Minimization of railhead edge stresses through shape optimization

The railhead is severely stressed under the localized wheel contact patch close to the gaps in insulated rail joints. A modified railhead profile in the vicinity of the gapped joint, through a shape optimization model based on a coupled genetic algorithm and finite element method, effectively alters the contact zone and reduces the railhead edge stress concentration significantly. Two optimization methods, a grid search method and a genetic algorithm, were employed for this optimization problem. The optimal results from these two methods are discussed and, in particular, their suitability for the rail end stress minimization problem is studied. Through several numerical examples, the optimal profile is shown to be unaffected by either the magnitude or the contact position of the loaded wheel. The numerical results are validated through a large-scale experimental study.

Clinically-based automatic implant fitting for shape optimization of fracture fixation plates

Complex bone contour and anatomical variations between individual bones complicate the process of deriving an implant shape that fits majority of the population. This thesis proposes an automatic fitting method for anatomically-precontoured plates based on clinical requirements, and investigated if 100% anatomical fit for a group of bone is achievable through manual bending of one plate shape. It was found that, for the plate used, 100% fit is impossible to achieve through manual bending alone. Rather, newly-developed shapes are also required to obtain anatomical fit in areas with more complex bone contour.

Shape optimization of RC flexural members

A natural velocity field method for shape optimization of reinforced concrete (RC) flexural members has been demonstrated. The possibility of shape optimization by modifying the shape of an initially rectangular section, in addition to variation of breadth and depth along the length, has been explored. Necessary shape changes have been computed using the sequential quadratic programming (SQP) technique. Genetic algorithm (Goldberg and Samtani 1986) has been used to optimize the diameter and number of main reinforcement bars. A limit-state design approach has been adopted for the nonprismatic RC sections. Such relevant issues as formulation of optimization problem, finite-element modeling, and solution procedure have been described. Three design examples-a simply supported beam, a cantilever beam, and a two-span continuous beam, all under uniformly distributed loads-have been optimized. The results show a significant savings (40-56%) in material and cost and also result in aesthetically pleasing structures. This procedure will lead to considerable cost saving, particularly in cases of mass-produced precast members and a heavy cast-in-place member such as a bridge girder.

Freeform Skeletal Shape Optimization of Compliant Mechanisms

Compliant mechanisms are elastic continua used to transmit or transform force and motion mechanically. The topology optimization methods developed for compliant mechanisms also give the shape for a chosen parameterization of the design domain with a fixed mesh. However, in these methods, the shapes of the flexible segments in the resulting optimal solutions are restricted either by the type or the resolution of the design parameterization. This limitation is overcome in this paper by focusing on optimizing the skeletal shape of the compliant segments in a given topology. It is accomplished by identifying such segments in the topology and representing them using Bezier curves. The vertices of the Bezier control polygon are used to parameterize the shape-design space. Uniform parameter steps of the Bezier curves naturally enable adaptive finite element discretization of the segments as their shapes change. Practical constraints such as avoiding intersections with other segments, self-intersections, and restrictions on the available space and material, are incorporated into the formulation. A multi-criteria function from our prior work is used as the objective. Analytical sensitivity analysis for the objective and constraints is presented and is used in the numerical optimization. Examples are included to illustrate the shape optimization method.

Framework for the Shape Optimization of Aerodynamic Profiles Using Genetic Algorithms

This study developed a framework for the shape optimization of aerodynamics profiles using computational fluid dynamics (CFD) and genetic algorithms. Agenetic algorithm code and a commercial CFD code were integrated to develop a CFD shape optimization tool. The results obtained demonstrated the effectiveness of the developed tool. The shape optimization of airfoils was studied using different strategies to demonstrate the capacity of this tool with different GA parameter combinations.

Shape Optimization for Hypersonic Arc-Wing Missiles

National Natural Science Foundation of China (NO.90916013)

Shape optimization of interior cutouts in composite panels

This paper presents validated results of the optimization of cutouts in laminated carbon-fibre composite panels by adapting a recently developed optimization procedure known as Evolutionary Structural Optimization (ESO). An initial small cutout was introduced into each finite element model and elements were removed from around this cutout based on a predefined rejection criterion. In the examples presented, the limiting ply within each plate element around the cutout was determined based on the Tsai-Hill failure index. Plates with values below the product of the average Tsai-Hill number and a rejection ratio (RR) were subsequently removed. This process was iterated until a steady state was reached and the RR was then incremented by an evolutionary rate (ER). The above steps were repeated until a cutout of a desired area was achieved.