Nonlocal Stochastic Bending Response of Functionally Graded Porous Nanobeams Under Thermal Environment Using FOPT

The present work demonstrates the size dependent stochastic bending response of functionally graded porous nanobeams under the thermal environment. The displacement field of the beam is defined based on the Reddy’s higher order beam theory. The nonlocal elasticity theory is used to establish the constitutive relation to take care of size effects. This theory explains that the stress at a point is a function of strains at all points in the continuum. The porosity in the nanobeam is modeled by modified power law. Further, two types of porosity distributions are considered, one is of uniform type and second one is of non-uniform type. The minimum potential energy principle is applied to obtain the governing equations and then solved by the finite element method. First order perturbation theory (FOPT) is used to analyze the randomness in the flexural behavior of nanobeams, and a comparison study have been performed between the FOPT results and MCS results to validate the FOPT-based model. Further parametric study is performed to investigate the influence of nonlocal parameter, material gradation, aspect ratio, porosity, random material properties, thermal environment, and boundary conditions on the degree of randomness in the deflection of porous FG nanobeams.