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The quality of life of patients who wear an orbital prosthesis would be vastly improved if their prostheses were also able to execute vertical and horizontal motion. This requires appropriate actuation and control systems to create an intelligent prosthesis. A method of actuation that meets the demanding design criteria is currently not available. The present work considers an activation system that follows a design philosophy of biomimicry, simplicity and space optimization. While several methods of actuation were considered, shape memory alloys were chosen for their high power density, high actuation forces and high displacements. The behaviour of specific shape memory alloys as an actuator was investigated to determine the force obtained, the transformation temperatures and details of the material processing. In addition, a large-scale prototype was constructed to validate the response of the proposed system.

This paper has experimentally addressed the determination of the convection coefficient for a nichrome and nickel-titanium (NiTi) shape memory alloy (SMA) wire subjected to constant load, heated by electrical current and cooled by free convection (with the current switched off). The entire cycle of actuation is such that the temperature field is allowed to reach a steady state during heating, and the ambient temperature during cooling. The experiments, in conjunction with a phenomenological model, suggest that the convection coefficient can be represented as h = a0 + a1I, where I is the electric current in the wire. The parameter h is highly sensitive to the material (nichrome or SMA) through the zeroth-order coefficient (a0) whereas it is weakly sensitive to I (or the strength of the heat source) through the first-order coefficient (a1). Further, for a given material, h (through a0) is strongly dependent on whether the wire is being heated or cooled. This is in contrast with the customary practice in the literature where h is taken to be identical for heating and cooling. Finally, a simple empirical model in terms of a convection-like parameter, α, is also tested (with a view towards control applications) and is found to be highly accurate in simulating the experimental results.

The thermal and electrical properties of shape memory alloys (SMA) are known to be different in their austenitic and martensitic phases. This paper addresses the determination of the phase-dependent heat capacity, thermal conductivity and electrical resistivity of a SMA wire. While the heat capacity measurements are relatively straightforward using a differential scanning calorimeter, the determination of the thermal conductivity and the electrical resistivity are more difficult in view of the possible non-uniformity in the material state of a SMA wire during a phase transformation. Experimental procedures are developed and used to determine these properties in either phase and, along with a previously developed finite-element code accounting for the non-uniform material states, the austenite and martensite properties are determined from the experimental data. For the SMA wire tested, the thermal conductivities of the austenite and martensite phases are determined to be 2.8×10-2 J (mm S K)-1 and 1.4×10-2 J (mm S K)-1 respectively, a difference of 100%. The electrical resistivities of the austenite and martensite phases are determined to be 8.371×10-4 Ω mm and 9.603×10-4 Ω mm respectively, a difference of about 14.7%.

In this paper, we address the issue of modeling the temperature distribution in a shape memory alloy (SMA) wire with variable thermal and electrical properties. This is done in the context of a one-dimensional (1D) boundary value problem where an initially martensitic SMA wire is electrically heated under zero-stress conditions. The model accounts for an evolution in the thermal conductivity, electrical resistivity and heat capacity during the phase transformation. The evolution in the 1D temperature field is found by implementing a Galerkin-based finite-element method. This is used in combination with a recursive iteration scheme to accurately determine the change in the material properties during a time step. The numerical approach is validated by comparing it with a known analytical solution with variable thermal properties. A parametric study on the SMA phase transformation indicates that, based on the considered values for the material properties, the heat capacity is the least important factor that needs to be accounted for, whereas the electrical resistivity is the most important. It is also demonstrated that the time required to complete a martensite to austenite transformation for a SMA wire subjected to an adiabatic boundary condition is lower if the model accounts for property variations. In fact, when the cyclic response of a SMA wire actuator subjected to an adiabatic boundary condition is the issue at hand, a model that does not account for property variations will predict a lower frequency of actuation than a model that does account for the property variations, as dealt with in this paper.

This paper considers the influence of variable thermal conductivity and electrical resistivity on the cyclic thermal response of a shape memory alloy (SMA) wire. The specific boundary value problem of an SMA wire under zero-stress conditions is considered, wherein the wire, in an initially martensitic state, is heated by electrical current and cooled by convection. An isothermal boundary condition is considered at the ends of the wire. The heating is continued until the transformation from martensite to austenite has essentially taken place. A Galerkin finite element method (FEM)-based numerical approach is used to solve the boundary value problem. The two key parameters of interest are the maximum possible transformation achievable (i.e. extent of actuation) and the time period for one cycle. It is seen that for short wires, the assumption of constant thermal conductivity underestimates the actuation and overestimates the cycle time significantly. The assumption of a constant electrical resistivity does not affect the actuation but significantly overestimates the cycle time. For long wires, the thermal conductivity effect is diminished whereas the electrical resistivity effect is very similar to that for the short wires.

The simplest theory of spatial rods is presented in a variational setting and certain necessary conditions for minimizers of the potential energy are derived. These include the Weierstrass and Legendre inequalities, which require that the vector describing curvature and twist belong to a domain of convexity of the strain energy function.

