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No / This paper presents a methodology for efficient shape parametrisation for automatic design optimisation using a partial differential equation (PDE) formulation. It is shown how the choice of an elliptic PDE enables one to define and parametrise geometries corresponding to complex shapes. By using the PDE formulation it is shown how the shape definition and parametrisation can be based on a boundary value approach by which complex shapes can be created and parametrised based on the shape information at the boundaries or the character lines defining the shape. Furthermore, this approach to shape definition allows complex shapes to be parametrised intuitively using a very small set of design parameters.

No / Pharmaceutical tablets have been the most dominant form for drug delivery and most of them are used in the oral administration of drugs. These tablets need to be strong enough so that they can tolerate external stresses. Hence, during the design process, it is important to produce tablets with maximum mechanical strength while conserving the properties of powder form components. The mechanical properties of these tablets are assessed by measuring the tensile strength, which is commonly measured using diametrical or axial compression tests. This work describes the parametric design and optimisation of solid pharmaceutical tablets in cylindrical and spherical shapes, which are obtained using a formulation based on the use of Partial Differential Equations (PDEs) for shape design. The PDE-based formulation is capable of parameterised complex shapes using the information from some boundary curves that describe the shape. It is shown that the optimal design of pharmaceutical tablets with a particular volume and maximum strength can be obtained using an automatic design optimisation which is performed by combining the PDE method and a standard method for numerical optimisation.