Methods for reliability based design optimization of structural components

Cost and quality are key properties of a product, possibly even the two most important. One definition of quality is fitness for purpose. Load-bearing products, i.e. structural components, loose their fitness for purpose if they fail. Thus, the ability to withstand failure is a fundamental measure of quality for structural components. Reliability based design optimization (RBDO) is an approach for development of structural components which aims to minimize the cost while constraining the probability of failure. However, the computational effort of an RBDO applied to large-scale engineering problems has prohibited it from employment in industrial applications. This thesis presents methods for computationally efficient RBDO. A review of the work presented on RBDO algorithms reveals that three constituents of an RBDO algorithm has rendered significant attention; i) the solution strategy for and numerical treatment of the probabilistic constraints, ii) the surrogate model, and iii) the experiment design. A surrogate model is ”a model of a model”, i.e. a computationally cheap approximation of a physics-based but computationally expensive computer model. It is fitted to responses from the physics-motivated model obtained via a thought-through combination of experiments called an experiment design. In Paper A, the general algorithm for RBDO employed in this work, including the sequential approximation procedure used to treat the probabilistic constraints, is laid out. A single constraint approximation point (CAP) is used to save computational effort with acceptable losses in accuracy. The approach is used to optimize a truck component and incorporates the effect that production related design variables like machining and shot peening have on fatigue life. The focus in Paper B is on experiment design. An algorithm employed to construct a novel experiment design for problems with multiple constraints is presented. It is based on an initial screening and uses the specific problem structure to combine one-factor-at-a-time experiments to a several-factors-at-a-time experiment design which reduces computational effort. In Paper C, a surrogate model tailored for RBDO is introduced. It is motivated by applied solid mechanics considerations and the use of the first order reliability method to evaluate the probabilistic constraint. An optimal CAP is furthermore deduced from the surrogate model. In Paper D, the paradigm to use sets of experiments rather than one experiment at a time is challenged. A new procedure called experiments on demand (EoD) is presented. The EoD procedure utilizes the core of RBDO to quantify the demand for new experiments and augments it by a D-optimality criterion for added robustness and numerical stability.