Eringen's nonlocal elasticity theory is extensively employed for the analysis of nanostructures because it is able to capture nanoscale effects.Previous studies have revealed that using the differential form of th...Eringen's nonlocal elasticity theory is extensively employed for the analysis of nanostructures because it is able to capture nanoscale effects.Previous studies have revealed that using the differential form of the strain-driven version of this theory leads to paradoxical results in some cases,such as bending analysis of cantilevers,and recourse must be made to the integral version.In this article,a novel numerical approach is developed for the bending analysis of Euler-Bernoulli nanobeams in the context of strain-and stress-driven integral nonlocal models.This numerical approach is proposed for the direct solution to bypass the difficulties related to converting the integral governing equation into a differential equation.First,the governing equation is derived based on both strain-driven and stress-driven nonlocal models by means of the minimum total potential energy.Also,in each case,the governing equation is obtained in both strong and weak forms.To solve numerically the derived equations,matrix differential and integral operators are constructed based upon the finite difference technique and trapezoidal integration rule.It is shown that the proposed numerical approach can be efficiently applied to the strain-driven nonlocal model with the aim of resolving the mentioned paradoxes.Also,it is able to solve the problem based on the strain-driven model without inconsistencies of the application of this model that are reported in the literature.展开更多
The size-dependent nonlinear buckling and postbuckling characteristics of circular cylindrical nanoshells subjected to the axial compressive load are investigated with an analytical approach. The surface energy effect...The size-dependent nonlinear buckling and postbuckling characteristics of circular cylindrical nanoshells subjected to the axial compressive load are investigated with an analytical approach. The surface energy effects are taken into account according to the surface elasticity theory of Gurtin and Murdoch. The developed geometrically nonlinear shell model is based on the classical Donnell shell theory and the von Karman＇s hypothesis. With the numerical results, the effect of the surface stress on the nonlinear buckling and postbuckling behaviors of nanoshells made of Si and Al is studied. Moreover, the influence of the surface residual tension and the radius-to-thickness ratio is illustrated. The results indicate that the surface stress has an important effect on prebuckling and postbuekling characteristics of nanoshells with small sizes.展开更多
文摘Eringen's nonlocal elasticity theory is extensively employed for the analysis of nanostructures because it is able to capture nanoscale effects.Previous studies have revealed that using the differential form of the strain-driven version of this theory leads to paradoxical results in some cases,such as bending analysis of cantilevers,and recourse must be made to the integral version.In this article,a novel numerical approach is developed for the bending analysis of Euler-Bernoulli nanobeams in the context of strain-and stress-driven integral nonlocal models.This numerical approach is proposed for the direct solution to bypass the difficulties related to converting the integral governing equation into a differential equation.First,the governing equation is derived based on both strain-driven and stress-driven nonlocal models by means of the minimum total potential energy.Also,in each case,the governing equation is obtained in both strong and weak forms.To solve numerically the derived equations,matrix differential and integral operators are constructed based upon the finite difference technique and trapezoidal integration rule.It is shown that the proposed numerical approach can be efficiently applied to the strain-driven nonlocal model with the aim of resolving the mentioned paradoxes.Also,it is able to solve the problem based on the strain-driven model without inconsistencies of the application of this model that are reported in the literature.
文摘The size-dependent nonlinear buckling and postbuckling characteristics of circular cylindrical nanoshells subjected to the axial compressive load are investigated with an analytical approach. The surface energy effects are taken into account according to the surface elasticity theory of Gurtin and Murdoch. The developed geometrically nonlinear shell model is based on the classical Donnell shell theory and the von Karman＇s hypothesis. With the numerical results, the effect of the surface stress on the nonlinear buckling and postbuckling behaviors of nanoshells made of Si and Al is studied. Moreover, the influence of the surface residual tension and the radius-to-thickness ratio is illustrated. The results indicate that the surface stress has an important effect on prebuckling and postbuekling characteristics of nanoshells with small sizes.
