Analysis and Design of Buckling Resistant Thin-Walled Structures via Computationally Efficient 3D Stress Analysis

  • Sergio A Minera Rebulla

Student thesis: Doctoral ThesisDoctor of Philosophy (PhD)


Performing detailed structural analysis of beam-like or thin-walled structures can be a complex task, especially if three dimensional stress profiles are required. Depending on the nature of the problem, i.e. geometry, dimensions, loading and boundary conditions, it may be possible to use simplified (numerical or analytical) beam or shell models. Nevertheless, their accuracy is limited to certain regions and far from singularities. Due to this limitation, three-dimensional finite element methods (FEM) are commonly employed. FEM is a robust methodology, but it may come with a high computational cost. Therefore, when analysing complex structures, it is common practice to split the problem in parts. A coarse mesh and/or a simplified model is used to describe the overall and global behaviour of the structure. After identifying regions (or scales) where more detail is needed, a more refined model is employed. This sub-modelling process can be cumbersome and time consuming. In this work, a new framework for solving this duality is proposed. A model, based on the Serendipity Lagrange (SL) polynomial
space, extends the capabilities of the Unified Formulation (UF) model to perform non-linear and large-deflection analyses of non-prismatic and curved beam-like structures. Special attention is given to the modelling of buckling and post-buckling of beams and thin-walled structures. The capability in recovering localised displacement and stress fields, numerical stability and efficiency
of the proposed model (UF-SL) are presented, discussed and compared with reference models. In addition, two new and novel methodologies for the design of buckling-resistant structures are presented. The first, the Localised Nominal Stiffness Method (LNS), exploits the accuracy and efficiency of the UF-SL model to identify and map regions of potential insensitivity to localised low stiffness variations. The result is then used to tailor the structure and improve its buckling and post-buckling performance. The second approach, Eigenstress Method, uses the resultant stress, recovered from the first eigenvector of a linear buckling analysis, as baseline for a new topology. The resulting geometry closely resembles that of the structure that optimises the buckling load, with a given structural weight. This method provides a method that is fast and intuitive for designing buckling-resistant structures.
Date of Award28 Nov 2019
Original languageEnglish
Awarding Institution
  • The University of Bristol
SupervisorAlberto Pirrera (Supervisor) & Paul M Weaver (Supervisor)

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