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In this investigation, the homotopy analysis method (HAM) is utilized for the pull-in and nonlinear vibration analysis of nanobeams based on the stress-driven model (SDM) of nonlocal elasticity theory. The physical properties of nanobeams are assumed not to vary through the thickness. The nonlinear equation of motion and the corresponding boundary condition are derived on the basis of the Euler–Bernoulli beam theory. For the solution purpose, the Galerkin method is employed for reducing the nonlinear partial differential equation to a nonlinear ordinary differential equation in the time domain, and then, the resulting equation is analytically solved using the HAM. In the results section, the influences of different parameters, including nonlocal parameter, electrostatic and intermolecular van der Waals forces and fringing field effect changes on the pull-in and nonlinear vibration response are investigated.

In this article, an analytical approach is proposed for the problem of an elastic halfspace under symmetrically distributed normal force with arbitrary profile including uniform pressure, Boussinesq flat-ended punch, conical punch and Hertz's spherical punch. The formulation of the work is on the basis of Mindlin's first strain gradient theory with five material length scale parameters. Also, the surface effects are taken into account using the Gurtin-Murdoch surface elasticity theory. The developed mathematical formulation is general so that it can be simply reduced to different strain gradient-based theories such as the modified versions of strain gradient and modified couple stress theories (MSGT and MCST), the simplified strain gradient theory (A-SGT), as well as the classical theory (CT). In the solution procedure, an analytical method is applied using the Fourier and Hankel transforms.In the numerical results, the effects of material length scale parameters and kind of punch on the surface displacements and stresses of the half-space are analyzed.The surface influences are also comprehensively studied. Moreover, comparisons are made between the predictions of MSGT, MCST, A-SGT and CT. This work shows that the material length scale parameters of Mindlin's first SGT play important roles in the response of half-space. Also, the presented results provide a comparison between the intensity of effects of strain gradient parameters and surface parameters. K E Y W O R D Sfourier transform, half-space contact problem, strain gradient theory, surface stress elasticity