1. Final Report
The Development of Design by Topology Optimization for Additive
Manufacture
Callum McLennan
2015
3rd
Year Individual Project
I certify that all material in this thesis that is not my own work has been identified and that no
material has been included for which a degree has previously been conferred on me.
Signed..............................................................................................................
College of Engineering, Mathematics, and Physical Sciences
University of Exeter

2. ii
Final Report
ECM3101/ECM3102/ECM3149
The Development of Design by Topology Optimization
for Additive Manufacture
Word count: 7864
Number of pages: 35
Date of submission: Wednesday, 29 April 2015
Student Name: Callum McLennan
Programme: BEng Mechanical Engineering
Student number: 620019882
Candidate number: 035779
Supervisor: Professor David Zhang

3. iii
Abstract
The work presented in this report provides a comprehensive background of topology
optimization theory and explores its opportunities, applications and challenges. The design
freedom offered by Additive Manufacture eliminates the requirement for simplifying optimal
structure. Thus the opportunity for using topology optimization for producing organic final
designs is discussed.
An aerospace bracket was optimized using TOSCA, a commercial SIMP algorithm, with the
objective of saving as much weight as possible while maintaining enough stiffness to satisfy
its performance requirements. To assess the prospect of producing successful designs from
raw optimization geometry, an iteration of the optimized bracket was manufactured and
mechanically tested so that its performance could be compared to the original design.
The aerospace bracket was used to explore two parameters of the topology optimization
process, the design domain and the mesh size, and recommendations were made for the
workflow accordingly. Specifically, an iterative method for developing the most effective
design space is presented and the mesh dependency of the output is investigated using Finite
Element Analysis.
The brackets mass was reduced by 45% with a factor of safety of 5. The 1.4kg saved per
bracket equates to significant savings in fuel costs. The success of the optimized bracket
under mechanical testing validates the use of topology optimization as a design process. With
regards to workflow, the iterative development of the design space was found to be an
effective solution to finding the true optimum result. A more refined mesh produced results
with greater detail but no benefits to performance were found through changing the mesh
size.
Keywords: Topology Optimization, Additive Manufacture, SIMP, Aerospace, Structural
Optimization
Acknowledgements: I would like to thank Professor David Zhang for his constant support
and supervisory assistance, James Bradbury from CALM, Dr. Tommy Shyng from X-AT and
Matthew Hilling for their time, their interest and their contributions.

4. iv
Table of contents
1. Introduction and background..............................................................................................1
1.1. Topology Optimization for Additive Layer Manufacture...........................................1
1.2. Scope & Objectives.....................................................................................................1
1.3. Jet Engine Loading Bracket (ELB) Specifications .....................................................2
2. Literature review.................................................................................................................3
2.1. Foundations of Structural Optimization......................................................................3
2.2. SIMP............................................................................................................................4
2.3. ESO .............................................................................................................................5
2.4. Additive Layer Manufacture (ALM)...........................................................................6
2.5. Topology Optimization for ALM................................................................................7
3. Methodology and theory.....................................................................................................9
3.1. Topology Optimization Concepts ...............................................................................9
3.2. Finite Element Analysis (FEA).................................................................................10
3.3. Strain Energy.............................................................................................................11
3.4. SIMP Theory.............................................................................................................12
3.5. The Min-Max formulation ........................................................................................13
3.6. Optimization Workflow ............................................................................................14
3.6.1. Finite element model setup................................................................................14
3.6.2. Topology optimization setup .............................................................................16
3.6.3. Post-processing ..................................................................................................16
3.7. Tensile testing ...........................................................................................................17
4. Design Process..................................................................................................................17
4.1. Outline of the design process ....................................................................................17
4.2. Finding the most suitable design domain..................................................................18

5. v
4.3. Investigation into the effects of refining the mesh....................................................20
4.4. Verifying the performance of an optimized bracket by mechanical testing .............20
5. Presentation of Results & Final Product Description .......................................................22
5.1. Mesh refinement models...........................................................................................22
5.2. Mechanical Testing of Iteration 1 .............................................................................25
5.3. Final Design ..............................................................................................................26
6. Discussion and conclusions ..............................................................................................27
7. Project management, consideration of sustainability and health and safety.....................28
7.1. Sustainability.............................................................................................................28
7.1.1. Life Cycle Analysis (LCA)................................................................................29
7.2. Project Management..................................................................................................31
7.3. Risk management......................................................................................................32
References................................................................................................................................34

6. 1
1. Introduction and background
1.1. Topology Optimization for Additive Layer Manufacture
Topology optimization methods solve the material distribution problem within a design
domain to find an optimal structure. The two most practical methods of topology
optimization are Solid Isotropic Material with Penalisation (SIMP) and Evolutionary
Structural Optimization (ESO).
Traditional manufacture processes such as machining and casting are unable to fully realise
the level of complexity inherent in optimal topology. For example, the requirement for tool
access during Computer Numerical Control (CNC) manufacture and the need for part
removal from a mould during casting critically limit design freedom.
In contrast, Additive Layer Manufacture (ALM) offers significant improvements in design
freedom and is far more capable of realising optimal topology. Over recent years,
improvements in ALM technology has rapidly developed its proficiency in manufacturing
parts of greater complexity with an expanding breadth of materials, including metals.
Therefore, the development of design for ALM through topology optimization methods is
essential for contemporary design and manufacture due to its potential efficiency for
producing high performance components whilst wasting less material than ever before.
1.2. Scope & Objectives
The aim of the project is to develop design for ALM by eliminating the requirement for
simplifying optimized topology. Most previous applications of topology optimization have
used the process as a tool to enhance creativity and merely influence the final design. An
example of this kind of approach is the process described by the Institute of Laser and System
Technologies at the University of Hamburg [1] where only a selection of structural principles
are translated from the optimization into the final design. This project is unique as it explores
the potential of topology optimization as a design process for creating organic designs that
are feasible for manufacture by ALM. Methods of best practice will be investigated and
suggestions shall be made concerning the design process workflow.
The focused objectives are as follows:

