### Abstract

A state space differential reproducing kernel (DRK) method is developed for the three-dimensional (3D) buckling analysis of simply-supported, carbon nanotube-reinforced composite (CNTRC) circular hollow cylinders and laminated composite ones under axial compression. The single-walled carbon nanotubes (CNTs) and polymer are used as the reinforcements and matrix, respectively, to constitute the CNTRC cylinder. Three different distributions of CNTs varying in the thickness direction are considered (i.e., the uniform distribution and functionally graded rhombus-, and X-type ones), and the through-thickness distributions of effective material properties of the cylinder are determined using the rule of mixtures. The 3D linear buckling theory is used, in which a set of membrane stresses is assumed to exist in the cylinder just before instability occurs, and this is regarded as the initial stresses introduced in the formulation. The Euler-Lagrange equations perturbed from the state of neutral equilibrium are derived using the Reissner mixed variational theorem. The primary field variables, displacement and transverse stress components, are expanded as the single Fourier series in the circumferential coordinate, and then interpolated in the axial coordinate using DRK interpolation functions. Finally, the state space equations of this problem are obtained, which represent a system of ordinary differential equations in the thickness coordinate. The state space DRK solutions of the critical load parameters of the cylinder can thus be obtained by means of the transfer matrix method combined with the successive approximation one, and the convergence and accuracy of the state space DRK solutions are validated by comparing these solutions with exact 3D ones available in the literature and approximate 3D ones obtained using the ANSYS software.

Original language | English |
---|---|

Pages (from-to) | 239-279 |

Number of pages | 41 |

Journal | CMES - Computer Modeling in Engineering and Sciences |

Volume | 97 |

Issue number | 3 |

Publication status | Published - 2014 Mar 27 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Software
- Modelling and Simulation
- Computer Science Applications

### Cite this

}

*CMES - Computer Modeling in Engineering and Sciences*, vol. 97, no. 3, pp. 239-279.

**A state space differential reproducing kernel method for the buckling analysis of carbon nanotube-reinforced composite circular hollow cylinders.** / Wu, Chih-Ping; Jiang, Ruei Yong.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A state space differential reproducing kernel method for the buckling analysis of carbon nanotube-reinforced composite circular hollow cylinders

AU - Wu, Chih-Ping

AU - Jiang, Ruei Yong

PY - 2014/3/27

Y1 - 2014/3/27

N2 - A state space differential reproducing kernel (DRK) method is developed for the three-dimensional (3D) buckling analysis of simply-supported, carbon nanotube-reinforced composite (CNTRC) circular hollow cylinders and laminated composite ones under axial compression. The single-walled carbon nanotubes (CNTs) and polymer are used as the reinforcements and matrix, respectively, to constitute the CNTRC cylinder. Three different distributions of CNTs varying in the thickness direction are considered (i.e., the uniform distribution and functionally graded rhombus-, and X-type ones), and the through-thickness distributions of effective material properties of the cylinder are determined using the rule of mixtures. The 3D linear buckling theory is used, in which a set of membrane stresses is assumed to exist in the cylinder just before instability occurs, and this is regarded as the initial stresses introduced in the formulation. The Euler-Lagrange equations perturbed from the state of neutral equilibrium are derived using the Reissner mixed variational theorem. The primary field variables, displacement and transverse stress components, are expanded as the single Fourier series in the circumferential coordinate, and then interpolated in the axial coordinate using DRK interpolation functions. Finally, the state space equations of this problem are obtained, which represent a system of ordinary differential equations in the thickness coordinate. The state space DRK solutions of the critical load parameters of the cylinder can thus be obtained by means of the transfer matrix method combined with the successive approximation one, and the convergence and accuracy of the state space DRK solutions are validated by comparing these solutions with exact 3D ones available in the literature and approximate 3D ones obtained using the ANSYS software.

AB - A state space differential reproducing kernel (DRK) method is developed for the three-dimensional (3D) buckling analysis of simply-supported, carbon nanotube-reinforced composite (CNTRC) circular hollow cylinders and laminated composite ones under axial compression. The single-walled carbon nanotubes (CNTs) and polymer are used as the reinforcements and matrix, respectively, to constitute the CNTRC cylinder. Three different distributions of CNTs varying in the thickness direction are considered (i.e., the uniform distribution and functionally graded rhombus-, and X-type ones), and the through-thickness distributions of effective material properties of the cylinder are determined using the rule of mixtures. The 3D linear buckling theory is used, in which a set of membrane stresses is assumed to exist in the cylinder just before instability occurs, and this is regarded as the initial stresses introduced in the formulation. The Euler-Lagrange equations perturbed from the state of neutral equilibrium are derived using the Reissner mixed variational theorem. The primary field variables, displacement and transverse stress components, are expanded as the single Fourier series in the circumferential coordinate, and then interpolated in the axial coordinate using DRK interpolation functions. Finally, the state space equations of this problem are obtained, which represent a system of ordinary differential equations in the thickness coordinate. The state space DRK solutions of the critical load parameters of the cylinder can thus be obtained by means of the transfer matrix method combined with the successive approximation one, and the convergence and accuracy of the state space DRK solutions are validated by comparing these solutions with exact 3D ones available in the literature and approximate 3D ones obtained using the ANSYS software.

UR - http://www.scopus.com/inward/record.url?scp=84897908709&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84897908709&partnerID=8YFLogxK

M3 - Article

VL - 97

SP - 239

EP - 279

JO - CMES - Computer Modeling in Engineering and Sciences

JF - CMES - Computer Modeling in Engineering and Sciences

SN - 1526-1492

IS - 3

ER -