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Size-Dependent Mechanical Behaviors of Defective FGM Nanobeam Subjected to Random Loading

Considering the uncertainties of the materials and loads, the nanobeam made of functionally graded materials were investigated based on the non-local elastic theory. The spline finite point method (SFPM) was established to analyze the bending behavior of the nanobeam-based Timoshenko theory. In comparison with finite element method (FEM), SFPM has higher accuracy. Further, the multi-source uncertainties are considered, material properties are quantified as interval parameters, and loads are taken as random parameters. To deal with the problems with two types of uncertainties coexisting, a hybrid uncertain analysis model was established, and the method of polynomial chaos expansion and dimensional wise (PCE–DW) analysis was proposed to predict the response of nanobeam in the hybrid uncertain system. Numerical examples ultimately illustrate the effectiveness of the model and solution techniques, compared with MCS. The results furtherly verify the efficiency and accuracy.