A meshfree unit-cell method for effective planar analysis of cellular beams. Computers & Structures. (A.R. Zainal Abidin, B.A. Izzuddin & F. Lancaster, 2017)


Highlights

• Novel method for planar analysis of cellular beams, as a precursor to accurate local buckling analysis of web components.
• Proposal of a unit-cell approach, taking advantage of identical cells along beam.
• Adoption and enhancement of Element Free Galerkin method for application around irregular plates with openings.
• Development of novel unit-cell super-element formulation utilising flexibility concepts.
• Realisation of considerable modelling and computational benefits, paving the way for direct application in design.

Abstract

This paper presents a novel approach for accurate and efficient planar response analysis of cellular beams, which provides the necessary input for local out-of-plane buckling analysis of web components. The proposed approach utilises the super-element concept defined for unit-cells, achieving further efficiencies through an enhanced Element-Free Galerkin (EFG) approach for establishing the planar super-element response. Several examples are presented, firstly at the level of unit-cells, where the computational benefits of the EFG method are highlighted, and finally at the overall level of cellular beams, where the superior performance of the unit-cell approach with virtually no compromise in accuracy is demonstrated.

Keywords

  • Meshfree methods;
  • Element-Free Galerkin method;
  • Planar response;
  • Cellular beams;
  • Unit-cell formulation

Link

Mathematics in Industry Seminar — Subsea Cable Laying

Mathematics in Industry Seminar was conducted on 25th May 2016 @ Faculty of Science, UTM. The talk was on “Subsea Cable Laying Problem”.

This industrial problem was from Ifactors Sdn. Bhd,
and first presented during the 3rd Mathematics in Industry Study Group Malaysia (MISG 2015), 6 – 10 April 2015 @ UTMKL

Thanks to the experts:
1. Emeritus Prof. Dr. John R. Ockendon
2. Assoc. Prof. Dr. Ian Hewitt

 

pdf links:
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Meshless local buckling analysis of steel beams with irregular web openings

Zainal Abidin, A. R. & Izzuddin, B. A. (2012) Meshless local buckling analysis of steel beams with irregular web openings. Engineering Structures, 50 (special issue), 197-206.

Highlights : ► Local buckling analysis via uncoupled planar/out-of-plane response and shifted local region. ► Formulation of unit cell response and discrete assembly for overall system response. ► Element Free Galerkin method and Rotational Spring Analogy for material and geometric stiffness. ► Buckling prediction in shifted region via reduced rank 2 iterative eigenvalue analysis. ► Favourable comparison against nonlinear FEA for several typical examples of perforated beams.

 

My Coding – Cellular Beams Meshing

Here is a set of coding to generate FEM meshing for a cellular beams (developed during my PhD study).

 

CellularBeam_Mesh 1
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