An experimental apparatus to model the systolic phase of a heartbeat has been developed to investigate the controversy surrounding the cause of high intraventricular pressures for HCM patients. The model, which is two-dimensional, has approximately seven times the volume of an average human heart and operates at Reynolds numbers which are similar to those measured in the left ventricle/aortic arch. Preliminary tests of the model show pressure time relationships similar to those found in vivo.

The determination of all the statically controllable deformations for the classical Kirchhoff-Clebsch theory for three-dimensional deformations of elastic inextensible rods is considered. The analysis shows that the most general deformation is the case in which a rod initially in the shape of a helix is deformed into another helix. The case of planar bending with no twist is also shown to give results that can be obtained from the theory of the planar elastica.

The multiple equilibrium solutions of both deep and shallow inextensible arches is investigated through the use of a segmental shooting technique. The original nonlinear boundary value problem governing the large deformations of these arches is solved using a sequence of linear initial value problems which converge iteratively to the required boundary conditions. This method has proved successful in previous studies to analyse these large deformation problems when there is initially only one unknown at the beginning of the arch that must be assumed. Extension of this method to the problem with two initial unknowns is presented here. In either case all equilibrium solutions can be found in a systematic fashion. When there are three initial unkowns the present method is not able to determine the totality of equilibrium shapes for a given problem and loading. However, in this case, it is possible to determine a number of equilibrium shapes using engineering judgement for the values of the initial unknowns.

To determine whether a relationship exists between the vertical bone depth in the paramedian palate (PP) of growing patients and age, gender, and palatal morphology. Clinically detectable traits may decrease the need for further imaging prior to implant placement for orthodontic anchorage.Cone beam computed tomagraphic scans (Newtom-9000, Verona, Italy) were acquired in 183 orthodontic patients (10-19 years old). Vertical bone depth was measured at nine unilateral locations in the PP of each subject. Measurements were analyzed with univariate and multivariate statistical tests.Significant variability in the bone thickness was found among locations and among subjects. Male subjects had significantly greater mean bone thickness in six of the nine locations measured, showing a mean of 1.22 mm more vertical bone than females showed at these locations. Age and palatal measurements did not demonstrate a clinically useful relationship with bone depth.Age and palatal morphology are not valid predictors of bone height in the PP. Because of the large variability of bone thickness in this region, computed tomographic imaging remains valuable prior to paramedian implant placement in growing individuals. The paramedian palate presents a promising region for palatal implant placements when the midpalatal suture is to be avoided.

While the Periotest continues to be used in assessing the integrity of implants, there are numerous reports of its inconsistencies. To understand more precisely what the Periotest is actually measuring, a mathematical model was developed that illustrates the effect that various geometric and clinical parameters have on the Periotest value (PTV). In addition, the model was validated with an in vitro experiment. Results of the mathematical model are shown to correlate with those obtained from the experimental test The PTV is very sensitive to the position at which the Periotest impacts the abutment and to angulation of the handpiece. It was shown that a change in position of 1 mm in striking height can produce a difference in PTV of between 1 and 2. Since the angulation of the handpiece can produce a difference in striking position of 2 mm, it must be controlled as well. The model also showed that the Periotest can detect changes in bone height of 0.5 mm.

This paper presents an approach of using FIR Median Hybrid Filters for analysis of eye tracking movements. The proposed filter can remove the eye blink artifact from the eye movement signal. The background of the project is described first. The whole idea is to put movements into eyes, which are used as static prosthesis, so that the ocular implant will have the same natural movement as the real eye. First step is to obtain the movement of the real eye. From the review of the eye movement methods, the electro-oculogram (EOG) is used to determine the eye position. Because the eye blink artifact is always corrupted in the EOG signal, it must be filtered out for the purpose of our project. The FIR Median Hybrid Filter is studied in the paper; its properties are explored with examples. Finally the filter is used to deal the real eye blink corrupted EOG signal. Examples are given of analysis procedure for eye tracking or a random moving target. The method is proved to be highly reliable.

Maintenance of the integrity of the abutment/implant interface is essential and is dependent on the abutment screw retaining a preload. Evaluation of this joint is usually done by manual assessment. The purpose of the current study was to determine whether the Periotest instrument could be used to evaluate abutment screw loosening. A custom-designed apparatus was constructed to measure abutment screw loosening. Abutment screws were torqued to 10, 20, 32, and 45 Ncm and then loosened. Objective assessment of screw loosening was carried out with the Periotest device. Subjective evaluation was done by 3 experienced clinicians. The Periotest was found to be more sensitive than manual detection of abutment screw loosening. With a change of 2 in the Periotest value, it was found that the tensile preload in the joint was lost. While the Periotest was more sensitive than manual evaluation, the instrument was not sensitive enough to indicate deterioration of abutment screw loosening prior to loss of tensile preload.

Optimization of a second-order multiply-connected inhomogeneous boundary-value problem was considered in terms of elastic torsion. External boundary and material proportions are the applied constraints in finding optimal internal configurations of the cross section. The optimization procedure is based on the numerical simulation of the membrane analogy and the results obtained indicate that the procedure is usable as an engineering tool. Optimal solutions are obtained for some representative cases of the torsion problem and they are presented in the form of tables and figures.

