Structural shape optimization of triangular shell

The key topic discussed in this paper concerns the geometrical issue of the structural optimization, where two approaches are used to obtain the best bending-free state of stress for a triangular shell. In the first approach, starting from an assigned initial shape, the unknown optimal geometry is obtained manipulating the form by means of an ad hoc parametric function, e.g. polynomial, exponential, etc., whose parameters are assumed as design variables. This approach allows to reduce drastically the number of the variables, on the other hand, the generality of the generated shapes depends strongly on the choice of the parametric function. The second is a much more general tool for the surface representation, namely, a CAGD (Computer Aided Geometric Design) technique has been implemented and the initial shape of the selected example has been approximated through a triangular Bézier surface made up of triangular patches. The approximate surface is controlled by the Cartesian coordinates of the points which define the Bézier control net and finally these coordinates are assumed as design variables. For both approaches a finite element analysis is performed to compute the objective function in each step and the optimization loop is managed by means of pre- and post- processes developed using MATLAB which also provides routines able to communicate with the FE solver DIANA 9. A MATLAB gradient-based algorithm (fmincon) is used to minimize the strain energy, i.e. to increase the shell stiffness, and consequently to reduce the bending stress component.