ROBUST MULTIOBJECTIVE OPTIMIZATION OF REINFORCED CONCRETE FRAMES USING RELIABILITY CONSTRAINTS

Resumo

In most structural engineering designs deterministic models are used with requirements
defined by standards, specifically, designs of reinforced concrete structures in Brazil are based on the
NBR 6118:2014. This standard recommends the use of safety coefficients, without the consideration
of the uncertainties associated to concrete structures designs. On the other hand, the Reliability-Based
Robust Design Optimization (RBRDO), that will be studied in this paper, is characterized by
optimization problems where the design uncertainties are treated statistically, allowing to measure the
level of structural reliability and performance variability. In this type of problem, some constraint
associated with the probability of failure is present in its formulation. The method to obtain the failure
probability in this work will be FORM (First Order Reliability Method). Robust optimization
problems aim to obtain a robust design, which in addition to a good performance, a low sensitivity to
uncertainties of the problem are intended. The robustness measures employed in this work are mean
and the standard deviation of functions of interest. This leads to a Robust Multiobjective Optimization
(RMO) problem, due to multiple objectives, which has several optimum solutions called Pareto points.
The main aim of the present research is to develop a computational tool to efficiently obtain robust
optimum pareto designs of reinforced concrete framed structures under uncertainties. Such optimum
pareto points will be found through Weighted Sums (WS), Min-Max e Normal Boundary Intersection
(NBI) methods that were implement in the Python language. In addition, it will be used pre-existing
in-house finite element libraries, which will be the method used for structural analysis. The reliability
and optimization public libraries, also in the same language, will be considered. The applications in
this work, is two 2D frames of reinforced concrete with one and three floors, with respectively 3 and
30 bars.