7. 2
1. Research topology optimization opportunities, applications, practical difficulties and
challenges.
2. Optimize an aerospace bracket reducing its weight as much as possible whilst
maintaining a reasonable factor of safety under loading.
3. Manufacture optimized geometry using ALM.
4. Mechanically test the manufactured part and compare its performance to the original
structure to validate topology optimization as a design process.
5. Explore best working practice for preparing the design domain for optimization.
6. Investigate the effects of refining and coarsening the mesh on the optimization output.
1.3. Jet Engine Loading Bracket (ELB) Specifications
Design projects within the aerospace industry make weight saving a primary objective. This
is due to the enormous potential savings in fuel costs over the component’s lifetime, even for
modest reductions in mass. Traditionally, weight saving is achieved late within the design
stages by local, manual changes made through repeated Finite Element Analysis (FEA)
processes or by using expensive materials.
Topology optimization has recently proved itself as an effective solution for designers
pursuing an ideal compromise between component stiffness and mass within the aerospace
industry.
Loading brackets on jet engines play an essential role; they must support the weight of the
engine during handling without breaking or warping. Despite only being in use periodically,
they remain attached during flight so must be economical in weight [2].
The bracket is to be manufactured from the titanium alloy Ti-6AI-4V (Table 1). This report
will be concerned with finding the optimal load path for the four static, steady state load
cases described in Figure 1. The values provided are the maximum loads the bracket will
experience during normal use.

8. 3
Figure 1: Engine loading bracket load cases and interfaces [2]
Table 1: Material properties utilised within the report [3],[4]
Material Young's Modulus
(Gpa)
Poisson's Ratio Yield (Tensile)
Strength
Ultimate Tensile
Strength (MPa)
Strain at
Break
Ti-6AI-4V 113.8 0.342 880 950 0.14
Nylon (PA 2200) 1.65 - - 48 0.18
2. Literature review
2.1. Foundations of Structural Optimization
In 1904 Michell first derived formulae for achieving structures with minimum weight with
associated stress constraints within various design domains [5]. It wasn’t until 1985 that these
structures, known as Michell structures, were proved to have minimal compliance for their
corresponding volume. Prager and Rozvany’s work on optimal layout theory [6] was
significant in making this optimization concept more practical. They were the first to propose
a geometrical method to optimize minimum weight for skeletal structures (grillages). This
method was based on the concept of a “ground structure” which contains all potential truss
members. The synonymous idea of a “design domain” is fundamental for the development of
the optimization workflow discussed in this report.

9. 4
The development of using computers to automate the solution of state equations using finite
element methods significantly increased potential for structural optimization. The first
numerical means of topology optimization, homogenization, was developed by Bendsoe and
Kikuchi in 1989 [7]. Homogenization produces microscopic holes within a structure due to
the material in each element being composed of both solid material and voids. Bendsoe’s
work developed this approach further and introduced Solid Isotropic Material with
Penalisation (SIMP). SIMP and Evolutionary Structural Optimization (ESO, introduced in
section 2.3) are currently the most practical approaches to structural optimization. Other
methods, such as the level set method and genetic algorithms, are still in their relative infancy
with regard to practical applications and shall not be discussed in this report.
Traditionally topology optimization is used as a part of the design process to minimize the
strain energy within the design domain for a load case with a constraint on material usage.
However, the approach has been evolved to be capable of optimizing structures for a large
range of problems including those involving multiple load cases, maximization of natural
frequency and even compliant mechanisms.
2.2. SIMP
Homogenization outputs contain continuous, anisotropic, porous material due to the
solid/void composition of each element. A method to eliminate these microscopic structures
and reduce the effect of the intermediate densities was first developed by Bendsoe and termed
the SIMP approach by Rozvany et al. in 1992 [8]. Optimal results therefore only contain
either solid or empty material.
Figure 2: Bridge problem solved by homogenisation (left) and SIMP (right) [9]
SIMP is an extremely simple approach to topology optimization and is very common in
commercial software. To illustrate this simplicity Sigmund published a 99 line Matlab code

