Numerical study of size effects in micro/nano plates by moving finite elements

Abstract

Bending of plates subjected to stationary transversal loading is studied within the strain-gradient elasticity. The complete formulation including the governing equations and boundary conditions is re-derived for the thin elastic functionally graded as well as homogeneous plate starting from the unified formulation admitting the assumptions of three plate bending theories [46]. The second-order strain gradient theory of elasticity (proposed by Mindlin) with using one microstructural length-scale parameter is employed instead of classical elasticity. Although the derived formulation for thin plate is simpler than for thick plates, it involves the 6th order derivatives of deflections instead of the 4th order derivatives in the classical elasticity. The original system of governing equations is decomposed into the system of 2nd order partial differential equations and new approximation method (MFE – moving finite elements) is proposed for numerical implementation of the derived formulation. The numerical experiments are performed for study the stability, convergence and efficiency of the method as well as for study of the size-effect in micro/nano plates.