Based on the nonlocal strain gradient theory(NSGT),the static bending behaviors of an axially functionally graded(AFG)Bernoulli-Euler microbeam subjected to concentrated and distributed loads are studied.The material ...Based on the nonlocal strain gradient theory(NSGT),the static bending behaviors of an axially functionally graded(AFG)Bernoulli-Euler microbeam subjected to concentrated and distributed loads are studied.The material property of the AFG microbeam changes continuously along the longitudinal direction.On the basis of the minimum potential energy principle,the equations of motion and associated classical and non-classical boundary conditions are derived.Then,Galerkin’s weighted residual method in conjunction with the normalization technique are utilized to solve the governing differential equations.The transverse deformations of the AFG microbeam suffering the sinusoidal distributed load within the framework of NSGT,nonlocal elasticity theory(NET),strain gradient theory(SGT)and classical elasticity theory(CET)are compared.It is observed that the bending flexibility of the microbeam decreases with the increase in the ratio of the material length scale parameter to the beam height.However,the bending flexibility increases with the increase in the material nonlocal parameter.The functionally graded parameter plays an important role in controlling the transverse deformation.This study provides a theoretical basis and a technical reference for the design and analysis of AFG micro-beams in the related regions.展开更多
基金The National Key Research and Development Program of China(No.2017YFC0307604)the Talent Foundation of China University of Petroleum(No.Y1215042)
文摘Based on the nonlocal strain gradient theory(NSGT),the static bending behaviors of an axially functionally graded(AFG)Bernoulli-Euler microbeam subjected to concentrated and distributed loads are studied.The material property of the AFG microbeam changes continuously along the longitudinal direction.On the basis of the minimum potential energy principle,the equations of motion and associated classical and non-classical boundary conditions are derived.Then,Galerkin’s weighted residual method in conjunction with the normalization technique are utilized to solve the governing differential equations.The transverse deformations of the AFG microbeam suffering the sinusoidal distributed load within the framework of NSGT,nonlocal elasticity theory(NET),strain gradient theory(SGT)and classical elasticity theory(CET)are compared.It is observed that the bending flexibility of the microbeam decreases with the increase in the ratio of the material length scale parameter to the beam height.However,the bending flexibility increases with the increase in the material nonlocal parameter.The functionally graded parameter plays an important role in controlling the transverse deformation.This study provides a theoretical basis and a technical reference for the design and analysis of AFG micro-beams in the related regions.
