Nonlinear bending response of functionally graded nanobeams with material uncertainties

作者：Lv, Zheng; Liu, Hu^*

来源：International Journal of Mechanical Sciences, 2017, 134: 123-135.

DOI：10.1016/j.ijmecsci.2017.10.008

• Functionally graded materials
• Nonlinear bending response
• Nanobeam
• Material uncertainty
• Nonlocal strain gradient theory
• Interval analysis method

Material uncertainties caused by the defects in molecular structure and the inaccurate measurements at nano-scale have been reported. The influence of these uncertainties on mechanical behaviors of nanostructures is crucial to the potential application in the field of structural health monitoring where high accuracy modeling is required. This study focuses on the influence of material uncertainties on nonlinear bending response of nanobeam made of functionally graded (FG) materials. Based on the nonlocal strain gradient theory, the size-dependent equilibrium differential equation of the FG nanobeam is derived by using the minimum total potential energy principle and the analytical formulation of the nonlinear bending response is deduced, in which the geometric nonlinearity is considered. The effect of variation of material parameters on the nonlinear bending response is studied subsequently. Considering the drawback of probabilistic method in the case of insufficient sample data, a non probabilistic uncertainty modeling for the FG nanobeam is developed by quantifying material uncertainties with interval parameters. Simultaneously, an iterative algorithm based interval analysis method (IA-IAM) is presented to solve this model. The combined effects of material uncertainties and size-dependent parameters as well as the power-law index of the FG material on the nonlinear bending response of the FG nanobeam are investigated in detail. Numerical results can provide helpful guidance for the reliability design of nanodevices.

• 出版日期2017-12
• 单位北京航空航天大学