基于準連續(xù)方法的碳納米結(jié)構(gòu)的靜力學和動力學特性的數(shù)值研究.pdf

1、Carbon nanostructures are perhaps one of the greatest scientific successes which possess superior material properties.Continuous efforts, involving experimental and theoretical studies, have been made for good understand

2、ing of their mechanical performance. Experimental studies require advanced instruments and expensive equipments.Moreover, it is still quite difficult to conduct and control experiments at such nanometer scale which would

3、 unavoidably cause a broad discrepancy in the results.Theoretical modeling approaches can predict structural behaviors of these carbon nanostructures with good repeatability, reproducibility and controllability and thus

4、they play an increasingly important role in the analysis of mechanical properties for carbon nanostructures.
　　A high-performance computing technique is urgently required for the investigation of such carbon nanostruc

5、tures in nanoscience and nanotechnology research and practical engineering.Atomistic simulations can precisely capture the delicate behaviors of carbon
　　nanostructures but at a high cost of computational resource and

6、 are apparently limited to a small size.This research adopts an exquisite quasi-continuum method to investigate the mechanical properties of carbon nanostructures.It employs the higher-order gradient
　　theory to estab

7、lish the constitutive model.Unlike the traditional continuum models, the higher-order gradient theory is developed at the atomic level and provides a sound linkage of the deformation of crystal lattice structure to that

8、of continuum displacement
　　field.The distinct superiority of this quasi-continuum method is incorporating the structural information of crystal lattice which is described by introducing a representative cell.In the c

9、arbon nanostructures, the atomic structure that each carbon atom is connected to three neighboring carbon atoms by the covalent bonds is selected as the representative cell.The deformation of C-C bond vector is approxima

10、ted by utilizing the higher-order Cauchy-Born rule whose involved second-order deformation gradient can accurately capture the bending effect and make the deformed C-C bond vector closer to the actual placement.Thus, the

11、 established constitutive model is more reasonable and accords extremely well with physical behaviors.
　　A widely used multi-body potential, Brenner potential, is employed for the calculation of the energy stored in t

12、he C-C covalent bonds.As far as single-walled carbon nanotubes (SWCNTs) are concerned, the initial equilibrium configuration is determined by minimizing the potential energy of the representative cell, structural paramet

13、ers and elastic properties, such as Young's moduli and Poisson's ratio, are thus obtained. However, there are some differences of the atomic structure between SWCNTs and single-walled carbon nanocones (SWCNCs) because th

14、e radius of SWCNCs increases in the longitudinal direction and this phenomenon gives rise to an effect on the mechanical properties.
　　Subsequently, with the constructed constitutive relationship, a novel mesh-free nu

15、merically computational framework is proposed to study mechanical behaviors of these carbon nanostructures.The mesh-free shape function is one of the critical factors in the development of a mesh-free method.The newly mo

16、ving Kriging interpolation possesses two distinct advantages, the higher order continuity and delta function property.The former fills the requirement of C1-continuous field function for the second-order deformation grad

17、ients involved in the higher-order deformation gradient constitutive
　　model and the latter automatically satisfies the essential boundary conditions. Consequently, the moving Kriging interpolation is fme and suitable

18、 to be adopted to construct the mesh-free shape function.In addition, by introducing a semivariogram model, corresponding to the covariance, the constructed mesh-free shape function as well as its first-and second-order

19、derivatives can be expressed simply and conveniently.
　　This research is a systemic theoretical and numerical study of mechanical behaviors of carbon nanostructures.It gives a comprehensive study of carbon nanostructu

20、res with various loadings and boundary conditions for static and dynamic problems.A SWCNT is regarded as a seamless cylindrical hollow shape formed by rolling up a rectangle graphite sheet and similarly, a SWCNC is treat

21、ed as a conical structure formed by mapping a tailored graphite sheet and connecting its two ends together.Several numerical examples are used to validate the present quasi-continuum approach.Computational results are co

22、mpared with those obtained from atomistic simulation and existing data, and are found to be in good agreement.Since the free choice of nodes in the mesh-free computational framework, it can largely reduce the degrees of

23、freedom of the system, and thus save a large amount of computational resources.A few nodes can ensure a high precision for homogenous deformation prior to buckling and an increasing number of nodes are needed to capture

24、the buckling behavior.This makes this proposed method much attractive in engineering applications.Elastic properties, buckling and post-buckling behaviors, vibration characteristic and mass detection of carbon nanostruct

25、ures with various constraints are further numerically simulated using the proposed mesh-free computational framework.
　　Finally, this approach is extended to the study of multi-layer carbon nanostructures with conside

26、ring the weak interlayer interaction which is contributed from van der Waals (vdW) force.In the present model, the vdW force between any two layers is considered
　　and the interatomic interaction between different lay

27、ers is treated as a tress rod, which is described by Lennard-Jones potential.This work provides a systemic and comprehensive understanding of mechanical performance of carbon nanostructures.It is noteworthy that
　　the