10. 5
able to perform an iterative SIMP topology optimization for the minimisation of compliance
subject to a volume constraint [10].
In 2001 Rozvany presented a review of the SIMP method and its advantages over other
approaches to structural optimization [11]. These include its efficiency (one variable per
element), robustness (suitable for almost any design condition), the ease in which the
penalization may be adjusted and its mathematical simplicity. In Bendsoe and Sigmund’s
2003 monograph of topology optimization SIMP was the primary focus [12].
2.3. ESO
An alternative to SIMP is Evolutionary Structural Optimization, introduced by Xie and
Stephen in 1993 [13]. ESO involves repeatedly removing small amounts of structurally
inefficient material to evolve the topology towards an optimum form. Based on engineering
heuristics, ESO has been found to generally reach optimum solutions [14]. Tanskanen [15]
proposed that by removing elements of low strain energy a form with constant strain energy
distribution is eventually found, minimising the compliance-volume product fundamental to
the original Michell structure.
Querin et al. [16] introduced an additive algorithm to ESO in 1999 allowing the re-
introduction of material to the structure. This was named Bi-directional Evolutionary
Structural Optimization (BESO).
In 2001 Zhou and Rozvany [17] found a numerical “tie-beam” example where ESO in fact
increased compliance by a factor of 10. In this case the ESO strategy fundamentally changed
the way in which the loads were transmitted and hence produced a non-optimal solution. The
tie-beam is a statically indeterminate structure which, when a boundary support is broken
through the ESO approach, has a completely different structural system that not even BESO
can rectify. Following this, Huang and Xie published an article on how the prescribed
boundary conditions must be checked and maintained at each iteration to avoid developing
non-optimal solutions [18].
In 2009 Zuo et al. combined the BESO approach with a genetic algorithm and found that with
a small number of iterations an optimal topology was found with better performance than the
local optimum found through the application of SIMP [19]. However, the SIMP algorithm is
used for the work contained in this report due to its simplicity and efficiency.

11. 6
2.4. Additive Layer Manufacture (ALM)
ALM is a term used to describe the process of building a part layer by layer. Originally the
process became widespread for prototyping applications and was referred to as RP (Rapid
Prototyping). However, over recent years advances in materials, processes and technology
have greatly enhanced the properties of parts produced in this way. Rapid Manufacture (RM)
is now used to describe the application of ALM to create fully functional components.
ALM technologies produce parts by the polymerisation, fusing or sintering of materials in
layers determined by the slicing of 3D CAD files. The absence of the requirement for tool
access or the creation of a mould significantly increases design freedom.
Usually, the part is “grown” along the z-axis processing one layer at a time. After one layer is
finished, the platform is lowered by one layer thickness and a new layer of material is coated.
With powder based systems such as Selective Laser Sintering (SLS) or Selective Laser
Melting (SLM), the powder is deposited using a traversing edge or a roller. The use of
support structures is common, especially in thermal processes such as SLM where layers are
prone to warp during manufacture. The support structure transfers the heat away from the
laser sight and prevents heat stresses.
SLS mainly processes thermoplastic materials such as nylon, glass filled nylon, aluminium
filled nylon and polystyrene. This means that the products have good mechanical properties
and may be used as functional components. SLS uses an infrared laser for the sintering of the
polymer particles. The brackets produced for this project were manufactured using Nylon
(PA 2200) with a layer thickness of 120µm as this offers an ideal balance between production
costs, mechanical properties, surface quality and accuracy [4]. On the axis of testing the parts
have the mechanical properties detailed in Table 1.
The introduction of fibre lasers (where the active gain medium is an optical fibre) allowed the
development of SLM, where particles are fully melted into dense parts [20]. This has further
increased the breadth of materials, especially metals, used and the mechanical properties of
parts. The engine loading bracket will be designed for manufacture with the titanium alloy
Ti-6AI-4V, a widely used metal in ALM with excellent mechanical properties (Table 1). This
report shall neglect the design of any required support structure but will acknowledge the
problems this brings to the design.

12. 7
2.5. Topology Optimization for ALM
As part of an industrially focused project called Atkins, Brackett et al. wrote an overview of
the issues and opportunities for the application of topology optimization methods for additive
manufacturing [21]. The main aspects analysed within the paper included:
 Achieving maximum geometric resolution in the optimization to take advantage of
ALM’s potential for detail.
 Tackling ALM constraints during optimization, specifically support structure
requirement.
 Handling the complex geometry post-optimization and pre-manufacture.
 ALM’s potential for realising intermediate density regions such as those produced
through homogenization methods.
 ALM’s potential for multi-material processes.
The paper highlights the fact that the financial cost of manufacture by ALM does not increase
with the complexity of the part unlike traditional processes. The benefit of this is that parts
can be built closer to the optimal topology. However, there are currently two main practical
difficulties to be overcome:
1 It is difficult to determine the geometric resolution required to achieve the correct level of
detail. As a mesh is refined, more detail presents itself and the topology moves closer to
the optimum. SLM machines may have a minimum feature size of around 0.04mm [22].
The resolution of optimization is poor in comparison for anything other than very small
parts. In summary; “It is no longer the manufacturing stage that is the limiting factor in
the realisation of optimal designs; it is the design stage” [21].
Brackett et al. suggest actions to improve the computational expense of achieving
topology of finer detail. The first is a hard-kill element elimination approach during a Bi-
directional Evolutionary Optimization (BESO) where elements that have remained at very
low modulus for several design cycles are completely removed from the design, reducing
the number of elements as the process continues. However, it was suggested that this
compromises the benefits of the Bi-directional aspect of the process. The second
approach involves iterative re-meshing throughout the optimization process. This means
areas with high stress gradients are refined and areas of low modulus are coarsened as the

