Nonlinear finite element analysis of a multiwalled carbon nanotube resting on a Pasternak foundation

In conjunction with the Reissner's mixed variational theorem and nonlocal Timoshenko beam theory, we develop a finite element method for the geometrically nonlinear bending analysis of a multiwalled carbon nanotube resting on an elastic foundation and with various boundary conditions. The effects of the van der Waals interaction and the interaction between the multiwalled carbon nanotube and its surrounding medium are considered. Numerical implementation shows that the finite element solutions converge rapidly, and their convergent solutions closely agree with those obtained using the differential quadrature method, based on a strong-form formulation, available in the literature.