-Uniform Rational B-splines (NURBS), subdivision surfaces, T-splines, and hierarchical B-splines, in that they can accommodate local variation in cell size, polynomial degree, and smoothness simultaneously over more varied mesh configurations. Mixed cell types (e.g., triangle and tetrahedron and quadrilateral and hexahedral cells in the same mesh) and T-junctions are also supported. The U-spline construction is presented for curves, surfaces, and volumes with higher dimensional generalizations possible. A set of requirements are given to ensure that the U-spline basis is positive, forms a partition of unity, is complete, and is locally linearly independent.

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Yes / Ophthalmologists rely on a device known as the Goldmann applanation tonometer to make intraocular pressure (IOP) measurements. It measures the force required to press a flat disc against the cornea to produce a flattened circular region of known area. The IOP is deduced from this force using the Imbert-Fick principle. However, there is scant analytical justification for this analysis. We present a mathematical model of tonometry to investigate the relationship between the pressure derived by tonometry and the IOP. An elementary equilibrium analysis suggests that there is no physical basis for traditional tonometric analysis. Tonometry is modelled using a hollow spherical shell of solid material enclosing an elastic liquid core, with the shell in tension and the core under pressure. The shell is pressed against a rigid flat plane. The solution is found using finite element analysis. The shell material is anisotropic. Values for its elastic constants are obtained from literature except where data are unavailable, when reasonable limits are explored. The results show that the force measured by the Goldmann tonometer depends on the elastic constant values. The relationship between the IOP and the tonometer readings is complex, showing potentially high levels of inaccuracy that depend on IOP.

Cases of brittle fractures in major bridges prompted AASHTO to publish its first fracture control plan in 1978. It focused on material and fabrication standards, and required periodic 24-month hands-on inspection of bridges with fracture critical members. The practical result of this plan was to significantly increase the life cycle cost of these bridges, rendering them uneconomical. Apart from the Point Pleasant Bridge that failed in 1967, no other bridge has collapsed in the USA following a fracture, even though large fractures have been observed in many other bridges. All these bridges showed some degree of redundancy and therefore could be reclassified as non-fracture critical if detailed analyses are carried out. The goal of this study is to provide guidance on redundancy evaluation of fracture critical bridges, specifically three girder bridges and twin box-girder bridges. The effect of various loading, analysis and geometric parameters on the post fracture response and the remaining load carrying capacity of the damaged bridge is evaluated through nonlinear finite element analysis of two well-documented structures: the Hoan Bridge and the twin box-girder bridge. Parameters such as damping definition, modelling of composite action, modelling of secondary elements, boundary conditions, and rate dependent material properties are found to be crucial in capturing the bridge response. A two-step methodology for system redundancy analysis of fracture critical bridges is proposed, leading to a reclassification of these elements as non-fracture critical for in-service inspection. The first step evaluates bridge capacity to withstand collapse following fracture based on whether the residual deformation is perceivable to people on or off the bridge. If the bridge satisfies the first step requirements, then the reserve load carrying capacity of the damaged bridge is evaluated in the second step. The Hoan Bridge failed to satisfy the proposed requirements in the first step and therefore its girders could not be reclassified as non-fracture critical. The twin box-girder bridge successfully resisted the collapse in two out three loading scenarios and displayed reserve load carrying capacity following full depth fracture in the exterior girder, and therefore can be reclassified as non-fracture critical for in-service inspection. / Ph. D.

Yes / An established statistical mechanical theory of amorphous polymer deformation has been incorporated as a plastic mechanism into a constitutive model and applied to a range of polymer mechanical deformations. The temperature and rate dependence of the tensile yield of PVC, as reported in early studies, has been modeled to high levels of accuracy. Tensile experiments on PET reported here are analyzed similarly and good accuracy is also achieved. The frequently observed increase in the gradient of the plot of yield stress against logarithm of strain rate is an inherent feature of the constitutive model. The form of temperature dependence of the yield that is predicted by the model is found to give an accurate representation. The constitutive model is developed in two-dimensional form and implemented as a user-defined subroutine in the finite element package ABAQUS. This analysis is applied to the tensile experiments on PET, in some of which strain is localized in the form of shear bands and necks. These deformations are modeled with partial success, though adiabatic heating of the instability causes inaccuracies for this isothermal implementation of the model. The plastic mechanism has advantages over the Eyring process, is equally tractable,and presents no particular difficulties in implementation with finite elements. / F. Boutenel acknowledges an Erasmus Programme Scholarship

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