Model Reduction For Composite Beam Modelling

In this thesis,a multi-scale framework for nonlinear problems is developed using a FE~2approach where at macro-scale Carrera's Unified Formula(CUF)higher-order structural theories are used,and the resulting non-linear problem is solved by means of the advanced ANM nonlinear solver.The achievements during the Ph D period can be summarised in the following three aspects:a linear macro-scale CUF-based model,a geometrically nonlinear macro-scale CUF-based beam model and a geometrically non-linear multi-scale CUF-based beam model.The linear macro-scale CUF-based model has been applied for the multi-field anal-ysis and free-vibration analysis.In the hygro-thermal-mechanical analysis of the lam-inated beams,several beam models are hierarchically derived by employing the CUF.Results regarding temperature,moisture,displacement and stress distributions are il-lustrated.With the comparison with the FEM-based model,it can be concluded that accuracy and efficiency can be achieved thanks to the CUF based beam model.Then,nonlinear structural modeling has been established by coupling the non-linear CUF and Asymptotic Numerical Method(ANM).It is one of the first studies that extends one-dimensional equivalent single layer CUF models coupled with ANM to account for geometrical non-linearities.Static nonlinear,post-buckling and snap-through analyses of beam structures have been presented,and the corresponding load-displacement and load-stress curves have been assessed.To address geometrically nonlinear problems in beam structures from different scales,a geometrically nonlinear CUF-based multi-scale beam model has been derived by coupling the proposed macroscopic model and the Multilevel Finite Element(also known as FE~2)framework.The solution procedure consists of a macroscopic/structural analysis and a microscopic/material analysis.The proposed framework is used in in-vestigating the effect of microscale imperfections(not straight carbon fibers)on the macroscale response(instability).Results are analyzed in terms of accuracy and com-putational costs towards full FEM solutions.Two factors have been identified for an imperfection sensitivity parametric analysis:the wavelength and the amplitude of the geometrical imperfection.