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

Chih-Ping Wu, Ruei Yong Jiang

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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 languageEnglish
Pages (from-to)239-279
Number of pages41
JournalCMES - Computer Modeling in Engineering and Sciences
Volume97
Issue number3
Publication statusPublished - 2014 Mar 27

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Reproducing Kernel
Kernel Methods
Circular Cylinder
Circular cylinders
Buckling
Nanotubes
Carbon nanotubes
Carbon
State Space
Composite
Composite materials
Transfer matrix method
Axial compression
Fourier series
Laminated composites
Single-walled carbon nanotubes (SWCN)
Rhombus
Ordinary differential equations
Initial Stress
Critical Load

All Science Journal Classification (ASJC) codes

  • Software
  • Modelling and Simulation
  • Computer Science Applications

Cite this

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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.",
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