Methods for reliability based design optimization of structural components

Abstract: Cost and quality are key properties of a product, possibly even the two most important. Onedefinition 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 fundamentalmeasure of quality for structural components. Reliability based design optimization(RBDO) is an approach for development of structural components which aims to minimizethe cost while constraining the probability of failure. However, the computational effort ofan RBDO applied to large-scale engineering problems has prohibited it from employment inindustrial applications. This thesis presents methods for computationally efficient RBDO.A review of the work presented on RBDO algorithms reveals that three constituentsof an RBDO algorithm has rendered significant attention; i ) the solution strategy for andnumerical treatment of the probabilistic constraints, ii ) the surrogate model, and iii) theexperiment design. A surrogate model is ”a model of a model”, i.e. a computationally cheapapproximation of a physics-based but computationally expensive computer model. It is fittedto responses from the physics-motivated model obtained via a thought-through combinationof experiments called an experiment design.In Paper A, the general algorithm for RBDO employed in this work, including the sequentialapproximation procedure used to treat the probabilistic constraints, is laid out. A singleconstraint approximation point (CAP) is used to save computational effort with acceptablelosses in accuracy. The approach is used to optimize a truck component and incorporatesthe effect that production related design variables like machining and shot peening have onfatigue life.The focus in Paper B is on experiment design. An algorithm employed to construct anovel experiment design for problems with multiple constraints is presented. It is based onan initial screening and uses the specific problem structure to combine one-factor-at-a-timeexperiments to a several-factors-at-a-time experiment design which reduces computationaleffort.In Paper C, a surrogate model tailored for RBDO is introduced. It is motivated by appliedsolid mechanics considerations and the use of the first order reliability method to evaluate theprobabilistic 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 atime is challenged. A new procedure called experiments on demand (EoD) is presented. TheEoD procedure utilizes the core of RBDO to quantify the demand for new experiments andaugments it by a D-optimality criterion for added robustness and numerical stability.