Design analysis and optimization of the

Hyperloop shell and chassis

Fangzhou Shao

Master of Science Thesis TRITA-ITM-EX 2019:564

KTH Industrial Engineering and Management

Machine Design

SE-100 44 STOCKHOLM

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Examensarbete TRITA-ITM-EX 2019:564

Designanalys och optimering av Hyperloop-skal och chassi

Fangzhou Shao

Godkänt

2019 -08-28

Examinator

Ulf Sellgren

Handledare

Moeen Rajput

Uppdragsgivare

Daniele Piva

Kontaktperson

Moeen Rajput

Sammanfattning

Ett Hyperloop-system utvecklas för närvarande av Integrated Transport

Research Lab (ITRL) vid KTH Royal Institute of Technology för att delta i den

kommande Hyperloop Pod-tävlingen. Hyperloop-gruppen vid KTH har utvecklat en

primärkonstruktion av chassi och skal. De har dock ingen aning om hur bra deras

nuvarande design är. Eftersom hastigheten är de enda kriterierna för denna tävling, vill

de också minska massan så mycket som möjligt. I detta avseende är det nödvändigt med

finita element- och optimeringsanalyser.

Syftet med denna masteruppsats är att analysera den aktuella skal- och

chassikonstruktionen för att utvärdera kvaliteten på dess fästen och integriteten hos

designen, samt att minska den totala massan samtidigt som styvheten uppfyller

specificerat krav. De använda verktygen är HyperMesh, Optistruct och HyperView som

är delar av programvaran HyperWorks från Altair.

Nyckelord: FE-analys, formoptimering, optimering av topologi, optistrukt,

kompositmaterial

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Master of Science Thesis TRITA-ITM-EX 2019:564

Design analysis and optimization of the Hyperloop shell and chassis

Fangzhou Shao

Approved

2018-08-28

Examiner

Ulf Sellgren

Supervisor

Moeen Rajput

Commissioner

Daniele Piva

Contact person

Moeen Rajput

Abstract

In the past decades of years, huge amounts of people chose to move to big cities

for better education and medical service, which also makes many cities are very

crowded and noisy. Moreover, the house rent in city center is some kind too expensive

for many people, especially for the youth. In this sense, more people are willing to live

in suburb instead of city center. Due to the larger distance between home and office,

people’s requirement for a faster public transportation method is enormous.

Elon Musk first publicly mentioned the concept of Hyperloop in 2012[1], which

is a sealed tube or system of tubes with nearly vacuum condition through which a pod

can transport people or objects at super high velocity. With the linear induction motor

and magnetic levitation technology, the drag force on the pod can be reduced

tremendously, thus increasing the peak velocity to 1200 km/h. To gather more ideas for

this concept, SpaceX holds the Hyperloop Pod Competition where worldwide teams

will design their own Hyperloop pod to demonstrate their technical feasibility of new

ideas [2].

A Hyperloop system is currently in development by the Integrated Transport

Research Lab (ITRL) at KTH Royal Institute of Technology to participate in the

upcoming Hyperloop Pod Competition. KTH Hyperloop group has some primary

design of chassis and shell. However, they have no idea how good of their current

design is. Furthermore, since the velocity is the only criteria for this competition, they

also want to reduce the mass as much as possible. In this sense, some finite element

analysis and optimization analysis are necessary.

The objective of this master’s thesis is to analyze the current shell and chassis

design to assess the quality of the attachments and integrity of the design and to reduce

the total mass while keeping the stiffness within the safety range. The used tools are

HyperMesh, Optistruct and HyperView which are parts of the software HyperWorks

from Altair.

Keywords: FE analysis, shape optimization, topology optimization, Optistruct,

composite material

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FOREWORD

This master’s thesis is the final part of the master’s program in Engineering Design,

Machine Design track at Royal Institute of Technology. This thesis is carried out from

February to July 2019 at the office of Sigma Industry.

I would like to thank everyone who has helped me in this Master’s thesis work.

Firstly, I would like to thank my supervisor at Sigma Industry, Moeen Rajput, for his

patience and guidance during the thesis work. His comments and instructions have

saved me a lot of time to learn a new software and keep me in the correct direction.

Secondly, I would like to thank all group members in Simulation & Analysis group in

Sigma Industry, especially the group leader, Daniele Piva. They all are experienced

analysts and gave me a lot of ideas and suggestions for my thesis work. Moreover, I

would like to thank my supervisor and examiner at Royal Institute of Technology, Ulf

Sellgren, for his suggestions and comments.

