In the current paper, size‐dependent mechanical analysis of functionally graded porous (FGP) nanobeams resting on Pasternak foundation in thermal environment is presented based on nonlocal strain gradient theory and Gurtin‐Murdoch surface elasticity theory. The nanobeam is modeled based on Euler‐Bernoulli beam theory, Timoshenko beam theory and Reddy's third‐order shear deformation theory and the set of the governing equations are solved for a clamped‐clamped FGP nanobeam using generalized differential quadrature method. Numerical results show that as porosity parameter increases, static deflection increases and critical buckling load decreases, but its effect on the fundamental frequency strongly depends on the porosity distribution pattern. It was revealed that among all studied porosity distribution patterns, the minimum value of the static deflection and maximum values of critical buckling load and fundamental frequency can be achieved using symmetric distribution pattern of pores. It is concluded that tensional residual stress reduces static deflection and increases both critical buckling load and fundamental frequency and temperature rise has reverse effects.

In this paper, a comprehensive study is presented for mechanical analysis of functionally graded porous (FGP) nanobeams resting on an elastic foundation. The nanobeam is modeled according to different beam theories along with nonlocal strain gradient theory and Gurtin-Murdoch surface elasticity theory. Using Hamilton's principle, the set of governing equations are derived, and exact solutions are presented using Navier's method for the static bending, mechanical buckling and free vibration analyses of simply supported FGP nanobeams. The effects of various parameters on static deflection, critical buckling load and fundamental natural frequency of FGP nanobeams are studied. It is shown that for all types of porosity distribution patterns, an increase in porosity parameter leads to an increase in static deflection, and a decrease in critical buckling load and effect of porosity parameter on fundamental natural frequency is dependent on the porosity distribution pattern. Numerical results confirm that tensional residual surface stress decreases static deflection and increases both critical buckling load and fundamental natural frequency, but compressive residual surface stress has opposite effects.