Structural optimization of thin shells under dynamic loads

Thin shell structures present immense structural and architectural potential in various fields of civil, mechanical, architectural, aeronautical and naval engineering. This kind of structures are in general designed by the finite element method using the conventional 'trial and error' procedure which can lead, in many cases, to a non-economical design, specially when a dynamic analysis is necessary. Aiming at developing a more efficient methodology for the design of thin shells, this paper develops a structural optimization procedure, using finite element discretisation, to obtain efficient design of thin shell structures under elastic behavior with viscous damping and dynamic loads. The Huang-Hinton finite element, which belongs to the family of degenerated shell elements, is used. The mesh generation on the shell surface is performed by means of a mapping from the parametric plan in the 2D space to the 3D shell surface using Coon patches. The design variables are the key-points coordinates and the Coon patches widths, To solve the nonlinear constrained optimization problem the Sequential Quadratic Programming algorithm is used. Many different optimization problems can be performed by the code. So, one can minimize the volume or the displacement or the acceleration at a point or maximize the first frequency of the structure. On the other hand the volume of the structure can be kept constant while minimizing the displacement at a given point or in all points of the shell, Several examples are considered illustrating the potentiality of this developed tool.