Papers by Keyword: Continuum Model

Abstract: Based on an explicit van der Waals (vdW) model, which can reproduce the interaction between any two layers of multi-walled carbon nanotube (MWCNT) and is dependent on the change of interlayer spacing and on the tube radii, the vibration analysis of multi-walled carbon nanotubes is carried out by using of the multi-layered Flugge shells model. The natural frequencies are analyzed in detail for with various radii and number of tubes. Furthermore, the natural frequencies of double-walled carbon nanotube with the innermost radii of 0.6 nm predicted based on the Flugge shell model are well compared with those from the Donnell shell one. The present investigation will be meaningful for the design and application of multi-walled carbon nanotubes as nano- resonators.

Abstract: This paper presents a multiscale method to estimate the elastic property of the 13_3 microtubule. A microtubule is viewed as being formed by rolling up its planar encounter into the tubular shape, and the transformation is written into a set of equations with three geometrical parameters. The representative cell is chosen as an unit of two pairs of tubulin momoners. With the appropriate longitudinal and lateral interactive potentials, the strain energy density is calculated by deviding the cell’s energy by its spacial volume. The elastic property of microtubule is determined by minimizing the strain energy density, and the elastic constants are calculated in the thereotical scheme of orthotropic elasticity due to the geometrical meanings of the induced parameters. The advantage of the proposed method and its future application are discussed.

Abstract: This paper introduces a multiscale modeling approach for carbon nanotubes (CNTs), in which a fine continuum model that has been developed by the present authors is employed to implement the continuum modleing. The entire domain is decomposed into a continuum modeling region and an atomic region with an overlapping region. For the atomic region, the atomic finite element method (AFEM) is used to trace the individual atomic motion. Whereas, the continuum region is viewed as the higher-order continuum media, and the mesh-free method is adopted to implement the continuum numerical discrization. For the overlapping region, the bridging domain method is used to efficiently couple two scales. Numerical computation is carried out and several examples are discussed.

Abstract: Numerical study of both the solidification of the binary alloy Al-4.1%wtCu and macrosegregation defects formation have been carried out. The mixture continuum model was used in the development of the mathematical model representing the solidification phenomena. This model included the conservative equations (mass, momentum, energy and species); these equations were numerically solved by using a finite volume approach.