13. 8
optimization converges. There has only been one commercial implementation of this
approach, within TOSCA software. Unfortunately this is currently limited to refinement
and coarsening on just two levels, which is not enough to achieve the desired level of
detail.
2 There are practical difficulties in handling the geometry from post optimization to
manufacture. It is a standard procedure to smooth the topology to reduce the effects of the
element boundaries. Unfortunately, to gain a CAD representation of the results the
topology needs to be “traced” by the designer or some form of feature recognition is
required.
Incorporating ALM manufacturing constraints in the optimization process would be a
convenient solution to these difficulties as there would be no need to alter the optimised
geometry in CAD. For example, supporting structure is required for Selective Laser
Melting (SLM) for overhangs under a particular angle to the horizontal, depending on the
horizontal distance. Avoiding the use of supporting structure is good practice for a
number of reasons:
i. It saves material.
ii. It eliminates the requirement for a skilled technician to generate and place support
structure for a specific build orientation.
iii. It can be particularly laborious to remove metal support structure and the requirement
for access to the support may introduce new constraints to the design.
So far there has been no integration of such constraints with commercial topology
optimization software.
Within the same paper, Brackett et al. explored some specific opportunities for topology
optimization for ALM, mainly with regard to realising optimal microstructure and
manufacturing composite parts.
ALM’s potential for small-scale detail allows for design on a sub-structure level. Therefore,
by mapping the grey scale output of homogenization methods of optimization, the volume
fraction of lattice cells may be assigned to the corresponding densities of the optimized
design. An example of this approach is illustrated in Figure 3. This concept has been
implemented in the most recent update of Altair OptiStruct which incorporates an algorithm
that can produce blended solid-and-lattice type structures. This first-to-market development

14. 9
will further increase the performance potential of optimization results [23].
Figure 3: Mapping microstructure volume fraction to grey scale homogenisation output [21]
This summary of challenges and opportunities by Brackett et al. has been the central
inspiration for this report. These ideas are used as themes throughout the application of
topology optimization on the engine support bracket.
3. Methodology and theory
3.1. Topology Optimization Concepts
Before topology optimization, extensive research was focused on size and shape
optimization. Any of these optimization processes may be defined as the manipulation of a
design variable to improve a structure’s performance. For a truss design, the design variable
during a size optimization would be the cross sectional area of its members. The structure is
optimized by finding the cross sectional areas that maximise its stiffness for a particular
weight [12].
Shape optimization is applicable for parts that incorporate the use of holes to save weight.
The optimization alters the shape of these holes to reduce the concentrations of stress,
resulting in a more structurally efficient part. The design variables would be the parameters
that control the shape of the holes in the original design.
Topology optimization is far more comprehensive. SIMP involves modifying the models
stiffness matrix so that it depends continuously on a function that is interpreted as a density of
material [12]. The optimal distribution of material is found through making material density a

15. 10
design variable. Furthermore, not only are the optimum shapes of any holes found, but the
number and locations.
Figure 4: Examples of sizing (top), shape (middle) and topology (bottom) optimization [12]
Topology optimization may be categorized by its application to two different types of
structure, continuum and discrete. Discrete structures refer to truss-based constructions
composed of many members. Continuum structures are single piece parts such as the engine
loading bracket in this report.
Commercial software is able to apply topology optimization algorithms through the
application of boundary conditions, design responses and constraints to a design domain.
The design domain encases all possible configurations of the design. It may contain space
that is fixed where material is functional and essential to the part, or voids where material
must be absent.
Figure 5: Design domain example
3.2. Finite Element Analysis (FEA)
The concept of developing a stiffness matrix through discretization with finite elements forms
the basis for the topology optimization process. FE Analysis is an integral part of the
optimization process. FEA is a numerical method for solving many problems in engineering

16. 11
and physics. It is particularly useful for scenarios involving complicated geometry, loading or
material properties where analytical solutions cannot be obtained.
Discretization is the process of modelling geometry by dividing its form into an equivalent
system of small bodies (finite elements). These elements never overlap and are connected at
points called nodes and boundary lines and/or surfaces.
During an analysis, the displacement of each node may be used to calculate the local values
of field variables such as stress and strain. These values are interpolated to approximate
values along the length of the elements.
The characteristics of a finite element model are portrayed through the element stiffness
matrix. This matrix contains the material and geometric behaviour of the model that specifies
its compliance under loading. The systems matrix is simply the superposition of the
individual stiffness matrices that are attributed with the simplified, linear characteristics of a
spring under loading with the stiffness properties of the system’s material.
During a SIMP optimization, every element is an independent design variable and is
determined to either be present (1) or void (0) in the final topology.
3.3. Strain Energy
The optimization algorithm pursues the optimal topology through minimising the design’s
compliance. Compliance is defined as the inverse of stiffness and is measured in elastic strain
energy.
Strain energy is the potential energy stored within a material due to work. As work is a force
applied over a measured distance, elastic strain energy may be described as the area beneath
the Force/Displacement graph for a particular part/material. The fundamental theory behind
obtaining results using FEA involves minimising the total potential energy of the system so
that equilibrium is achieved. This is based on the concept of virtual work, which states that if
a particle is under equilibrium, under a set of a system of forces, then for any displacement,
the virtual work is zero. The total potential energy within a discretised structure is the sum of
the energy contributions of each individual element. Therefore, the optimization may directly
quantify compliance through FEA and maximise stiffness by manipulating the density of the
elements.

