The Application of Topology Optimisation to the Design of Steel I-Section Beam Web Openings James Kingman, MEng Graduate1 Konstantinos Tsavdaridis, Lecturer1 Vassili Toropov1,2 , Professor of Aerospace and Structural Engineering 1School of Civil Engineering 2School of Mechanical Engineering cn09jjk@leeds.ac.uk k.tsavdaridis@leeds.ac.uk v.v.toropov@leeds.ac.uk

A beam with Web Openings Perforated Beams Benefits: 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

Services Passing Through Web Openings Perforated Beams Benefits: 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

Hexagonal Web Openings 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

Sinusoidal and Elliptical Opening Types 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

Plots of von Mises’ Stress at yield load level 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

Local modelling approach employed in parametric study 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?