I want to express my thankfulness to Altair Engineering for providing me with

the license of the software and very useful online lessons so that I can complete my

thesis work.

Finally, I am thankful to all the group member in KTH Hyperloop group. Their

enthusiasm and hard work motivate me a lot.

Fangzhou Shao

Stockholm, August, 2019

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NOMENCLATURE

Use 12 pt Times New Roman, Italic and 6 pt before and 12 pt after, to describe the

content of this chapter in two or three justified rows, e.g. Here are the Notations and

Abbreviations that are used in this Master thesis. (Only include the lists that are

applicable). The lists are written in 12 pt Times New Roman, 6 pt before.

Notations

Symbol Description

𝜎1𝑡_𝑢 Tensile strength in zero-degree

𝜎1𝑐_𝑢 Compression strength in zero-degree

𝜎1 Stress in zero-degree

𝜎2𝑡𝑢 Tensile strength in 90-degree

𝜎2𝑐_𝑢 Compression strength in 90-degree

𝜎2 Stress in 90-degree

𝑆 Shear strength

𝜀1𝑡_𝑢 Max tensile strain in zero-degree

𝜀1𝑐_𝑢 Max compression strain in zero-degree

𝜀1 Max strain in zero-degree

𝜀2𝑡𝑢 Max tensile strain in 90-degree

𝜀2𝑐𝑢 Max compression strain in 90-degree

𝜀2 Max strain in 90-degree

𝜀12_𝑢 Max plane strain

𝜀12 Plane strain

𝐹12 Normal interaction term in Tsai-Wu failure theory

Abbreviations

CFD Computational Fluid dynamics

FEM Finite Element Analysis

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TABLE OF CONTENTS

SAMMANFATTNING (SWEDISH) 1

ABSTRACT 3

FOREWORD 5

NOMENCLATURE 7

TABLE OF CONTENTS 9

1 INTRODUCTION 11

1.1 Background 11

1.2 Purpose 11

1.3 Delimitations 12

1.4 Method 12

2 FRAME OF REFERENCE 13

3 IMPLEMENTATION 15

4 RESULTS 17

5 DISCUSSION AND CONCLUSIONS 19

5.1 Discussion 19

5.2 Conclusions 19

6 RECOMMENDATIONS AND FUTURE WORK 21

6.1 Recommendation 21

6.2 Future work 21

7 REFERENCES 23

APPENDIX A: SUPPLEMENTARY INFORMATION 25

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1 INTRODUCTION

This master’s thesis is about the design, analysis and optimization of the chassis and

shell of the Hyperloop pod. The background, the purpose, the limitations and the

method(s) used will be described in this chapter.

1.1 Background

The Hyperloop transport concept was proposed by Elon Musk in the Hyperloop White

Paper published in 2012. This system was introduced with the goal of combining

cutting-edge engineering technologies to create the fifth mode of transportation. By

utilizing a low-pressure tube as the operation environment and implementing magnetic

levitation, the drag forces exerted on the vehicle can be reduced dramatically which

would facilitate achieving a peak velocity of 1200m/s.

The Hyperloop Pod competition is a competition sponsored by SpaceX where

worldwide teams will gather together to show their own Hyperloop pods to demonstrate

the feasibility of the new ideas about Hyperloop concept. All pods are judged only on

one criteria: maximum velocity with successful deceleration i.e. without crashing.

There are two key rules according to the Hyperloop Competition Rules and

Specification. One is that all teams have to use their own communication system. The

other is Pods must be designed and tested to propel themselves to within 100 feet of the

far end of the tube before stopping.

An Hyperloop system is currently in development by the Integrated Transport

Research Lab (ITRL) at KTH Royal Institute of Technology to participate in the

upcoming 2020 Hyperloop Pod Competition. To design the Hyperloop vehicle,

knowledge from different fields like aerodynamics, control theory and magnetic

physics should be gathered and put into practice. The competition will take place in

July and most design work has been done. However, there still exist great possibilities

to improve the performance of both shell and chassis.

1.2 Purpose

Although the chassis and shell have been designed, the structure analysis for these parts

have not been done. The current design of chassis and shell should be analyzed in finite-

element analysis to get the stress distribution and deformation under different load

conditions, including lifting, acceleration and braking processes. Only when analysis

results are available, KTH Hyperloop can check whether the current designs are

qualified or not.

