Isogeometric dynamic analysis of shells based on the nonlinear micropolar theory

Abstract

Studying the large-amplitude forced vibration characteristics of micropolar shell-type structures is the main objective of this paper. In order to obtain the full geometrically nonlinear model of micropolar theory, the micromorphic seven-parameter shell kinematic is first developed. Via a nonlinear micro-motion map, the extracted formulation is fitted for the micropolar continuum. As a result, possessing three stress–strain fields with eighteen independent elastic parameters of a linear material, the proposed micropolar shell theory is able to capture the inhomogeneity and size-effects. On the basis of Hamilton’s principle, the variational form of governing equations of motion is determined. The finite element isogeometric solution approach is then utilized to produce the geometry and approximate the displacement field in mid-surface area of shell. This would be helpful for resolving the locking and instability issues of the traditional low-order standard finite element shell models. By discretizing the period of harmonic vibration, a numerical method is also implemented in time domain. To demonstrate the microstructural effects, dynamic behavior of micropolar plate- and shell-type structures are investigated in several parametric studies. Since the classical strain and stress tensors are retained in present micropolar elasticity, both the large macro- and micro-deformations are captured for the first time.