| Summary: | The work presented in this thesis constitutes the main body of research carried out to develop a new technique for solidification simulation by using the Medial Axis Transformation (MAT) technique in combination with other geometric reasoning and numerical methods. The aspects of casting solidification researched include a review of existing geometric reasoning techniques and employability of MAT in combination with other methods. In the first phase of research, MAT was used to present a one-dimensional interpolation scheme that provided quick results compared to the numerical methods and evolving temperature solutions in time when compared to modulus method. The scheme successfully predicted the location of hotspots and provided an acceptable temperature distribution. Learning from, and owing to limitations posed by the interpolation scheme, a new innovative and hybrid technique was then proposed that for the first time unifies geometric and numerical methods, thereby inheriting their advantages and overcoming their respective limitations. The inscribed radius and other relevant geometric information were extracted from MAT. This was then combined with the Heuvers' Circle method. A new equation, based on Chvorinov's classic rule and modulus method, was derived that enabled the proposed technique to utilise the radius information of the casting to obtain effective interface boundary conditions for an optimal solution. The proposed method was then tested on a range of casting geometries, including those from the foundries. The problems arising from complexity of the medial axes were resolved by developing a sorting technique to select the most effective Heuvers' radii and a scaling framework was also developed to obtain realistic values. Finally the application of this technique to 3D castings was conceptualised and demonstrated through a case study. Thus an effective technique has been developed that not only retains the simplicity, ease of use, speed of the conventional geometric reasoning techniques but also the accuracy and sensitivity to material properties and boundary conditions offered by the numerical methods. The proposed method is capable of providing optimal solutions in two FE simulations.
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