Moreover, since the only judging criteria of Hyperloop Pod Competition is to

reach the maximum speed with successful deceleration. Apparently, the whole vehicle

should be as light as possible to reach a higher velocity. In this sense, optimization

should be done to reduce the weight of the shell and chassis parts as much as possible

to increase the peak velocity that the pod can reach.

The current thesis project will be done in collaboration with Sigma Industry East

North and KTH Hyperloop team.

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1.3 Delimitations

It is good practice to define and describe limitations of the project/task in the

introductory chapter.

● Only chassis and shell design should be analysed

● Available material should be figured out by structure group in KTH Hyperloop

● The validation of the final design in reality test will be not within the scope

● 70% of finite element analysis and 30% of design

● Vibration and response analysis will not be part of the scope

● The simulation will be based on the current design. Any changes from KTH

Hyperloop on the current design will not be taken into consideration.

1.4 Method

The thesis work can be divided into three parts: Literature review and research, analysis

for chassis and shell, optimization for chassis and shell.

The first part is the literature review and research, including reading the material

about the Hyperloop concept and Hyperloop Pod Competition so that I can have a basic

understanding of the rules and constraints for my future design. Reading the final

reports from other groups in past few years’ competition can also help to generate some

new ideas to reduce the weight and increase the stiffness. Moreover, some research

articles about the simulation and optimization are necessary. The general methodology

to conduct the analysis and optimization from these articles can make the work more

efficient. The literature research also contains the time to learn how to use the software,

including how to do the inertia relief analysis and how to do the optimization analysis

and what’s the correct steps for optimization.

The second part is the analysis for the chassis and shell that are made of

aluminum and carbon fiber respectively. Three loading cases of lifting, braking and

acceleration should be conducted and we can get the displacement, strain and stress of

all components to check whether the performance of current design is good.

The final part is the optimization for the chassis and shell and generation of the

new design. According to simulation results from the second part, the critical areas on

the chassis and shell can be figured out. According to the results of size and topology

optimization analysis, some unnecessary parts can be removed while the critical parts

should be enhanced.

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2 FRAME OF REFERENCE

The reference frame is a summary of the existing knowledge and former performed

research on the structure analysis and optimization analysis on metal and composite

material. This chapter presents the theoretical reference frame that is necessary for this

thesis project.

2.1 Finite Element Analysis

Finite element analysis uses mathematical approximation to simulate real

physical systems. With simple and interacting elements, a finite number of unknowns

can be used to approximate a real system with infinite unknowns.

Finite element analysis is to solve complex problems with simpler problems.

Because the actual problem is replaced by a simpler problem, this solution is not an

exact solution, but an approximate solution. Since most practical problems are difficult

to obtain an accurate solution, finite element analysis is time-saving, highly accurate

with proper element number, and adaptable to various complex shapes, thus becoming

an effective engineering analysis tool. Finite element analysis is used widely in

structure analysis, heat transfer, mass flow, electromagnetic potential and so on [3].

The concept of finite element has been produced and applied centuries ago, for

example, using a polygon to approximate the circle to find the circumference of the

circle.

There are many types of analysis that are used under different conditions. The

two most common methods are static analysis and Inertia relief analysis.

2.1.1 Static Analysis

Static analysis is the simplest and most common analysis in engineering fields, which

is used to determine the stress, strain, displacement and forces in structures with

external loads. When conducting linear static analysis, external forces, pressure,

acceleration forces and constraint points should be specified.

Figure 1. Example of FEM static analysis [4]

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2.1.2 Inertia Relief Analysis

Inertia Relief analysis is applied to the system that is not fully constrained or moves at

a long distance. The linear static analysis requires that the system is constrained, or the

singularities will occur in the stiffness matrix, making the results invalid.

When conducting inertia relief analysis, the external loads will be balanced by

a set of translational and rotational accelerations instead of traditional reaction forces.

One example is the satellite in the aerospace, which gets the external propulsion force

from the engine and moves at a long distance in the space without constraints. Then,

the inertia relief analysis is necessary to calculate the stress, strain and so on.

Since the Hyperloop will run along the tube, the inertia relief analysis should be

applied for the braking and acceleration process.

2.2 Structure Optimization

The purpose of the structure optimization is to find the optimal material distribution to

achieve some given objectives under certain limitations or requirements. Some

common objectives are to minimize the weight, minimize the cost or increase the

rigidity of the structure.

