Optimization of Structures Using the Finite Element Method

The optimization code presented in this paper takes fullest advantage of the finite element modelling of structures. The link between the finite element model and the optimization problem is maintained by so-called design elements, which give this code a wide applicability and flexibility. Furthermore, the cost function and the constraints are regarded as a part of the finite element definition, rather than to be part of the optimization code. Therefore different cost functions and constraints can be used on structures, in order to meet the specific design requirements of the problem at hand. This is achieved by means of user-supplied routines on finite element level only. The gradient of the cost function and constraints are determined analytically, avoiding numerical differentiation. As a result a general purpose-structural optimization program, called Optisys, was obtained. As an example, simulation of bone remodelling will be discussed in this paper. This example can be regarded as a combined shape and material-property optimization problem, since bone remodelling is the change of shape and property of natural bone due to a change of external loading.