It is showed that all equations of the linearized Gurtin-Murdoch model of surface elasticity can be derived, in a straightforward way, from a simple second-order expression for the ratio of deformed surface area to in...It is showed that all equations of the linearized Gurtin-Murdoch model of surface elasticity can be derived, in a straightforward way, from a simple second-order expression for the ratio of deformed surface area to initial surface area. This elementary derivation offers a simple explanation for all unique features of the model and its simplified/modified versions, and helps to clarify some misunderstandings of the model already occurring in the literature. Finally, it is demonstrated that, because the Gurtin-Murdoch model is based on a hybrid formulation combining linearized deformation of bulk material with 2nd-order finite deformation of the surface, caution is needed when the original form of this model is applied to bending deformation of thin-walled elastic structures with surface stress.展开更多
Presented in this paper is a precise investigation of the effect of surface stress on the vibration characteristics and instability of fluid-conveying nanoscale pipes.To this end,the nanoscale pipe is modeled as a Tim...Presented in this paper is a precise investigation of the effect of surface stress on the vibration characteristics and instability of fluid-conveying nanoscale pipes.To this end,the nanoscale pipe is modeled as a Timoshenko nanobeam.The equations of motion of the nanoscale pipe are obtained based on Hamilton＇s principle and the Gurtin-Murdoch continuum elasticity incorporating the surface stress effect.Afterwards,the generalized differential quadrature method is employed to discretize the governing equations and associated boundary conditions.To what extent important parameters such as the thickness,material and surface stress modulus,residual surface stress,surface density,and boundary conditions influence the natural frequency of nanoscale pipes and the critical velocity of fluid is discussed.展开更多
Multilayered nanoscale structures are used in several applications.Because the effect of surface energy becomes nontrivial at such a small scale,a modified continuum theory is required to accurately predict their mech...Multilayered nanoscale structures are used in several applications.Because the effect of surface energy becomes nontrivial at such a small scale,a modified continuum theory is required to accurately predict their mechanical behaviors.A Gurtin–Murdoch continuum model of surface elasticity is implemented to establish a computational scheme for investigating an elastic multilayered system under axisymmetric loads with the incorporation of surface/interface energy.Each layer stiffness matrix is derived based on the general solutions of stresses and displacements obtained in the form of the Hankel integral transform.Numerical solutions to the global equation,which are formulated based on the continuity conditions of tractions and displacements across interfaces between layers,yield the displacements at each layer interface and on the top surface of the multilayered medium.The numerical solutions indicate that the elastic responses of multilayered structures are affected significantly by the surface material properties of both the top surface and interfaces,and that they become size dependent.In addition,the indentation problem of a multilayered nanoscale elastic medium under a rigid frictionless cylindrical punch is investigated to demonstrate the application of the proposed solution scheme.展开更多
基金Financial support of the Natural Science and Engineering Research Council (NSERC)
文摘It is showed that all equations of the linearized Gurtin-Murdoch model of surface elasticity can be derived, in a straightforward way, from a simple second-order expression for the ratio of deformed surface area to initial surface area. This elementary derivation offers a simple explanation for all unique features of the model and its simplified/modified versions, and helps to clarify some misunderstandings of the model already occurring in the literature. Finally, it is demonstrated that, because the Gurtin-Murdoch model is based on a hybrid formulation combining linearized deformation of bulk material with 2nd-order finite deformation of the surface, caution is needed when the original form of this model is applied to bending deformation of thin-walled elastic structures with surface stress.
文摘Presented in this paper is a precise investigation of the effect of surface stress on the vibration characteristics and instability of fluid-conveying nanoscale pipes.To this end,the nanoscale pipe is modeled as a Timoshenko nanobeam.The equations of motion of the nanoscale pipe are obtained based on Hamilton＇s principle and the Gurtin-Murdoch continuum elasticity incorporating the surface stress effect.Afterwards,the generalized differential quadrature method is employed to discretize the governing equations and associated boundary conditions.To what extent important parameters such as the thickness,material and surface stress modulus,residual surface stress,surface density,and boundary conditions influence the natural frequency of nanoscale pipes and the critical velocity of fluid is discussed.
基金supported by the Civil Engineering Centennial Scholarship of Chulalongkorn University,Thailand Research Fund under Grant MRG6280116the TRF Senior Research Scholar under Grant RTA 6280012.
文摘Multilayered nanoscale structures are used in several applications.Because the effect of surface energy becomes nontrivial at such a small scale,a modified continuum theory is required to accurately predict their mechanical behaviors.A Gurtin–Murdoch continuum model of surface elasticity is implemented to establish a computational scheme for investigating an elastic multilayered system under axisymmetric loads with the incorporation of surface/interface energy.Each layer stiffness matrix is derived based on the general solutions of stresses and displacements obtained in the form of the Hankel integral transform.Numerical solutions to the global equation,which are formulated based on the continuity conditions of tractions and displacements across interfaces between layers,yield the displacements at each layer interface and on the top surface of the multilayered medium.The numerical solutions indicate that the elastic responses of multilayered structures are affected significantly by the surface material properties of both the top surface and interfaces,and that they become size dependent.In addition,the indentation problem of a multilayered nanoscale elastic medium under a rigid frictionless cylindrical punch is investigated to demonstrate the application of the proposed solution scheme.
