Size-dependent nonlinear analysis of three-dimensional cantilever beams with strain gradient effects using mixed finite element method

In this study, the geometric nonlinear behavior of three-dimensional size-dependent beams is investigated using the mixed finite element method. Nonlinear von-Karman terms are considered in the strain-- displacement relation to capture the geometric nonlinear deformations at higher load magnitudes. The torsion-- bending deformation of size-dependent beams is studied using the simplified form of ro…