Parameter Free Shape Design of Shell and Membrane Structures
Further progress has been made in the field of parameter free shape design of thin shells and membrane structures applying the so-called parameter free technique. Coordinates of finite element nodes are directly used as design variables which combines two striking advantages: minimal effort to set up the design problem and almost unlimited dimension of design space. New, sophisticated sensitivity filtering guarantees mesh independent results; the quality of mesh is controlled by Plateau regularization based on ideal element templates. Exact semi-analytic and adjoint sensitivity analysis is the basic key to an efficient and accurate optimization procedure. It appears that basic algorithms like feasible directions and augmented Lagrange methods are best suited for the problems at hand. Finally, a highly efficient, massively parallel code has been implemented. The procedure is applied to the free form design of geometrically non-linear shells including large displacements and instability with respect to minimization of weight and maximization of lowest eigenfrequency. A broad range of applications in architecture, civil, automotive and aerospace engineering will be presented as there are bead design of plates, pressure bulk heads, local effects of load application and the all-over-design of free form thin shells.References: Bletzinger, K.-U., Firl, M., Linhard, J., Wüchner, R.: Optimal shapes of mechanically motivated surfaces, CMAME, 199, 5-8, pp. 324-333 (2010).