Computer simulation of the nonlinear static behavior of axially functionally graded microtube with porosity

Static analysis of microstructures, including bending and buckling, is widely practiced in the fabrication and creation of applications such as actuation, sensing, and energy recovery. This article aims to inquire about the static behavior of non-uniform and imperfect microtubes through a numerical solution. Based on the modified couple stress theory, the first-order shear deformation theory and Von-Karman nonlinear theory, and employing the energy conservation method, the linear and nonlinear governing equations are derived. The porosity-dependent material in both ceramic and metal phases makes the functionally graded materials which are varied along tube length, moreover, cross-sections are also considered uniform and nonuniform via three valuable functions. Finally, the linear and nonlinear equations are solved utilizing the generalized differential quadrature method (GDQM) coupled with the numerical iteration method.