Some results in topology optimization applied to biomechanics

This paper presents the application of a topology optimization algorithm based in homogenization theory. Three examples in structural design will be solved numerically. The first two are formulated such that analytical solutions can also be developed. To obtain this goal, the microscopic structure that we considered is formed of laminates because for this type of composite materials there is an explicit dependence of the homogenized coefficients on the design variables. The last example regards bone remodelling. Here, where it is impossible to obtain the analytical solution, the applied algorithm produces numerical results which are in good agreement with Wolffʹs Law.