Application of an optimisation algorithm to configure an internal fixation device

Fractures of long bones are sometimes treated using various types of fracture fixation devices including internal plate fixators. These are specialised plates which are used to bridge the fracture gap(s) whilst anatomically aligning the bone fragments. The plate is secured in position by screws. The aim of such a device is to support and promote the natural healing of the bone. When using an internal fixation device, it is necessary for the clinician to decide upon many parameters, for example, the type of plate and where to position it; how many and where to position the screws. While there have been a number of experimental and computational studies conducted regarding the configuration of screws in the literature, there is still inadequate information available concerning the influence of screw configuration on fracture healing. Because screw configuration influences the amount of flexibility at the area of fracture, it has a direct influence on the fracture healing process. Therefore, it is important that the chosen screw configuration does not inhibit the healing process. In addition to the impact on the fracture healing process, screw configuration plays an important role in the distribution of stresses in the plate due to the applied loads. A plate that experiences high stresses is prone to early failure. Hence, the screw configuration used should not encourage the occurrence of high stresses. This project develops a computational program in Fortran programming language to perform mathematical optimisation to determine the screw configuration of an internal fixation device within constraints of interfragmentary movement by minimising the corresponding stress in the plate. Thus, the optimal solution suggests the positioning and number of screws which satisfies the predefined constraints of interfragmentary movements. For a set of screw configurations the interfragmentary displacement and the stress occurring in the plate were calculated by the Finite Element Method. The screw configurations were iteratively changed and each time the corresponding interfragmentary displacements were compared with predefined constraints. Additionally, the corresponding stress was compared with the previously calculated stress value to determine if there was a reduction. These processes were continued until an optimal solution was achieved. The optimisation program has been shown to successfully predict the optimal screw configuration in two cases. The first case was a simplified bone construct whereby the screw configuration solution was comparable with those recommended in biomechanical literature. The second case was a femoral construct, of which the resultant screw configuration was shown to be similar to those used in clinical cases. The optimisation method and programming developed in this study has shown that it has potential to be used for further investigations with the improvement of optimisation criteria and the efficiency of the program.

Natural and engineered kallikrein inhibitors: an emerging pharmacopoeia

The kallikreins and kallikrein-related peptidases are serine proteases that control a plethora of developmental and homeostatic phenomena, ranging from semen liquefaction to skin desquamation and blood pressure. The diversity of roles played by kallikreins has stimulated considerable interest in these enzymes from the perspective of diagnostics and drug design. Kallikreins already have well-established credentials as targets for therapeutic intervention and there is increasing appreciation of their potential both as biomarkers and as targets for inhibitor design. Here, we explore the current status of naturally occurring kallikrein protease-inhibitor complexes and illustrate how this knowledge can interface with strategies for rational re-engineering of bioscaffolds and design of small-molecule inhibitors.

Active transonic aerofoil design optimization using robust multiobjective evolutionary algorithms

The use of adaptive wing/aerofoil designs is being considered, as they are promising techniques in aeronautic/ aerospace since they can reduce aircraft emissions and improve aerodynamic performance of manned or unmanned aircraft. This paper investigates the robust design and optimization for one type of adaptive techniques: active flow control bump at transonic flow conditions on a natural laminar flow aerofoil. The concept of using shock control bump is to control supersonic flow on the suction/pressure side of natural laminar flow aerofoil that leads to delaying shock occurrence (weakening its strength) or boundary layer separation. Such an active flow control technique reduces total drag at transonic speeds due to reduction of wave drag. The location of boundary-layer transition can influence the position and structure of the supersonic shock on the suction/pressure side of aerofoil. The boundarylayer transition position is considered as an uncertainty design parameter in aerodynamic design due to the many factors, such as surface contamination or surface erosion. This paper studies the shock-control-bump shape design optimization using robust evolutionary algorithms with uncertainty in boundary-layer transition locations. The optimization method is based on a canonical evolution strategy and incorporates the concepts of hierarchical topology, parallel computing, and asynchronous evaluation. The use of adaptive wing/aerofoil designs is being considered, as they are promising techniques in aeronautic/ aerospace since they can reduce aircraft emissions and improve aerodynamic performance of manned or unmanned aircraft. This paper investigates the robust design and optimization for one type of adaptive techniques: active flow control bump at transonic flow conditions on a natural laminar flow aerofoil. The concept of using shock control bump is to control supersonic flow on the suction/pressure side of natural laminar flow aerofoil that leads to delaying shock occurrence (weakening its strength) or boundary-layer separation. Such an active flow control technique reduces total drag at transonic speeds due to reduction of wave drag. The location of boundary-layer transition can influence the position and structure of the supersonic shock on the suction/pressure side of aerofoil. The boundarylayer transition position is considered as an uncertainty design parameter in aerodynamic design due to the many factors, such as surface contamination or surface erosion. This paper studies the shock-control-bump shape design optimization using robust evolutionary algorithms with uncertainty in boundary-layer transition locations. The optimization method is based on a canonical evolution strategy and incorporates the concepts of hierarchical topology, parallel computing, and asynchronous evaluation. Two test cases are conducted: the first test assumes the boundary-layer transition position is at 45% of chord from the leading edge, and the second test considers robust design optimization for the shock control bump at the variability of boundary-layer transition positions. The numerical result shows that the optimization method coupled to uncertainty design techniques produces Pareto optimal shock-control-bump shapes, which have low sensitivity and high aerodynamic performance while having significant total drag reduction.

