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James Kingman, MEng Graduate1
Konstantinos Tsavdaridis, Lecturer1
Vassili Toropov1,2 ,
Professor of Aerospace and Structural Engineering
1School of Civil Engineering2School of Mechanical Engineering
[email protected] [email protected] [email protected]
The Application of Topology Optimisation to the Design of Steel
I-Section Beam 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
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
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?