Nonlocal nonlinear thermal bending and postbuckling analysis of FG porous nanobeams

Present research deals with the nonlinear thermal bending and postbuckling behavior of functionally graded (FG) porous nanobeams. Based on the Euler-Bernoulli beam theory and von-Karman nonlinearity, the nonlinear equilibrium equations are extracted on the basis of the nonlocal elasticity theory. With the establishment of the principle of virtual displacement, the Chebyshev-Ritz method is utilized to obtain the matrix form of the governing equations. Two different strategies, including the Newton-Raphson method and direct displacement control scheme, are proposed to extract the nonlinear trajectories. Afterward, based on the power series method, the steady-state heat conduction (HC) equation is solved for the FG porous nanobeam. Numerical investigations are given to discuss the influences of the power-law index, porosity volume fraction, nonlocal parameter, and boundary conditions on the nonlinear thermal stability of the FG porous nanobeam. It is shown that the thermal postbuckling curves of the graded nanobeam with porosities are higher than of the nanobeam with the perfect type of material distribution.

Keywords:

FG porous nanobeam , Nonlinear thermal stability , Nonlocal theory , Ritz method