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Mathematical Problems in Engineering
Volume 2018 (2018), Article ID 6092479, 16 pages
Research Article

Nonlinear Analysis for the Crack Control of SMA Smart Concrete Beam Based on a Bidirectional B-Spline QR Method

1College of Civil Engineering and Architecture, Guangxi University, Nanning 530004, China
2The Key Laboratory of Disaster Prevention and Structural Safety of the Education Ministry, Guangxi University, Nanning 530004, China
3Electric Power Research Institute of Guangxi Power Grid Co., Ltd., Nanning 530023, China
4Department of Geotechnical Engineering, Tongji University, Shanghai 200092, China

Correspondence should be addressed to Shuang-bei Li

Received 1 August 2017; Revised 10 November 2017; Accepted 16 November 2017; Published 11 January 2018

Academic Editor: Fabrizio Greco

Copyright © 2018 Yan Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A bidirectional B-spline QR method (BB-sQRM) for the study on the crack control of the reinforced concrete (RC) beam embedded with shape memory alloy (SMA) wires is presented. In the proposed method, the discretization is performed with a set of spline nodes in two directions of the plane model, and structural displacement fields are constructed by the linear combination of the products of cubic B-spline interpolation functions. To derive the elastoplastic stiffness equation of the RC beam, an explicit form is utilized to express the elastoplastic constitutive law of concrete materials. The proposed model is compared with the ANSYS model in several numerical examples. The results not only show that the solutions given by the BB-sQRM are very close to those given by the finite element method (FEM) but also prove the high efficiency and low computational cost of the BB-sQRM. Meanwhile, the five parameters, such as depth-span ratio, thickness of concrete cover, reinforcement ratio, prestrain, and eccentricity of SMA wires, are investigated to learn their effects on the crack control. The results show that depth-span ratio of RC beams and prestrain and eccentricity of SMA wires have a significant influence on the control performance of beam cracks.