This optimization process is an iterative process. The first step is to think of a

design. The second step is to evaluate whether the requirements or limitations are

satisfied or not through finite element analysis. If it’s fulfilled, the optimization is

determined. If not fulfilled, new changes should be made and repeat the previous steps.

In this sense, the time spent on the optimization process depends on how much

extent the designer wants to improve the original design. In most cases, optimization

takes quite a long time and the result depends heavily on the designer’s knowledge and

experience.

Figure 2. Difference between size, shape and topology optimization [5]

2.2.1 Size Optimization

Sizing optimization is the simplest form of structural optimization. The objective is to

optimize the structure by adjusting sizes of the components like thickness of the

component and so on. When optimizing the composite materials, size optimization will

be conducted to determine the most suitable thickness of plies. Thus, it can help

engineers to reduce development time of products made of composite materials.

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2.2.2 Shape Optimization

In shape optimization, the purpose is to adjust the shape and inner boundary dimensions

of the structural design to find the optimal geometry of the structure to achieve customer

requirements like minimizing the weight and so on.

2.2.3 Topology Optimization

The most general form of structural optimization is topology optimization. The purpose

is to find the optimum distribution of material.

With topology optimization, the optimal material distribution can be found in the

design space of uniformly distributed materials to achieve some objectives. Compared

with size and shape optimization, topology optimization has more design freedom than

other two optimization methods, which is one of the most promising aspects of

structural optimization.

2.3 Composite Material

Composite materials are new materials that is made of a combination if two or more

different materials to optimize the combination of material components of different

properties. The history of composite use can date back to ancient times. The straw-

reinforced clay that has been used to build houses in ancient ages and the reinforced

concrete that has been used for hundreds of years are two typical composite materials.

Since composite materials are used widely in high-tech fields like aerospace and

military due to its high stiffness, high tensile strength, low weight, high chemical

resistance, high temperature tolerance and low thermal expansion, composite materials

are more and more important in the development of modern science and technology.

The development of the composite material has become one of the most important

indicators to measure the advanced level of science and technology in a country.

A generally defined composite material must meet the following conditions [6]:

● Composite materials must be man-made and designed and manufactured

according to the requirements;

● Composite materials must be composed of two or more chemically and physically

different material components. There should exist some distinct interfaces

between the components;

● Composite materials not only maintain the advantages of the properties of the

various components, but also achieve the comprehensive properties that cannot be

achieved with a single constituent material

2.3.1 Laminate Theory

A ply, or a lamina, is a single layer of a composite material which consists of fibres

embedded in matrix [7]. To define the material characteristics of a lamina, three

orthogonal axes are established as length (L), width (W) and transverse (T).

There are mainly four different laminae as shown in Figure 3. The first type is

unidirectional, where the fibers are placed in the same direction in the lamina. The

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second type is bi-directional, where the fibers are commonly placed in two

perpendicular directions in the lamina. The third type is discontinuous fiber, where the

discontinuous fibers are placed in random directions. The final one is woven fiber,

which is quite similar to bi-directional fibers.

Figure 3. Different kinds of plies [7]

To form a laminate, several plies will be assembled together as shown in Figure

4.

Figure 4. Laminate example [8]

2.3.2 Failure Modes in Composite Materials

Dislike the steel and aluminum, the failure modes of carbon fiber are quite complicated

since carbon fiber is orthotropic instead of isotropic. The failure is caused by different

loading conditions. In this sense, we will divide the failure modes according to the load

types as tensile failure, compressive failure and interlaminar failure.

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Tensile failure implies that the fracture in laminate is caused by the tensile

forces. There are two conditions that the tensile force is longitudinal to the fibers or

transverse to the fibers. For a unidirectional lamina, if the longitudinal loads cause the

fracture, it is a fibre dominated failure mode. If it is transverse loads that cause the

fracture, it is matrix dominated failure mode.

Actually, these concepts are quite easy to understand. Since the lamina is super

strong along the fiber direction and quite weak in the transverse direction, the fiber will

contribute more to the whole stiffness in the longitudinal direction and the matrix will

contribute more to the whole stiffness in the transverse direction.

Compression failure implies that the fracture is caused by the compression

forces. When the compression load applied on the laminate increases, the fibers will

bend, thus causing fracture.

