Quadratic tetrahedral micropolar element for the vibration analysis of three-dimensional micro-structures

Abstract

The micropolar continuum theory (MPT) is able to describe the influence of micro-structures on the mechanical behavior of materials where the classical theories of elasticity are unable to interpret. In this paper, the free vibration analysis of three-dimensional (3D) micropolar structures with different geometries is presented. To this aim, first, based on the 3D linear elasticity, MPT is formulated. Then a novel size-dependent quadratic tetrahedral element is developed by the user element subroutine (UEL) within commercial finite element software ABAQUS to study the free vibration behavior of micropolar structures with various geometries. The length scale parameter effects on the dimensionless natural frequencies of micropolar structures with various geometries are studied.