Size-dependent large deformation analysis of microscale functionally graded beams and frames

Abstract

The size-dependent large deformation analysis of microscale functionally graded (FG) beam and frame structure is carried out using a corotational beam element. The material properties are graded in the thickness direction according to a power-law distribution in terms of volume fractions of the constituent materials, and they are predicted by Mori–Tanaka homogenization scheme. The element with and without Poisson ratio effect is derived from the modified couple stress theory and Euler–Bernoulli beam theory. To improve the element performance, the solution of the nonlinear equilibrium equations of a beam segment is employed to interpolate the displacement field. An incremental/iterative algorithm is used with the arc-length method to solve the nonlinear equation of the structure and to trace the equilibrium paths. Numerical results reveal that the large deformation is overestimated by ignoring the microstructural size effect and Poisson’s ratio effect. It is also shown that the influence of the power-law index on the large deformation becomes more significant for the structure associated with a higher size scale parameter. The influence of the material gradation, the microstructural size parameter and the Poisson’s ratio effect on the large deformation response of the microscale FG beams and frames is investigated in detail.