Double-shock control bump design optimization using hybridized evolutionary algorithms

This study investigates the application of two advanced optimization methods for solving active flow control (AFC) device shape design problem and compares their optimization efficiency in terms of computational cost and design quality. The first optimization method uses hierarchical asynchronous parallel multi-objective evolutionary algorithm and the second uses hybridized evolutionary algorithm with Nash-Game strategies (Hybrid-Game). Both optimization methods are based on a canonical evolution strategy and incorporate the concepts of parallel computing and asynchronous evaluation. One type of AFC device named shock control bump (SCB) is considered and applied to a natural laminar flow (NLF) aerofoil. The concept of SCB is used to decelerate supersonic flow on suction/pressure side of transonic aerofoil that leads to a delay of shock occurrence. Such active flow technique reduces total drag at transonic speeds which is of special interest to commercial aircraft. Numerical results show that the Hybrid-Game helps an EA to accelerate optimization process. From the practical point of view, applying a SCB on the suction and pressure sides significantly reduces transonic total drag and improves lift-to-drag (L/D) value when compared to the baseline design.

Unsteady natural convection in a triangular enclosure under isothermal heating

The fluid flow and heat transfer inside a triangular enclosure due to instantaneous heating on the inclined walls are investigated using an improved scaling analysis and direct numerical simulations. The development of the unsteady natural convection boundary layer under the inclined walls may be classified into three distinct stages including a start-up stage, a transitional stage and a steady state stage, which can be clearly identified in the analytical and numerical results. A new triple-layer integral approach of scaling analysis has been considered to obtain major scaling relations of the velocity, thicknesses, Nusselt number and the flow development time of the natural convection boundary layer and verified by direct numerical simulations over a wide range of flow parameters.

Scaling of natural convection of an inclined flat plate : ramp cooling condition

A scaling analysis is performed for the transient boundary layer established adjacent to an inclined flat plate following a ramp cooling boundary condition. The imposed wall temperature decreases linearly up to a specific value over a specific time. It is revealed that if the ramp time is sufficiently large then the boundary layer reaches quasi-steady mode before the growth of the temperature is finished. However, if the ramp time is shorter then the steady state of the boundary layer may be reached after the growth of the temperature is completed. In this case, the ultimate steady state is the same as if the start up had been instantaneous. Note that the cold boundary layer adjacent to the plate is potentially unstable to Rayleigh-Bénard instability if the Rayleigh number exceeds a certain critical value for this cooling case. The onset of instability may set in at different stages of the boundary layer development. A proper identification of the time when the instability may set in is discussed. A numerical verification of the time for the onset of instability is presented in this study. Different flow regimes based on the stability of the boundary layer have also been discussed with numerical results.

Natural convection boundary-layer adjacent to an inclined flat plate subject to sudden and ramp heating

The natural convection thermal boundary layer adjacent to an inclined flat plate subject to sudden heating and a temperature boundary condition which follows a ramp function up until a specified time and then remains constant is investigated. The development of the flow from start-up to a steady-state has been described based on scaling analyses and verified by numerical simulations. Different flow regimes based on the Rayleigh number are discussed with numerical results for both boundary conditions. For ramp heating, the boundary layer flow depends on the comparison of the time at which the ramp heating is completed and the time at which the boundary layer completes its growth. If the ramp time is long compared with the steady state time, the layer reaches a quasi steady mode in which the growth of the layer is governed solely by the thermal balance between convection and conduction. On the other hand, if the ramp is completed before the layer becomes steady; the subsequent growth is governed by the balance between buoyancy and inertia, as for the case of instantaneous heating.

