A Robust Approach to Topology Optimization Accounting for Geometric Imperfections

Performance and cost efficiency are important demands in the design of civil structures such as bridges and high-rise buildings. This thesis investigates topology optimization as a tool for achieving these goals during the design process. In order to determine the best structural layout, topology optimization seeks the optimal material distribution in a predefined design domain using numerical optimization. Besides the efficiency and performance of the optimized structure, robustness with respect to uncertain variations in the system is another essential requirement for practical applicability. Variable boundary conditions, uncertain material properties and geometric imperfections are important examples of uncertainties in civil engineering. Topology optimization often leads to structures consisting of slender elements which are particularly sensitive to geometric imperfections. Moreover, imperfections affect the stability of a structure and induce large displacement phenomena such as P-Δ effects. The main goal of this thesis is therefore to develop a robust approach to topology optimization which takes into account geometric imperfections. Large displacements effects are incorporated in the optimization by means of a total Lagrangian formulation for geometric nonlinear mechanics. Robust optimization is considered in a probabilistic framework where uncertainties are modeled as random variables characterized by a probability distribution. A weighted sum of the mean and standard deviation of the performance is minimized in the robust optimization problem in order to obtain well-performing structures that are also insensitive to the uncertain variations in the system. During the optimization these stochastic moments of the performance are estimated by means of uncertainty quantification techniques such as Monte Carlo sampling and the stochastic perturbation method. It is shown that the robust designs obtained in this way achieve a good nominal performance and are also much less sensitive to imperfections.status: publishe