Application of Evolutionary Structural Optimization to Reinforced Concrete Structures

Abstract

The present thesis has the objective to create a procedure for the automatic preliminary design of reinforced concrete structures, based on the Evolutionary Structural Optimization method (ESO). The developed algorithm performs heuristic topology optimization based on multiple criteria, in subsequent optimization cycles executed in series. In each ESO cycle, it is possible to perform material addition, removal or transition between a couple of materials, i.e. steel, concrete and void. Each optimization cycle is governed by an optimality criterion chosen from: stiffness, Von Mises, Drucker-Prager, tension stress criteria or linear interpolation of previous ones. The finite element analysis used in the algorithm regards all materials as linear elastic. The reaching of maximum strength and failure of materials is not taken into account.

The automated design process of reinforced concrete structures has been separated in two problems: the form-finding of reinforced concrete structure as a whole and the definition of internal distribution between steel and concrete. The first problem is solved, in the first optimization cycle, with a ``standard'' ESO procedure, with the only difference in choosing a Von Mises optimization criterion over a ``classical'' stiffness criterion. The second problem is solved, in the second and third optimization cycles, combining in series two additional ``modified'' ESO procedures and introducing gradual transition in optimization criteria through linear interpolation of sensitivity numbers. The combined criteria for the second cycle are a Von Mises and Drucker-Prager optimization criteria, while for the third cycle, a Drucker-Prager and tensile stress optimization criteria. Moreover, additional geometrical constraints are applied, to ensure a set minimal distance between steel and outer boundaries, i.e. concrete cover, and to ensure optimal angle preservation for steel members found during optimization, introducing two new ``density'' matrices called \emph{cover} and \emph{mask}.
Summarizing, the preliminary design of reinforced concrete structures is dealt with three cycles of ESO optimization procedures executed in series, with optimization criteria that gradually change with continuity between the different cycles over the whole process.

The developed procedure has been tested on several case studies, both from ESO and reinforced concrete literature. The defined ESO process has been found to generate solutions with steel correctly placed in tensile stress zones both to resist bending and shear. Generally, the presence of remaining tensile stresses in concrete zones in the solutions is absent or very limited, and in latter cases their magnitude is very small compared to other stresses.
Obtained solutions cannot be directly used as such for reinforcement layouts definition but, in combination with principal stresses plots and engineering judgement, they are able to suggest useful resulting reinforcement layouts.

As result of the specificities introduced for addressing the design of reinforced concrete structures, the ESO method has been extended for the case of topological optimization of composite materials with macro structure, with different optimization criteria applied to component materials, with one component material that has different resistance in tension and compression and with geometrical constraints for one component material.

The complete MATLAB code is published in the annex.