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

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

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.

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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

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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

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:

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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.

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.

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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

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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.

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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.

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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

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

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

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

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.

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]

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].

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

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.

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

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:

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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.

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

Orig

ina

l B

ra

ck

et

Design Domain

Design Domain

Volume (m^3) Optimal Topology

Itera

tio

n 1

5.52E-04

Itera

tio

n 2

1.12E-03

Itera

tio

n 3

1.67E-03

Itera

tio

n 4

2.17E-03

Itera

tio

n 5

2.09E-03

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.

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

22

Figure 13: Testing jig assembly

5. Presentation of Results & Final Product

Description

5.1. Mesh refinement models

Table 4: Mesh refinement study

23

Figure 14: Optimization convergence for Design A

Figure 15: Optimization convergence for Design B

Figure 16: Optimization convergence for Design C

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

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

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

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 case5

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

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

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

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

31

7.2. Project Management

Figure 25: Project Gantt chart

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.

33

Table 6: Risk Assessment

ID Risk Item Effect Cause

Lik

eli

ho

od

Sev

erit

y

Ris

k r

ati

ng

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

34

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