A novel size-dependent model is developed herein to study the bending behavior of beam-type micro/nano-structures considering combined effects of nonlocality and micro-rotational degrees of freedom. To accomplish this...A novel size-dependent model is developed herein to study the bending behavior of beam-type micro/nano-structures considering combined effects of nonlocality and micro-rotational degrees of freedom. To accomplish this aim, the micropolar theory is combined with the nonlocal elasticity. To consider the nonlocality, both integral (original) and differential formulations of Eringen’s nonlocal theory are considered. The beams are considered to be Timoshenko-type, and the governing equations are derived in the variational form through Hamilton’s principle. The relations are written in an appropriate matrix-vector representation that can be readily utilized in numerical approaches. A finite element (FE) approach is also proposed for the solution procedure. Parametric studies are conducted to show the simultaneous nonlocal and micropolar effects on the bending response of small-scale beams under different boundary conditions.展开更多
An analytical approach is proposed to study the postbuckling of circular cylindrical shells subject to axial compression and lateral pressure made of functionally graded graphene platelet-reinforced polymer composite ...An analytical approach is proposed to study the postbuckling of circular cylindrical shells subject to axial compression and lateral pressure made of functionally graded graphene platelet-reinforced polymer composite (FG-GPL-RPC). The governing equations are obtained in the context of the classical Donnell shell theory by the von K′arm′an nonlinear relations. Then, based on the Ritz energy method, an analytical solution approach is used to trace the nonlinear postbuckling path of the shell. The effects of several parameters such as the weight fraction of the graphene platelet (GPL), the geometrical properties, and distribution patterns of the GPL on the postbuckling characteristics of the FG-GPL-RPC shell are analyzed.展开更多
By the atomistic and continuum finite element models, the free vibration behavior of single-walled carbon nanotubes （SWCNTs） is studied. In the atomistic finite element model, the bonds and atoms are modeled by the ...By the atomistic and continuum finite element models, the free vibration behavior of single-walled carbon nanotubes （SWCNTs） is studied. In the atomistic finite element model, the bonds and atoms are modeled by the beam and point mass elements, respectively. The molecular mechanics is linked to structural mechanics to determine the elastic properties of the mentioned beam elements. In the continuum finite element approach, by neglecting the discrete nature of the atomic structure of the nanotubes, they are modeled with shell elements. By both models, the natural frequencies of SWCNTs are computed, and the effects of the geometrical parameters, the atomic structure, and the boundary conditions are investigated. The accuracy of the utilized methods is verified in comparison with molecular dynamic simulations. The molecular structural model leads to more reliable results, especially for lower aspect ratios. The present analysis provides valuable information about application of continuum models in the investigation of the mechanical behaviors of nanotubes.展开更多
文摘A novel size-dependent model is developed herein to study the bending behavior of beam-type micro/nano-structures considering combined effects of nonlocality and micro-rotational degrees of freedom. To accomplish this aim, the micropolar theory is combined with the nonlocal elasticity. To consider the nonlocality, both integral (original) and differential formulations of Eringen’s nonlocal theory are considered. The beams are considered to be Timoshenko-type, and the governing equations are derived in the variational form through Hamilton’s principle. The relations are written in an appropriate matrix-vector representation that can be readily utilized in numerical approaches. A finite element (FE) approach is also proposed for the solution procedure. Parametric studies are conducted to show the simultaneous nonlocal and micropolar effects on the bending response of small-scale beams under different boundary conditions.
文摘An analytical approach is proposed to study the postbuckling of circular cylindrical shells subject to axial compression and lateral pressure made of functionally graded graphene platelet-reinforced polymer composite (FG-GPL-RPC). The governing equations are obtained in the context of the classical Donnell shell theory by the von K′arm′an nonlinear relations. Then, based on the Ritz energy method, an analytical solution approach is used to trace the nonlinear postbuckling path of the shell. The effects of several parameters such as the weight fraction of the graphene platelet (GPL), the geometrical properties, and distribution patterns of the GPL on the postbuckling characteristics of the FG-GPL-RPC shell are analyzed.
文摘By the atomistic and continuum finite element models, the free vibration behavior of single-walled carbon nanotubes （SWCNTs） is studied. In the atomistic finite element model, the bonds and atoms are modeled by the beam and point mass elements, respectively. The molecular mechanics is linked to structural mechanics to determine the elastic properties of the mentioned beam elements. In the continuum finite element approach, by neglecting the discrete nature of the atomic structure of the nanotubes, they are modeled with shell elements. By both models, the natural frequencies of SWCNTs are computed, and the effects of the geometrical parameters, the atomic structure, and the boundary conditions are investigated. The accuracy of the utilized methods is verified in comparison with molecular dynamic simulations. The molecular structural model leads to more reliable results, especially for lower aspect ratios. The present analysis provides valuable information about application of continuum models in the investigation of the mechanical behaviors of nanotubes.
