In this paper we present a set of MATLAB routines for evaluation of the moment-curvature relationship of reinforced concrete cross sections. This is a topic of major importance for both academic and practical design purposes in the context of structural engineering. The computational routines were developed to be simple, general and flexible. This allows wide practical application and future improvements and modifications. The well-known fibers approach is employed, but an alternative development of the method is also presented. This is interesting from the conceptual point of view. Finally, numerical comparisons are presented to validate the routines.
In this work, we present a non-intrusive polynomial chaos expansion (PCE) approach for topology optimization in the context of stationary heat conduction. The robust topology optimization problem and its sensitivity in both its variational and approximate forms are discussed. Sensitivity analysis of the statistical moments and PCE are described in detail. The variational boundary value problems were solved using the finite element method. The material distribution approach with the SIMP model was employed to represent the design. The numerical examples presented show applications addressing heat generation with uncertain magnitude, heat generation at uncertain location and damage with uncertain location. These examples prove that uncertainty-based optimization is able to obtain more robust designs than deterministic approaches.
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