Papers by Keyword: Continuum Theory

Abstract: The transverse nonlinear vibration of a nanobeam fully clamped at both two ends was investigated using a strain gradient type of nonlocal continuum theory. The small scale effect was considered to the mechanical model at nanoscale. The axial elongation of the nanobeam was taken into account and the nonlinear partial differential equation governing the transverse motion was derived. Subsequently, a perturbation method was applied to the nonlinear governing equation. The dynamical responses of the nanobeam such as transverse displacement and resonant angular frequency were obtained and they were compared with those by a numerical method. The comparison indicated the validity of the present nonlinear model and the multiple-scales analysis method.

Abstract: It is a key step of finite element method analysis to generate engineering structure mesh. The continuous conceptual model of discontinuous substance is studied. How to select similar-continuous micro-particle size is researched. The continuous conceptual model of soil body and the continuous conceptual method of geotechnical engineering are approached based on the deep mixing pile composite foundation. The results show that finite element method mesh generation based on material-continuous-nature need to more consider, and the minimum of the element size is those of similar-continuous micro-particle and the maximum is limited by the scope of geotechnical engineering project. While the material continuous nature is considered, the continuum theory would be satisfied to simulate engineering structure with finite element method.

Abstract: It is commonly believed that continuum mechanics theories may not be applied at the nanoscale due to the discrete nature of atoms. We developed a nanoscale continuum theory based on interatomic potentials for nanostructured materials. The interatomic potential is directly incorporated into the continuum theory through the constitutive models. The nanoscale continuum theory is then applied to study the mechanical deformation and thermal properties of carbon nanotubes, including (1) pre-deformation energy; (2) linear elastic modulus; (3) fracture nucleation; (4) defect nucleation; (5) electrical property change due to mechanical deformation; (6) specific heat; and (7) coefficient of thermal expansion. The nanoscale continuum theory agrees very well with the experiments and atomistic simulations without any parameter fitting, and therefore has the potential to be utilized to complex nanoscale material systems (e.g., nanocomposites) and devices (e.g., nanoelectronics).