This thesis presents a computational model for the topology optimisation of three-dimensional elastic structures. The model uses a material distribution approach based on a porous material with a local periodic microstructure. The equivalent properties of the porous material are computed by an asymptotic homogenisation method. 
   Using a multiple load criteria that considers distinct loads applied at different periods of time, the optimal solution is obtained by the minimisation of compliance (that maximises the overall structural stiffness), subjected to an isoperimetric constraint on volume. Using this approach, the final topologies have a large amount of material at intermediate density values, and consequently, do not characterise a well-defined structure. To overcome this problem two different approaches are tested. Firstly, one considers a constraint on the structure perimeter combined with a penalty on intermediate densities. Secondly, a material cost function is introduced at the resource constraint level to increase the cost associated with regions occupied by material with intermediate densities. For these formulations, the necessary conditions for optimum are derived by the stationarity of the Augmented Lagrangian associated with the optimisation problem. These conditions are numerically solved through a suitable finite element discretisation. 
   The model is tested in several numerical applications, both in structural and bone remodelling examples. The bone remodelling application is justified by the fact that the bone tissue is a natural cellular material in constant adaptation. Furthermore, one of the main factors regulating this adaptation process is the local mechanical environment. Some alterations in the original formulation are considered in order to better capture and simulate the bone remodelling process.