17. 12
3.4. SIMP Theory
The optimization software utilised during this investigation was TOSCA by FE-Design which
was acquired by Dassault Systemes in 2013. The University of Exeter holds several licenses
for ABAQUS and, through communication with Dassault Systemes, TOSCA was installed on
a computer for this project.
The optimization process may be divided into four steps: pre-processing; Finite Element
Analysis (using ABAQUS); optimization and post-processing. During pre-processing
TOSCA checks the user-defined settings such as optimization type, objectives and constraints
and performs a sensitivity analysis.
The sensitivity analysis involves finding the derivative of the displacement field for every
element, which is considered as a function of the design variables (the density of the
elements). A filtering technique is used to ensure mesh independency. This involves
modifying the sensitivity of a specific element through the influence of a weighted average of
the densities of the surrounding elements.
ABAQUS will then perform a FE analysis to calculate the data required for the optimization
step. TOSCA withdraws the data necessary for the optimization at a particular design cycle
based on a certain algorithm.
Figure 6: SIMP flow chart [24]

18. 13
In simple terms, the algorithm steps are:
1. Compute the compliance of this design. If there is only marginal improvement over
the previous iteration, stop the process.
2. Compute the update of the density variable to comply with the volume constraint.
3. Repeat the iteration loop.
3.5. The Min-Max formulation
An optimal topology is specific to a set of boundary conditions. Unfortunately, many
components must perform under several loading conditions. This is the case for the Engine
Loading Bracket.
The Min-Max formulation, or the Bound formulation, is the most convenient method used in
commercial software for optimizing for multiple load cases. Instead of merely minimising
strain energy, the algorithm minimises the strain energy for the load case that produces the
most strain energy at that particular iteration. Consequently, the final topology is the optimal
compromise in performance for all the load cases [25].

19. 14
3.6. Optimization Workflow
3.6.1. Finite element model setup
Solidworks was used to define the design space geometry which was imported into ABAQUS
as a SAT file. The geometry was split into cells using the cutting tool to allow the creation of
a “Design” set for the design domain and a “Non-Design” set for the fixed geometry. These
sections were assigned Ti-6AI-4V material properties (Table 1).
Figure 7: Topology optimisation workflow used throughout the project

20. 15
Figure 8: Design (turquoise) and Non-Design (yellow) sets
N.B. The volume of space occupied by the design domain is critical to the creation of an
optimal design. The algorithm may only alter the density of the elements already present at
the beginning of the process. For this reason it is critical to maximise the volume of the
design domain to increase the number of possible configurations. Non-design space was
defined as:
i. Volumes of the part critical to operational or sizing specifications,
ii. interfaces,
iii. or volumes of space inhabited by other parts while the component is in use.
During use, the load is transferred to Interface 1 of the bracket through a pin, as displayed in
Figure 1. This was translated into the model by creating kinematic coupling through rigid
elements to reference points in the centre of each hole. The loads from Figure 1 were applied
to these reference points as well as boundary conditions to ensure that the holes do not rotate
in a manner that would be impossible with a pin through them. Encastre conditions were set
at the bolt holes.
Figure 9: Kinematic coupling
Each load was applied in a separate step and was deactivated for any subsequent steps. This
was critical in the preparation for the Min-Max approach.

21. 16
Before meshing some edges on the geometry had to be managed to avoid poor elements.
Broken edges were merged and some faces were combined to avoid sharp corners. The part
was meshed with C3D10 elements as higher order elements reduce numerical instability
during the optimization process [25].
Due to the length of an optimization process, it was deemed good working practice to run a
finite element analysis before setting up the optimization to ensure that the correct boundary
conditions had been applied.
3.6.2. Topology optimization setup
Within the Optimization tab, the “Design” set was chosen for a topology optimization and the
SIMP algorithm was selected. Two categories of design responses were created; strain energy
and volume. For the Design Objective, the strain energies for each load step were highlighted
with equal weighting and “Minimise the maximum design response” was selected.
Under Constraints, the volume design response was highlighted and constrained to be equal
or less than a fraction of the original volume. The optimization job was then submitted and
while the process was running its progress could be checked through the plot tool. This
allows the user to check that the strain energy and the volume of material used is converging
over several iterations.
3.6.3. Post-processing
The optimization creates a parameter file that may be opened in TOSCA.smooth. Here the
optimal topology is smoothed and transferred as IGES surfaces so that it may be imported as
a geometry back into ABAQUS for testing. Smoothing is an iterative procedure that reduces
the sharp-edged nature of the geometry’s surface that has been obtained by removing
individual tetrahedral elements from the design volume.
Figure 10: Post-processing summary

22. 17
The optimization report was checked to determine the load case that caused the most strain
energy within the bracket for the final iteration of the optimization. Within the setup of these
finite element models, only the load case responsible for this strain energy was applied and
plastic material properties were included. Otherwise, the boundary conditions were identical.
The location of max principal stress was located using the contour tool and a mesh
convergence was performed for every model.
Once the mesh was refined non-linear geometry was switched on and the increment size was
fixed to 0.2. A history output was created for displacement parallel to the applied force and
plotted to detect the point of plastic deformation.
3.7. Tensile testing
Tensile testing is the method of physically testing how a material or a product reacts when a
force is applied to it in tension. It does so by measuring the force required to extend the
specimen until failure. Testing multiple specimens allows designers to predict how materials
and products will behave in service.
The direct output of a tensile test is the data required to create a force/displacement curve.
This information is useful for many objectives including determining batch quality, reducing
material costs, ensuring compliance is within industry standards and aiding the design
process. During this project tensile testing shall be used to investigate the performance of an
aerospace bracket designed solely through topology optimization. The results shall contribute
to the validation of topology optimization as a design process.
FEA was performed using PA 2200 material properties (Table 1) on the original bracket to
determine which testing machine’s loading capacities would be required to test the brackets
to failure (<20kN or <300kN). The brackets expected point of failure was easily within the
Lloyd Instruments EZ20’s 20kN maximum load.
4. Design Process
4.1. Outline of the design process
For the purpose of developing the design process, several iterations of the bracket were
produced to explore the effects of two central design parameters:

