Conjugate and Directional Chaos Control Methods for Reliability Analysis of CNT–Reinforced Nanocomposite Beams under Buckling Forces; A Comparative Study

Document Type : Research Paper


1 University of Zabol

2 hefei university of technology


The efficiency and robustness of reliability methods are two important factors in the first-order reliability method (FORM). The conjugate choice control (CCC) and directional chaos control method (DCC) are developed to improve the robustness and efficiency of the FORM formula using the stability transformation method. In this paper, the CCC and DCC methods are applied for the reliability analysis of a nanocomposite beam as a complex engineering problem, which is reinforced by carbon nanotubes (CNTs) under buckling force. The probabilistic model for nanocomposite beam is developed through the buckling failure mode which is computed by using the Euler-Bernoulli beam model. The robustness and efficiency CCC and DCC are compared using the stable solution and a number of call limit state functions. The results demonstrate that the CCC method is more robust than the DCC in this case, while the DCC method is simpler than the CCC.


Main Subjects

[1] Keshtegar, B., Limited Conjugate Gradient Method for Structural Reliability Analysis, Engineering with Computers, doi:10.1007/s00366-016-0493-7, pp. 1-9, 2016.
[2] Rashki, M., Miri, M. and Moghaddam, M.A., A New Efficient Simulation Method to Approximate the Probability of Failure and Most Probable Point. Structural Safety, Vol. 39, pp. 22-9, 2012.
[3] Keshtegar, B. and Miri, M., An Enhanced HL-RF Method for the Computation of Structural failure probability Based on Relaxed Approach, Civil Engineering Infrastructures, Vol. 1:, pp. 69-80, 2013.
[4] Keshtegar, B. and Miri, M., Introducing Conjugate Gradient Optimization for Modified HL-RF Method, Engineering Computations, Vol. 31, pp. 775-790, 2014.
[5] Yang, D., Chaos Control for Numerical Instability of First Order Reliability Method, Commun. Non-linear Sci. Numer. Simulat., Vol. 15, pp. 3131–3141, 2010.
[6] Gong, J.X. and Yi, P., A Robust Iterative Algorithm for Structural Reliability Analysis, Struct. Multidisc. Optim., Vol. 43, pp. 519–527, 2011.
[7] Liu, P.L. and Kiureghian, A.D., Optimization Algorithms for Structural Reliability, Struct. Saf., Vol. 9, pp. 161–177, 1991.
[8] Meng, Z., Li, G., Yang, D. and Zhan, L., A New Directional Stability Transformation Method of Chaos Control for First Order Reliability Analysis, Struct. Multidiscipl. Optim., DOI: 10.1007/s00158-016-1525-z, pp. 1-12, 2016.
[9] Keshtegar, B., Stability Iterative Method for Structural Reliability Analysis Using a Chaotic Conjugate Map, Nonlinear Dyn., Vol. 84, No. 4, pp. 2161-2174, 2016.
[10] Keshtegar, B., Chaotic Conjugate Stability Transformation Method for Structural Reliability Analysis, Computer Methods in Applied Mechanics and Engineering, Vol. 310, pp. 866-885, 2016.
[11] Keshtegar, B. and Miri, M., Reliability Analysis of Corroded Pipes Using Conjugate HL–RF Algorithm Based on Average Shear Stress Yield Criterion, Engineering Failure Analysis, Vol. 46, pp. 104–117, 2014.
[12] Vodenitcharova, T. and Zhang, L., Bending and Local Buckling of a Nanocomposite Beam Reinforced by a Single-Walled Carbon Nanotube, International journal of solids and structures, Vol. 43, pp. 3006-3024, 2006.
[13] Thai, H-T and Vo, T.P., A Nonlocal Sinusoidal Shear Deformation Beam Theory with application to Bending, Buckling, and Vibration of Nanobeams, International Journal of Engineering Science, Vol. 54, pp. 58-66, 2012.
[14] Arani, A.G., Maghamikia, S., Mohammadimehr, M. and Arefmanesh, A., Buckling Analysis of Laminated Composite Rectangular Plates Reinforced by SWCNTs Using Analytical and Finite Element Methods, Journal of Mechanical Science and Technology, Vol. 25, pp. 809-820, 2011.
[15] Rafiee, M., Yang, J. and Kitipornchai, S., Thermal Bifurcation Buckling of Piezoelectric Carbon Nanotube Reinforced Composite Beams, Computers & Mathematics with Applications, Vol. 66, pp. 1147-1160, 2013.
[16] Wattanasakulpong, N. and Ungbhakorn, V., Analytical Solutions for Bending, Buckling and Vibration Responses of Carbon Nanotube-Reinforced Composite Beams Resting on Elastic Foundation, Computational Materials Science, Vol. 71, pp. 201-208, 2013.
[17] Kolahchi, R., Bidgoli, M.R., Beygipoor, G. and Fakhar, M.H., A Nonlocal Nonlinear Analysis for Buckling in Embedded FG-SWCNT-Reinforced Microplates Subjected to Magnetic Field, Journal of Mechanical Science and Technology, Vol. 29, pp. 3669-3677, 2015.
[18] Mosharrafian, F. and Kolahchi, R., Nanotechnology, Smartness and Orthotropic Nonhomogeneous Elastic Medium Effects on Buckling of Piezoelectric Pipes, Struct Eng Mech., Vol. 58, pp. 931-947, 2016.
[19] Barzoki, A.M., Arani, A.G., Kolahchi, R. and Mozdianfard, M., Electro-Thermo-Mechanical Torsional Buckling of a Piezoelectric Polymeric Cylindrical Shell Reinforced by DWBNNTs with an Elastic core, Applied Mathematical Modelling, Vol.;36, 2983-2995, 2012.
[20] Kolahchi, R., Hosseini, H. and Esmailpour, M., Differential Cubature and Quadrature-Bolotin Methods for Dynamic Stability of Embedded Piezoelectric Nanoplates Based on Visco-Nonlocal-Piezoelasticity Theories, Composite Structures, Vol. 157, pp. 174-186, 2016.
[21] Tan, P. and Tong, L., Micro-Electromechanics Models for Piezoelectric-Fiber-Reinforced Composite Materials, Composites science and technology, Vol. 61, pp. 759-769, 2001.