Analysis and applications of variational sensitivity information in structural optimisation

This thesis is concerned with the analysis of the internal structure of sensitivities of engineering structures with respect to modifications in shape. The impact of the chosen models on the computed optimal designs, especially the influence of the chosen shape parametrisation, is analysed. This knowledge enables the design engineer to understand and improve the models systematically whereas they are usually set up entirely by engineering experience and intuition. The weaknesses of the models are detected and improved design descriptions are proposed. This human controlled process is called design exploration. The aim of this thesis is to contribute new substantial capabilities to the corresponding methods. The generic concept is applied to shape optimisation of shell structures. The design of such structures is extremely important for their stability, robustness and load-bearing capacity. The variational design sensitivity analysis for a nonlinear solid shell is performed and especially the pseudo load matrix and the sensitivity matrix are derived. Within the scope of this thesis, only static nonlinear structural analysis and hyperelastic material behaviour are considered.