Scaling of natural convection of an inclined flat plate : sudden cooling condition

The natural convection boundary layer adjacent to an inclined plate subject to sudden cooling boundary condition has been studied. It is found that the cold boundary layer adjacent to the plate is potentially unstable to Rayleigh-Bénard instability if the Rayleigh number exceeds a certain critical value. A scaling relation for the onset of instability of the boundary layer is achieved. The scaling relations have been developed by equating important terms of the governing equations based on the development of the boundary layer with time. The flow adjacent to the plate can be classified broadly into a conductive, a stable convective or an unstable convective regime determined by the Rayleigh number. Proper scales have been established to quantify the flow properties in each of these flow regimes. An appropriate identification of the time when the instability may set in is discussed. A numerical verification of the time for the onset of instability is also presented in this study. Different flow regimes based on the stability of the boundary layer have been discussed with numerical results.

Natural convection in attic-shaped spaces subject to sudden and ramp heating boundary conditions

In this study, a discussion of the fluid dynamics in the attic space is reported, focusing on its transient response to sudden and linear changes of temperature along the two inclined walls. The transient behaviour of an attic space is relevant to our daily life. The instantaneous and non-instantaneous (ramp) heating boundary condition is applied on the sloping walls of the attic space. A theoretical understanding of the transient behaviour of the flow in the enclosure is performed through scaling analysis. A proper identification of the timescales, the velocity and the thickness relevant to the flow that develops inside the cavity makes it possible to predict theoretically the basic flow features that will survive once the thermal flow in the enclosure reaches a steady state. A time scale for the heating-up of the whole cavity together with the heat transfer scales through the inclined walls has also been obtained through scaling analysis. All scales are verified by the numerical simulations.

Natural convection in attics subject to instantaneous and ramp cooling boundary conditions

A fundamental study of the fluid dynamics inside an attic shaped triangular enclosure with cold upper walls and adiabatic horizontal bottom wall is reported in this study. The transient behaviour of the attic fluid which is relevant to our daily life is examined based on a scaling analysis. The transient phenomenon begins with the instantaneous cooling and the cooling with linear decreases of temperature up to some specific time (ramp time) and then maintain constant of the upper sloped walls. It is shown that both inclined walls develop a thermal boundary layer whose thicknesses increase towards steady-state or quasi-steady values. A proper identification of the timescales, the velocity and the thickness relevant to the flow that develops inside the cavity makes it possible to predict theoretically the basic flow features that will survive once the thermal flow in the enclosure reaches a steady state. A time scale for the cooling-down of the whole cavity together with the heat transfer scales through the inclined walls has also been obtained through scaling analysis. All scales are verified by the numerical simulations.

Natural convection and heat transfer in attics subject to periodic thermal forcing

The heat transfer through the attics of buildings under realistic thermal forcing has been considered in this study. A periodic temperature boundary condition is applied on the sloping walls of the attic to show the basic flow features in the attic space over diurnal cycles. The numerical results reveal that, during the daytime heating stage, the flow in the attic space is stratified; whereas at the night-time cooling stage, the flow becomes unstable. A symmetrical solution is seen for relatively low Rayleigh numbers. However, as the Ra gradually increases, a transition occurs at a critical value of Ra. Above this critical value, an asymmetrical solution exhibiting a pitchfork bifurcation arises at the night-time. It is also found that the calculated heat transfer rate at the night-time cooling stage is much higher than that during the daytime heating stage.

Radiation effects on natural convection laminar flow from a horizontal circular cylinder

The effect of radiation on natural convection flow from an isothermal circular cylinder has been investigated numerically in this study. The governing boundary layer equations of motion are transformed into a non-dimensional form and the resulting nonlinear systems of partial differential equations are reduced to convenient boundary layer equations, which are then solved numerically by two distinct efficient methods namely: (i) implicit finite differencemethod or the Keller-Box Method (KBM) and (ii) Straight Forward Finite Difference Method (SFFD). Numerical results are presented by velocity and temperature distribution of the fluid as well as heat transfer characteristics, namely the shearing stress and the local heat transfer rate in terms of the local skin-friction coefficient and the local Nusselt number for a wide range of surface heating parameter and radiation-conduction parameter. Due to the effects of the radiation the skin-friction coefficients as well as the rate of heat transfer increased and consequently the momentum and thermal boundary layer thickness enhanced.