Multiscale CUF-FE~2 nonlinear analysis of composite beam structures

摘要

In this paper, a new paradigm for Carrera's Unified Formulation (CUF) based on multiscale structural modelling is accomplished by bridging micromechanics and the advanced CUF one-dimensional/beam structural theories by means of the Multilevel Finite Element (also known as FE2) framework. Under the framework of the FE2 method, the analysis is divided into a macroscopic/structural problem and a microscopic/material problem. At the macroscopic level, several higher-order refined beam elements can be easily implemented via CUF by deriving a fundamental nucleus that is independent of the approximation order over the thickness and the number of nodes per element (they are free parameters of the formulation). The unknown macroscopic constitutive law is obtained by numerical homogenisation of a Representative Volume Element (RVE) at the microscopic level. Vice versa, the microscopic deformation gradient is calculated from the macroscopic model. Information is passed between the two scales in a FE2 sense. The resulting nonlinear problem is solved through the Asymptotic Numerical Method (ANM) that is more reliable and less Newton-Raphson's one. The developed models are used as a first attempt to investigate the microstructure effect on the macrostructure geometrically nonlinear response. The proposed paradigm is used for investigating the effect of microscale imperfections (not straight carbon fibres) on the macroscale response (instability). Results are assessed in terms of accuracy and computational costs towards full FEM solutions. Three factors have been considered for an imperfection sensitivity parametric analysis: the defect wavelength as well as the amplitude and the size of RVE. (C) 2019 Elsevier Ltd. All rights reserved.