23. 18
 The design domain.
 The mesh size.
Additionally, an early iteration of the optimized bracket was manufactured and mechanically
tested for the purpose of validating the use of topology optimization as a design procedure for
this particular bracket.
Figure 11: Design process
4.2. Finding the most suitable design domain
Section 3.6.1 describes the necessity for maximising the volume of the design domain.
However, as described in section 2.4, more detail presents itself in the final topology with a
more refined mesh. It is counterproductive to enlarge the design domain to the extent at
which the optimization time is unreasonable to achieve good resolution.

24. 19
Therefore, the design domain was expanded gradually to evaluate where the bulk of material
was distributed within the optimal results. Areas where the boundaries of the design domain
prohibited the further distribution of material were expanded for the next iteration. These
areas shall henceforth be referred to as “flat spots” and are shown in yellow in Table 2.
The primary aim of this stage of the design process was to determine the space where
material wants to occupy so that volume is invested in the right areas. It is extremely
important that the engineer has enough knowledge of the component’s interface requirements
so that material is not distributed where it will act as an obstruction.
Table 2: Design domain development
OriginalBracket
Design Domain
Design Domain
Volume (m^3) Optimal Topology
Iteration1
5.52E-04
Iteration2
1.12E-03
Iteration3
1.67E-03
Iteration4
2.17E-03
Iteration5
2.09E-03

25. 20
Table 2 illustrates how the design space developed throughout the process created in Figure
11. Iterations 1-4 gradually increased the volume of the domain at flat spots. It became clear
that the algorithm found optimal results by enveloping interface 1 with material.
Little information regarding the use of the bracket is available. The reasonable assumption
was made that the attachment is of the form defined in Figure 1 and requires at least 90
degrees of access to the holes. Therefore the domain was re-designed for Iteration 5,
increasing non-design space to prevent obstruction of the interface.
4.3. Investigation into the effects of refining the mesh
Once an ideal design domain had been developed, the volume fraction constraint was
decreased until the optimization no longer converged on a solution due to being overly
constrained. The final design is the result of relaxing the volume constraint until a solution
was found once again, consequently achieving a result of minimal mass. Once this occurred,
the mesh was refined over several iterations. The performance of these models were tested
and compared in ABAQUS.
Mesh refinement allows for the expression of finer detail within the optimal topology.
However, the objective of the FEA testing was to determine whether the refined mesh
produces the same structure with a better portrayal of the boundaries, or in a different
structure altogether.
The topological detail was quantified through the number of holes present in each design and
the computational process time was recorded so that conclusions could be made on the value
of a refined mesh.
4.4. Verifying the performance of an optimized bracket by
mechanical testing
Topology optimization often results in complex, novel structures that bear little resemblance
to previous designs. For it to be a useful tool for engineers, the designer must trust the
process and its results. Furthermore, it only takes a small error in the application of the
boundary conditions during the optimization setup to obtain an unsuitable design.

26. 21
With this in mind a sample of the optimized bracket was mechanically tested to validate the
algorithm as a design process. Due to the time it takes for a component to be manufactured
and the preparations required for mechanical testing, Iteration 1 from Table 2 was
manufactured. The original bracket was also manufactured and tested as a baseline.
Table 3: Testing bracket properties
Bracket Mass (g) Percentage reduction
Original 450
Optimized 255 43.33%
Figure 12 displays the jig that was designed to allow the EZ20 to apply horizontal loading to
the parts. It was decided that both parts would be tested until failure so that a comprehensive
comparison of performance could be made. Additionally, a rate of extension of 10mm/minute
was chosen to simulate a similar speed to a crane beginning to lift an engine from an aircraft
via the engine loading brackets.
Figure 12: Original and optimized bracket pre-mechanical testing

27. 22
Figure 13: Testing jig assembly
5. Presentation of Results & Final Product
Description
5.1. Mesh refinement models
Table 4: Mesh refinement study

28. 23
Figure 14: Optimization convergence for Design A
Figure 15: Optimization convergence for Design B
Figure 16: Optimization convergence for Design C

29. 24
All the mesh refinement models reached a solution. The Min-Max method was successful in
finding a result that minimises the strain energy for all the load cases with equal weighting.
As expected, as the mesh is refined more detail is present in the optimal structure. This can be
seen qualitatively from the pictures and quantitatively from the number of holes in Table 4.
At the final iteration, Designs A and C portray similar maximum strain energies and Design
B has a slightly larger result. This is due to the fact that the model is still slightly over
constrained. Ideally the volume constraint should be relaxed slightly further to ensure that all
the designs converge fully within 50 iterations. Additionally, the trend in stiffness of the
designs corresponds to the trend in the slight differences in volume between them.
It is interesting to note the more erratic nature of the volume fraction throughout the
iterations as the mesh is coarsened. An explanation for this is that the elements within Design
A are of a much higher volume than those of Design C. Therefore the algorithm is able to
make finer adjustments to the volume to reach optimal designs when there is a finer mesh.
When plastic material properties were applied to the optimal topologies they were loaded
until yielding occurred to assess their performance and factors of safety. Design A was the
least compliant when loaded in this direction and Design B was the most compliant. This
validates the information from the optimization outputs displayed in Table 4. Design C was
Figure 17: Finite Element Analysis of designs A, B and C at 284.8kN

