An adaptive shell model with variable-kinematics for the analysis of laminated structures

Student thesis: Doctoral ThesisDoctor of Philosophy (PhD)


The overarching aim of the thesis is to develop a numerically efficient framework for the analysis of laminated shell structures. There are two parts to this thesis, the first part focuses on the derivation of a continuum shell element with generalised kinematic descriptions—referred to as a variable-kinematics continuum shell (VKCS) element—to analyse the nonlinear displacement and 3D stress field responses in complex shell structures. The second part focuses on the development of a VKCS element with adaptive through-thickness refinement, for applications to the progressive delamination analysis in an explicit dynamic solver.
The proposed element allows the users to control the model fidelity in the in-plane and through-thickness directions independently simply by modifying a few input parameters, therefore it has an anisotropic kinematic refinement scheme. With this feature, the element kinematics can be customised on a case-by-case basis, thereby presenting a one-size-fits-all solution, where only one model is required to analyse a wide range of laminates for any level of model fidelity. Also, the adaptive VKCS model alleviates the need for a ply-byply model to simulate delamination propagation, by kinematically refining the through-thickness displacement fields ‘on-the-fly’. In order to enforce kinematic compatibility across an adaptive finite element domain, a variable-kinematics transition element formulation and a through-thickness re-meshing algorithm have been developed. Apart from that, an approach to initiate cohesive segment has been proposed, where it allows the insertion of cohesive segment at high stress threshold, as well as guaranteeing traction equilibrium in an explicit solver without needing any regularisation parameter.
The thesis has studied many numerical benchmarks on both the elastic and failure analysis of laminated shells in order to validate the VKCS model. To name a few, the examples include the linear elastic 3D stress fields in a twisted shell with variable-thickness, nonlinear 3D stress fields in a ‘snapped’ laminated roof, post-buckling responses of a wind turbine blade substructure, delamination propagation in a multi-layered plate subjected to a static indentation load, and the unstable delamination propagation along the free edge of a laminate. Apart from that, the thesis also presents numerical studies on the effects of an anisotropic kinematic refinement scheme on the performance of nonlinear implicit solvers, the allowable mesh sizes for higher-order Cohesive Zone Model (CZM), and the computational efficiency of higher-order CZM—in the polynomial degree sense—in an explicit solver.
Overall, the VKCS model proves to be a robust, numerically stable, accurate and computationally efficient tool for the elastic and progressive delamination analysis of laminated shells. The work undertaken in this thesis has led to the following conclusions. Firstly, a model that utilises higher-order basis functions, along with an anisotropic kinematic refinement scheme has a fast solution convergence rate in displacements and 3D stresses, when compared against conventional finite element formulations with isotropic kinematic refinement schemes. Secondly, numerical experiments have suggested that higher-order models up to order 3 are computationally efficient for the nonlinear static and progressive damage analysis of laminated composites. Beyond order 3, the models cease to be computationally efficient due to competing factors such as the steep increase in the computational cost per integration point, and the reduction in the stable time increment of an explicit solver as the model order increases. Thirdly, the numerical studies showed that the adaptive delamination model offers a saving of 10–15% in CPU time when compared against a ply-by-ply model. Finally, the present work has proved that it is possible for an adaptive delamination model to be robust and numerically stable in an explicit dynamic solver without any ad hoc regularisation, while attaining the same level of accuracy as a ply-by-ply model.
Date of Award12 May 2020
Original languageEnglish
Awarding Institution
  • The University of Bristol
SupervisorStephen R Hallett (Supervisor), Luiz F Kawashita (Supervisor) & Alberto Pirrera (Supervisor)

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