James Kingman, MEng Graduate1

Konstantinos Tsavdaridis, Lecturer1

Vassili Toropov1,2 ,Professor of Aerospace and Structural Engineering

1School of Civil Engineering2School of Mechanical Engineering

cn09jjk@leeds.ac.uk k.tsavdaridis@leeds.ac.uk v.v.toropov@leeds.ac.uk

The Application of Topology Optimisation to the Design of Steel

I-Section Beam Web Openings

Perforated BeamsBenefits: Perforations in the web of steel I-section beams increase

the mass to stiffness ratio of the section Longer spans or increased load capacities can be

achieved without increasing material usage

A beam with Web Openings

Perforated BeamsBenefits: Services can also be passed through openings reducing

overall storey height Some perforation shapes are considered aesthetically

pleasing

Services Passing Through Web Openings

Fabrication of Perforated Beams

Castellation/Profile Cutting: A “parent” I-section is cut and welded to form a deeper

section with web openings Classic fabrication method first suggested 100 years ago Considered the most cost effective Geometry and layout of perforations significantly

constrained

Fabrication of Perforated Beams

Plate Assembly: Three flat plates are welded together to form the I-section Openings are cut into the web prior to assembly Only recently commercially implemented Almost any conceivable web opening geometry or

configuration can be fabricated

Perforation Shapes

Development: Initially only hexagonal openings were considered Circular openings first investigated in the 1980s Circular openings are currently the most popular

Hexagonal Web Openings

Perforation Shapes

Current Research: Sinusoidal openings Elliptical openings

Sinusoidal and Elliptical Opening Types

Perforation Shapes

Limitations of Current Research: All of the currently considered opening types are

restricted by the requirement that they can be fabricated using the castellation process

New opening shapes are developed through engineering intuition and experience

Can an Improved Web Perforation Concept be Developed using Structural

Optimisation Tools?

Topology Optimisation

Background: The most general structural optimisation tool Most effective when used at a conceptual design level Yields information on the optimum number, location and

shape of openings within a structural continua

Structural Optimisation Problem Types a) Sizing b) Shape c) Topology

Topology Optimisation

Solution Techniqiues: Topology optimisation is the most challenging class of

structural optimisation problems The Solid Isotropic Material with Penalisation (SIMP)

technique is currently considered to be the most effective

Topology Optimisation

The SIMP Techniqiue: Based on finite element modeling Density of finite elements are design variables Penalisation employed to attain a clear solid-void design

Studies on a Steel I-Beam

Approach: Model a five meter long simply supported 305x165x40 UB

with a uniformly distributed load applied to the top flange Define the web the area to be topology optimised Optimise for maximum stiffness subject to a constraint on

the available material

Studies on a Steel I-Beam

Result: Very irregular truss-like design

Iterative Optimisation Process

Studies on a Steel I-Beam

Manufacturing Constraints: Design generated using topology optimisation was highly

irregular Manufacturing constraints can be applied to improve the

rationality of topology optimised designs Topology optimisation rerun with symmetry constraints

Lines of Enforced Symmetry

Studies on a Steel I-Beam

Result: Regular truss like design with some interesting features

Iterative Optimisation Process

Performance of Optimised Beam

Aim: Compare the structural performance of a beam with

circular web openings and a beam with a topology optimised web

Beam Web Designs for Comparison

Performance of Optimised Beam

Determination of Structural Performance: Beams with web openings often exhibit complex behavior Full scale testing was outside of the scope of the project Extensive evidence in the literature that geometric and

materially nonlinear Finite Element Analysis can accurately simulate the behavior of beams with web openings

Nonlinear Finite Element Analysis Employed

Performance of Optimised Beam

Finite Element Analysis Approach: Multistep approach:

Nominal properties for S355 steel used Modeling approach previously calibrated against

experimental samples

Linear Static Analysis

Eigenvalue Buckling Analysis

Imperfections Applied to

Mesh

Geometric and Materially

Nonlinear Analysis

Results

Comparison of Circular and Topology Optimised Beam: Total weight of both beams is identical Topology optimised beam found to have improved

structural characteristics

Plots of von Mises’ Stress at yield load level

Results

Studies on a Steel I-Beam

Conclusion: Topology optimisation led to a design with improved

structural characteristics Significant effort required to develop the design Lengthy analysis procedure required to verify the capacity

of the section Approach would not be suitable for every day design of

beams

Parametric Study

Aim: Conduct a parametric study to determine the topologically

optimum web opening type for the wide range of beam cross sections found in practice

Parametric Study

Approach: A local modeling approach on a short length of beam was

employed Internal forces applied directly to the short length of beam Same topology optimisation approach as previously

detailed

Local modelling approach employed in parametric study

Parametric Study

Results: Depth of Section found to be critical parameter Different opening types suggested for shallow and deep

beams

Optimal opening topology for beams below 700mm deep

Optimal opening topology for beams deeper than 700mm

Conclusions

Increasing popularity of plate assembly fabrication technique enables new web opening designs to be considered

Topology optimisation can lead to web designs that have beneficial properties when compared to currently used opening types

A topologically optimum web opening concept has been suggested for both deep and shallow beams

Recommendations

Investigate the performance and failure modes of the suggested opening concept

Investigate the manufacture of the suggested opening concept

Develop design equations that can be used for the routine design of the topologically optimum web opening concept

Questions?