Nanowires, nanofibers and nanotubes have been widely used as the building blocks in micro/nano-electromechanical systems, energy harvesting or storage devices, and small-scaled measurement equipment. We report that th...Nanowires, nanofibers and nanotubes have been widely used as the building blocks in micro/nano-electromechanical systems, energy harvesting or storage devices, and small-scaled measurement equipment. We report that the sur- face effects of these nanobeams have a great impact on their deflection and internal forces. A simply supported nanobeam is taken as an example. For the displacement and shear force of the nanobeam, its dangerous sections are different from those predicted by the conventional beam theory, but for the bending moment, the dangerous section is the same. Moreover, the values of these three quantities for the nanobeam are all distinct from those calculated from the conventional beam model. These analyses shed new light on the stiffness and strength check of nanobeams, which are beneficial to engineer new-types of nano-materials and nano-devices.展开更多
The finite_element_displacement_perturbation method (FEDPM)for the geometric nonlinear behaviors of shells of revolution subjected to pure bending moments or lateral forces in one of their meridional planes (Ⅰ) was e...The finite_element_displacement_perturbation method (FEDPM)for the geometric nonlinear behaviors of shells of revolution subjected to pure bending moments or lateral forces in one of their meridional planes (Ⅰ) was employed to calculate the stress distributions and the stiffness of the bellows. Firstly, by applying the first_order perturbation solution (the linear solution)of the FEDPM to the bellows, the obtained results were compared with those of the general solution and the initial parameter integration solution proposed by the present authors earlier, as well as of the experiments and the FEA by others.It is shown that the FEDPM is with good precision and reliability, and as it was pointed out in (Ⅰ) the abrupt changes of the meridian curvature of bellows would not affect the use of the usual straight element. Then the nonlinear behaviors of the bellows were discussed. As expected, the nonlinear effects mainly come from the bellows ring plate,and the wider the ring plate is, the stronger the nonlinear effects are. Contrarily, the vanishing of the ring plate, like the C_shaped bellows, the nonlinear effects almost vanish. In addition, when the pure bending moments act on the bellows, each convolution has the same stress distributions calculated by the linear solution and other linear theories, but by the present nonlinear solution they vary with respect to the convolutions of the bellows. Yet for most bellows, the linear solutions are valid in practice.展开更多
In order to analyze bellows effectively and practically, the finite_element_displacement_perturbation method (FEDPM) is proposed for the geometric nonlinear behaviors of shells of revolution subjected to pure bending ...In order to analyze bellows effectively and practically, the finite_element_displacement_perturbation method (FEDPM) is proposed for the geometric nonlinear behaviors of shells of revolution subjected to pure bending moments or lateral forces in one of their meridional planes. The formulations are mainly based upon the idea of perturba_ tion that the nodal displacement vector and the nodal force vector of each finite element are expanded by taking root_mean_square value of circumferential strains of the shells as a perturbation parameter. The load steps and the iteration times are not as arbitrary and unpredictable as in usual nonlinear analysis. Instead, there are certain relations between the load steps and the displacement increments, and no need of iteration for each load step. Besides, in the formulations, the shell is idealized into a series of conical frusta for the convenience of practice, Sander's nonlinear geometric equations of moderate small rotation are used, and the shell made of more than one material ply is also considered.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos 11672334,11672335 and 11611530541the Fundamental Research Funds for the Central Universities under Grant No 15CX08004A
文摘Nanowires, nanofibers and nanotubes have been widely used as the building blocks in micro/nano-electromechanical systems, energy harvesting or storage devices, and small-scaled measurement equipment. We report that the sur- face effects of these nanobeams have a great impact on their deflection and internal forces. A simply supported nanobeam is taken as an example. For the displacement and shear force of the nanobeam, its dangerous sections are different from those predicted by the conventional beam theory, but for the bending moment, the dangerous section is the same. Moreover, the values of these three quantities for the nanobeam are all distinct from those calculated from the conventional beam model. These analyses shed new light on the stiffness and strength check of nanobeams, which are beneficial to engineer new-types of nano-materials and nano-devices.
文摘The finite_element_displacement_perturbation method (FEDPM)for the geometric nonlinear behaviors of shells of revolution subjected to pure bending moments or lateral forces in one of their meridional planes (Ⅰ) was employed to calculate the stress distributions and the stiffness of the bellows. Firstly, by applying the first_order perturbation solution (the linear solution)of the FEDPM to the bellows, the obtained results were compared with those of the general solution and the initial parameter integration solution proposed by the present authors earlier, as well as of the experiments and the FEA by others.It is shown that the FEDPM is with good precision and reliability, and as it was pointed out in (Ⅰ) the abrupt changes of the meridian curvature of bellows would not affect the use of the usual straight element. Then the nonlinear behaviors of the bellows were discussed. As expected, the nonlinear effects mainly come from the bellows ring plate,and the wider the ring plate is, the stronger the nonlinear effects are. Contrarily, the vanishing of the ring plate, like the C_shaped bellows, the nonlinear effects almost vanish. In addition, when the pure bending moments act on the bellows, each convolution has the same stress distributions calculated by the linear solution and other linear theories, but by the present nonlinear solution they vary with respect to the convolutions of the bellows. Yet for most bellows, the linear solutions are valid in practice.
文摘In order to analyze bellows effectively and practically, the finite_element_displacement_perturbation method (FEDPM) is proposed for the geometric nonlinear behaviors of shells of revolution subjected to pure bending moments or lateral forces in one of their meridional planes. The formulations are mainly based upon the idea of perturba_ tion that the nodal displacement vector and the nodal force vector of each finite element are expanded by taking root_mean_square value of circumferential strains of the shells as a perturbation parameter. The load steps and the iteration times are not as arbitrary and unpredictable as in usual nonlinear analysis. Instead, there are certain relations between the load steps and the displacement increments, and no need of iteration for each load step. Besides, in the formulations, the shell is idealized into a series of conical frusta for the convenience of practice, Sander's nonlinear geometric equations of moderate small rotation are used, and the shell made of more than one material ply is also considered.