30. 25
chosen as the final design as the final mass reduction is largest. With plastic warping
occurring at approximately 180kN, Design C still performs with a factor of safety of 5.
5.2. Mechanical Testing of Iteration 1
Both the original and the optimized bracket failed due to brittle fracture with little plastic
deformation. The stiffness of the optimized bracket is extremely similar to the original and
the lines are nearly identical for the first 2mm of extension. It is estimated that a flaw within
the material is responsible for the slight slip in the loading of the original bracket at 2mm
extension.
After this point the optimized bracket starts to behave slightly more plastically while the
original brackets’ loading increases at a relatively constant gradient. The original bracket fails
with very little plastic deformation at a loading of 9460N.
The optimized bracket withstood slightly more plastic
deformation and failed at a loading of 10665N.
It may be concluded that the optimized bracket performed
extremely satisfactorily in comparison to the original,
especially taking into account the fact that it was
manufactured using 43.33% less material. The stiffness of
both brackets seem to be extremely similar with nearly
Figure 18: Mechanical testing results
Figure 19: Area for calculation of
8.88J strain energy

31. 26
identical strain energies of 8.88J over the first 3.2mm of extension. This effectively validates
the success of the SIMP algorithm in its application to the engine loading bracket.
5.3. Final Design
Figure 21: Final Design
Figure 20: Sites of failure for original (left) and optimized (right) brackets

32. 27
Volume 2.55x10-4
m3
Mass 1.13kg
Percentage of mass
saved from original
design
44.8%
Factor of safety at most
compliant load case
5
Final Design Properties
Table 5: Final Design Properties and Performance Comparison
Despite the fact that this bracket has been designed using a computational algorithm, there
are several aspects of the design that identify with engineering ingenuity. The smooth
surfaces ensure very low stress concentrations. The image of the right side of the bracket
displayed in Figure 21 highlights the truss-like nature of the side profile ensuring that much
of the stress is tensile or compressional.
6. Discussion and conclusions
Figure 22: Optimization summary
Comprehensive research into the theory behind topology optimization was applied in the
context of re-designing an engine loading bracket. The original parts’ mass was reduced by
1.4kg (44.8% volume reduction). The current cost of jet fuel is £643 per 1000kg. Assuming a
jet flies 5000 hours annually, this would equate to a saving of £179 per year per bracket [26].
This is extremely significant. The optimized design is most compliant under its vertical case
with a factor of safety of 5.
During the development of the final design, methods of best practice were investigated for
the optimization of similar parts. It was found that an iterative approach to developing the
design space was successful as it allows the designer to determine where the bulk of material

33. 28
is distributed in optimal results. This allows the design space to be systematically
manipulated to provide the algorithm with a maximal number of possible configurations
while promoting computational efficiency as finite elements are not wasted within the design
volume.
The effect of refining the mesh on the optimization’s result was also investigated. The
conclusion was made that refining the mesh allows the expression of finer detail and a greater
number of holes within the optimal topology. This had no significant effect on the
performance of the designs for these particular parts. However, there was slight variation in
how well each of these designs converged. It is therefore recommended that the volume
constraint be relaxed to the point that the algorithm converges before 50 iterations for results
to be deemed fully optimal.
An optimized bracket’s topology was physically realised through Selective Laser Sintering
and its performance mechanically tested and compared to the original bracket. Under its
horizontal loading condition the optimal bracket outperformed the original bracket, failing at
a load 12.5% greater with a similar stiffness for much of the extension. This contributes to the
validity of manufacturing parts designed by topology optimization directly using ALM.
However, several samples would require testing before it can be determined that the degree to
which the parts’ performance has actually been enhanced.
The greatest challenges in implementing this design process for the manufacture of
components lie in the pre-manufacture stages. The desirability of minimising the use of
support structure was discussed. The suggested method for achieving this involves
developing the algorithm to penalise the radii and overhang geometry requiring support
during the optimization. Currently there is little freedom to alter optimized geometry.
This report has focussed on the role of the engineer when implementing topology
optimization in design. The methodology developed allows successful designs to be created
efficiently while still being validated at every stage of the process.
7. Project management, consideration of
sustainability and health and safety
7.1. Sustainability