The small oscillation of a stiffened string about its static equilibrium configuration is studied. The solution requires both the static and dynamic shape of the rod to be determined and since the governing equations do not lend themselves to an analytical solution a Runge-Kutta integration technique was used. Experimental results for the natural frequencies are compared to the numerical solution for a particular stiffened string.

An accurate approximate method for the solution of the generalized plane stress problem of finite elastic deformation of a rotating annular disk is given. The method is applicable to both compressible and incompressible materials. Use of the nonlinear governing differential equation is avoided by considering the disk to be an aggregate of discrete coaxial rings, equations of motion, force balance and compatibility relations being formulated for the rings. Results are given for neo-Hookean disks and disks of a compressible material which has a strain energy function proposed by Blatz and Ko [7].

A method is presented for the analysis of thin rods loaded by concentrated and distributed loads. The technique is also applicable to non-uniform rods. The solution of a nonlinear differential equation is avoided by considering the rod as a series of short rod segments. Each segment undergoes only small strains and small relative rotations so that the differential equation governing its shape is linear and easily solvable. The method is illustrated by two problems; the stiffened caternary and the tapered cantilever under distributed and concentrated loads.

The problem of optimal nonhomogeneity of a bar subjected to Saint-Venant torsion is formulated as a variational problem so that the necessary conditions for optimality may be derived. In this formulation, the shear modulus function G(x,y) which varies in a jumplike manner is to be optimized with the specified composition of two different elastic materials. It is shown in this paper that a prismatic, nonhomogeneous bar can, in fact, be optimized, and the maximum torsional rigidity is achieved by performing the proposed iterative procedure based on the derived necessary conditions. As a numerical example, the optimal solutions for prismatic bars with cross-sectional shapes of a square and an equilateral triangle are obtained by the computer program which uses the Finite Element Method formulated on the basis of the hybrid stress approach.

One-dimensional wave propagation theory is used to investigate the forces, velocities, and displacements in a series of elastic rods connected to rigid elements. The method is applied to the case of two subsystems that collide. The technique allows the calculations to be done during a short-lived event such as a collision.

A method of solving inhomogeneous problems for slightly compressible elastic isotropic materials is outlined and illustrated using a two-parameter family of solutions.

Finite torsion of a circular bar of isotropic compressible hyperelastic material is considered. A procedure suggested by Truesdell is used to obtain solutions for a particular strain energy function although the method used is not restricted to this particular form. The procedure is applicable if the volume strain is small. Results for finite twist with the length prevented from changing and with the length allowed to change so that the resultant longitudinal force is zero are presented.

By using the theory of small deformations superposed on large compressibility effects for nearly incompressible materials can be considered. A procedure suggested by Truesdell is outlined and used for the problems of straightening, stretching and shearing of an annular wedge and the telescopic shear of a cylindrical tube.

A theory is developed for the transverse deflections when a rectangular plate having a bitrapezoidal cross section is subjected to a uniform longitudinal curvature. The theoretical solutions are compared with earlier results presented by Lamb and Fung and Wittrick. Experimental results are compared with the theory and good agreement is obtained over the range of curvatures tested.

A numerical method is proposed for the analysis of the extension and expansion of a thick-walled cylindrical tube of compressible hyperelastic material. The method is based on the division of the tube into a number of thin-walled concentric tubes and the use of the non-linear governing differential equation is avoided. Numerical results obtained by using a Hewlett Packard 9820A programmable desk calculator are presented for plane strain and zero resultant axial force and for two strain energy functions. Results from the method applied to the incompressible neo-Hookean material are compared to results from the exact solution of the problem for this material.

The finite elastic inflation of a thin spherical shell is considered for compressible isotropic materials. A numerical method is used which allows the inflation problem to be done for any strain energy function. This method reduces to the solution of two nonlinear algebraic equations which can be solved on a desk-type programmable calculator.

An exact description of the complex physical effects and processes which occur in buildings during dynamic loading is virtually impossible. It is therefore important to choose a physical model representing a simplified structure which on one hand describes behaviour of a real building and on the other can be treated by the known mathematical apparatus.

This paper describes a numerical procedure developed to analyze piping and duct systems. The procedure combines transfer matrix and finite element methods and was used to predict the transmission loss of a piping network constructed of rigid‐walled, square cross‐section tubing. The network consisted of one input, one output, and several segments made up of straight pipes and 90° elbows. These were interconnected at several “T” junctions. The junctions and elbows were treated using finite element models that took into account two‐dimensional wave propagation. These were connected to straight pipes in which one‐dimensional wave propagation was assumed. This led to a much reduced connective matrix for each finite element model. The solution of the entire network was then obtained by solving a relatively small system of linear equations. Experimental measurements of the network transmission loss were made using a two‐microphone transfer function technique with random “white” noise and a dual channel FFT analy...