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Using topology optimization technique to determine the optimized layout of steel reinforcing bars in concrete structures

  1. Abstract This study presents an optimization procedure based on the modified Bi-directional evolutionary structural optimization (BESO) approach to optimize both location and orientation of discrete reinforcing steel bars within concrete structures, while satisfying the prescribed realistic volumetric ratio of steel amount into the continuum concrete. Opposed to the strut-and-tie model (STM) mechanism, both tension and compression are taken into account in reinforcing bars. The optimization variables are only applicable to steel reinforcements that are modelled as discrete truss bars embedded into a concrete domain. The flexible orientation of each reinforcing bar is achieved by employing a heuristic orientation finding scheme according to principal strain direction into a two-dimensional (2D) BESO algorithm. Also, apart from ranking the sensitivity number of each reinforcing bar, an update scheme for design variables is developed due to the asymmetric property of concrete in tension and compression. The capability of the proposed optimization method is shown through two cases. It can be concluded that the proposed method obtains a rational reinforcement layout under a volume constraint on steel used in reinforced concrete (RC) structures. Reinforcing bars playing high contribution to the structural behavior are remained within a constant concrete domain, which provides a valuable suggestion for the distribution of steel reinforcements. 2. Keywords: Reinforced concrete structures, BESO topology optimization, discrete reinforcing bar, heuristic orientation scheme, update scheme 3. Introduction In structural concrete design, disturbed regions, so called as 'D-regions', has been a challenge for decades. Opposed to 'B-regions' (Bernoulli or Beam regions) where design procedure is maturely established according to beam theory and cross-sectional analysis, D-region is defined by a structural part with nonlinear strain distribution, for which traditional approaches for slender beams are not appropriate for design. Current practice towards design and analysis of such regions of the structure is using strut-and-tie model (STM) [1] which is well known as a generalization of truss analogy model [2, 3]. The concrete struts represent elements in compression while the tensile ties are carried by steel reinforcements. However, the selection of STM is usually uncertain, especially for an irregular RC structural member under complicated loading and boundary conditions, because it is mainly based on stress trajectories, load path methods or empirical observations. The optimization technique has been regarded by researchers as an efficient tool to distribute reinforcements within the concrete structure. Initially, the discrete topology optimization based on the truss ground structure approach, that allows the truss topology design problem to be viewed as a generalized sizing problem, has been used to search for the optimal STMs in reinforced concrete structures [4, 5]. The continuous reinforced concrete domain is discretized by a predefined layout where the fixed truss ties correspond to the actual reinforcements and the ties with cross-sectional areas equal to zero or nearly zero are removed through the topology optimization process. In both works of Biondini [6] and Ali and White [7], an automatic search technique for truss models consistent with the elastic stress trajectories in reinforced concrete members were proposed based on ground structure approach and linear mathematical programming technique. Also, genetic algorithms have been applied to truss topology optimization to seek the best layout of the location of reinforcing ties and compressive struts within the reinforced concrete beam [8]. More recently, Amir and Sigmund [9] presenting a truss topology optimization by embedding a truss ground structure into a concrete continuum damage model, so that the distribution of embedded steel reinforcement is optimized. However, the predefined ground structure have dominant influence on the resulting topology, which is chosen mainly relying on the intuition and experience of designers. As opposed to truss topology optimization that require designers to define node locations and element connections a priori, using continuum topology optimization to achieve a novel layout design of reinforced concrete structures has attracted a large amount of researchers in recent years [10-16]. However, these studies all proposed to use a truss-like structure obtained from single-material topology optimization so as to predict a strut-and-tie model. As the name suggests, the reinforced concrete structure is composed of two materials: concrete and steel. Hence, incorporating different mechanical properties of concrete and steel into topology optimization has emerged to gain a more effective reinforced concrete structure [17-19]. Luo and Kang [20] developed a two-material topology optimization, in which the resulting topology is much like a steel-concrete composite structure, with volume constraint on steel and strength constraint on concrete. Rather than impose stress constraints, the complete non-linear elasto-plastic response for both concrete and steel were modelled in Bogomolny and Amir et al. [21]. Also, Luo et al. [22] proposed an effective continuum topology optimization method, aiming at minimizing the costs of steel reinforcements subjected to a shrinkage volume constraint and yield constraints on concrete phases. From the review of these works, RC structure is commonly treated as composite material structure, however, in real application, the volumetric ratio of steel used into the continuum concrete is rarely over 1% [9], which cannot be achieved properly by modelling steel reinforcements as continuum elements in topology optimization problem. Also, from a construction perspective, the required postprocessing of continuum members in tension regions to discrete bars is less practical. In order to benefit from both continuum and truss topology optimization, the truss ground structure and continuum finite elements are combined onto a mesh of shared nodes where tension members are presented by truss elements resulting in reinforcing steel design while continuum elements are implemented as concrete to carry compression. This idea was initially proposed in Moen and Guest et al. [23] and then topology optimization using a hybrid truss-continuum model was further developed in Gaynor et al. [24] that using

  • Date:

    19 June 2016

  • Publication Status:

    Published

  • Library of Congress:

    TA Engineering (General). Civil engineering (General)

  • Dewey Decimal Classification:

    624 Civil engineering

  • Funders:

    Edinburgh Napier Funded

Citation

Li, M., Zhang, H. & Wong, S. H. F. (2016). Using topology optimization technique to determine the optimized layout of steel reinforcing bars in concrete structures. In Herskovits, J. (Ed.). Proceedings of 5th International Conference on Engineering Optimization, 789-798. ISBN 978-85-7650-548-8

Authors

Keywords

Reinforced concrete structures, BESO topology optimization, discrete reinforcing bar, heuristic orientation scheme, update scheme

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