34. 29
The motives behind the development of the themes contained within this report are driven by
the requirement to improve sustainability within design and manufacture. Sustainability is an
essential factor for contemporary engineering. Every project must be carefully considered so
that its positive impact is not compromised by any negative implications involved at any
stage during the project’s life. Sustainable design achieves this by integrating social,
environmental and economic conditions into the product so that it is functional, profitable and
environmentally friendly.
The pursuit of sustainability is frequently denoted through three R’s: Reduce, Reuse and
Recycle.
Reducing the weight of an aerospace component has a substantial improvement on its
environmental impact and cost over its lifetime due to fuel costs. Removing human trial and
error is an extremely desirable factor in the highly iterative process. Currently, the decision
on how a new design should look is inspired purely by previous designs. If used effectively
topology optimization will have a huge impact on efficiency. Additionally, removing
estimation from the process greatly reduces the risk of concept changes causing significant
costs deep within a project.
The additional freedom that manufacture by AM provides encourages sustainable
development. Without the constraints of traditional processes parts can be designed to last
longer and perform better.
Both topology optimization and additive manufacture are extremely effective in reducing the
use of materials. Redundant material is immediately eliminated in the concept stage and there
is an extremely limited requirement for the subtraction of material during manufacture.
Furthermore, any support structure removed from a part may be re-ground and re-used during
the manufacture of another component.
7.1.1. Life Cycle Analysis (LCA)
LCA is a method of quantitatively assessing the environmental impact of a product over its
life from the extraction of raw materials through its manufacture, assembly, transportation,
use and its eventual disposal.
LCAs of both the optimized and original bracket were performed and compared. The original
bracket is assumed to be machined from high performance stainless steel with approximately

35. 30
50% material wastage. Additive manufacture has not been included in the processes within
the LCA Calculator by Naked Creativity and IDC [27] so it was estimated that laser cutting
machines operated at a similar energy usage. Other assumptions made during the analysis
were that there is 10% material wastage during the manufacture of the optimized bracket and
that the materials and manufacture take place within the UK. The percentage of stainless steel
recycled (60%) was determined to be slightly higher than titanium (50%) due to the demand
for bulk products that require the material. Both analyses are for the production of a batch of
10 brackets.
The major environmental impact for both brackets lies within material and manufacture.
However, the manufacture of the optimized bracket produced significantly less emissions.
This analysis, combined with the potential fuel savings described in Section 6, make this
optimization exceptionally successful in the context of sustainability.
Figure 23: LCA Comparison
Figure 24: Optimized
bracket LCA
Figure 24: Original
Bracket LCA

36. 31
7.2. Project Management
Figure 25: Project Gantt chart

37. 32
Listed below are the specific tools and resources employed dynamically and concurrently
with one another to guarantee the efficiency and quality of the project delivery.
 Gantt chart: Figure 26 displays the project Gantt chart as it appeared within the
preliminary report submitted in December 2014. This document was used as a
baseline to determine whether the project was on schedule. Aims and objectives
gained more focus during the literature review, problem identification and solution
development stages but all the tasks above remained essential to the success of the
project.
 Logbook: A project logbook was utilised to great effect for the project duration. Its
primary uses involved building an organised database of ideas while exploring the
literature and making notes during meetings with the project supervisor, X-AT and
CALM. The logbook was especially useful as a tool to enhance creativity and was
frequently used for rough sketches, data, notes and ideas.
 Preliminary report: The preliminary report was used as a tool to define the initial
scope of the project objectives. This removed any ambiguity from the aims so that the
results gathered were relevant from the offset. An initial schedule risk assessment was
included which is expanded on in section 7.3.
 Supervisor meetings: Frequent meetings with the project supervisor were extremely
beneficial for brainstorming and discussing problems encountered throughout the
project. Gaining this insight meant that all short term goals were carefully considered
and the project was kept on schedule.
7.3. Risk management
The consideration of health and safety has been an integral aspect of the completion of this
project. The principle document prepared to address this was a Risk Assessment. A Risk
Assessment is an effective documented process that measures the likelihood of an event
occurring as well as its possible consequences.
The Risk Assessment in Table 6 is split into two sections. Section A corresponds to schedule
risk and Section B corresponds to health and safety risk. The strategy to evaluate the risks to
health and safety is detailed using Tables 7 and 8 based on the college guidelines.

38. 33
Table 6: Risk Assessment
ID Risk Item Effect Cause
Likelihood
Severity
Riskrating
Action to minimise risk
A1 Illness Delays in schedule NA 1 3 3 Schedule activities to be completed with ample time before the
deadline.
A2 Conflicting deadlines Delays in schedule Poor time
management
1 3 3 Use Gantt chart effectively
A3 3rd party unable to help with manufacture
or mechanical testing
Planned work outputs
impossible
Poor project
management
1 3 3 Open communications and planning as early as possible and
discuss possible adjustments to the scope with project supervisor.
B1 Mechanical testing injury Injury to eye Broken part
projectile
2 2 4 Plastic screen shield
B2 Workshop injury Minor injury Machinery/Loose
material hazard
2 2 4 Wear protective suitable clothing and eyewear whenever in the
workshop
B3 Back pain Minor injury Working with
poor posture
2 1 3 Ensure comfort when working for long periods of time at a
computer.
Table 7: Risk Assessment Key
KEY
Score A Severity of injury Score B
1 Very minor injury; abrasions/contusions 1
2 Minor injuries; cuts/burns 2
3 Major injuries; fractures/cuts/burns/damage to internal organs 3
4 Severe injury; amputation/eye loss/permanent disability 4
5 Death 5
Risk Rating
(Product of A x B)
Action to be taken
High (6+) Improve control measure; consider stopping work. Conducting work at
this level of risk is to be reported to the project supervisor.
Medium (3-5) The existing control measures are sufficient to control the risk, but the
work activity should be continually monitored and reassessed if there are
any sigificant changes.
Low (1-2) Maintain control measures and review if there any changes
RISK RATING MATRIX
Table 8: Risk Rating Matrix

39. 34
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