The interlaminar failure is due to transverse normal stresses, transverse shear

stresses or even in compression. The interlaminar failure will cause delamination

between plies or fiber/matrix interface failure.

Figure 5. Failure modes of the composite materials [9]

2.3.3 Composite Material Failure Theory

Lamina failure theories can be classified in three catalogs [10]:

1. Non‐interactive or limit theories: failure is determined by comparing lamina

stresses or strains with corresponding ultimate strains or strengths. The limitation

is that the interaction between stress components are not taken into consideration.

Examples of such theories are maximum strain criteria and maximum stress criteria.

2. Interactive theories: overall failure can be predicted by one failure criteria that

includes all stress components and their interaction. The limitation is that the failure

mode cannot be figured out. Examples of such theories are Tsai-Wu criteria and

Tsai-Hill criteria.

3. Partially interactive or failure-mode-based theories: different failure criteria will

be applied to the failure of matrix, fiber and interface, which is close to the reality.

Examples of such theories are Hashin failure criteria and Puck failure criteria

Maximum Stress Criteria:

−𝜎1𝑐_𝑢 < 𝜎1 < 𝜎1𝑡_𝑢

−𝜎2𝑐_𝑢 < 𝜎2 < 𝜎2𝑡_𝑢

|𝜏12| < 𝑆

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Maximum Strain Criteria:

−𝜀1𝑐_𝑢 < 𝜀1 < 𝜀1𝑡_𝑢

−𝜀2𝑐_𝑢 < 𝜀2 < 𝜀2𝑡_𝑢

|𝜀12| < 𝜀12_𝑢

Tsai-Hill Criteria:

𝜎12

𝜎1_𝑢2−

𝜎1𝜎2𝜎1_𝑢2

+𝜎2

2

𝜎2_𝑢2+

𝜏122

𝜏12_𝑢2= 1

Tsai-Wu Criteria:

𝜎12

𝜎1𝑐_𝑢𝜎1𝑡_𝑢+

𝜎22

𝜎2𝑐_𝑢𝜎2𝑡_𝑢+

𝜏122

𝜏12_𝑢2+ 2𝐹12𝜎1𝜎2 +

𝜎1𝜎1𝑡_𝑢

−𝜎1

𝜎1𝑐_𝑢+

𝜎2𝜎2𝑡_𝑢

−𝜎2

𝜎2𝑐_𝑢= 1

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3 IMPLEMENTATION

In this chapter, the working process is described. A structured process is often called a

method and its purpose is to help to reach the goals for the project. Requirements

should be figured out at the beginning of the project. According to these requirements,

the concept can be generated.

3.1 Requirements Specification

As this project aims to reduce the weight of chassis and shell while increasing the

stiffness, structure analysis and optimization analysis should be developed. With these

analysis results, new design can be generated. In this section, the requirements needed

to be fulfilled will be listed.

3.1.1 Feature

After understanding of the Hyperloop concept and discussing with the KTH Hyperloop

group, the feature requirements for shell and chassis are finalized as shown below.

● Easy to install

● Robust to finish the competition

● Rigid to hold all components

● Easy access for maintenance

● Safe to handle

● Light to increase the peak velocity

3.1.2 Hyperloop Pod Competition Requirements

According to Hyperloop competition rules and requirements, the pod should move on

the I-shape beam in the tube provided by SpaceX. In this sense, there are some

constraints for

Figure 6. Tube and I-shape beam dimension [11]

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Table 1.Competition constraints

Pod constraints Tube constraints:

Mass < 1500 kg Outer diameter: 72 in

Length dimension: 5-14 feet Inner diameter: 70.6 in

Safety factor > 2 Length: 1.25km

Internal P: 0.125-14.7 PSI

Concrete height: 10.4 in

Since the components including the friction braking system, current braking

system, electronic system and etc. are finalized, the corresponding intersection parts

should be maintained.

Moreover, the friction braking pad and I-beam should always be in contact, or

the friction braking system will not work. In this sense, another requirement is that the

displacement of the friction braking system in transverse direction cannot be over 2

millimeters.

3.2 Pod Design Description

Before working on the simulation, the interfaces between chassis and the other

components should be figured out so that we can know how to model the structure and

how to apply the boundary conditions.

Understanding the basic functions and positions of all components are the first

step of the analysis. There are five main systems in the pod [12]:

● Propulsion System: Double Sided Linear Induction Motor (DSLIM) is used to

provide the propulsion forces to the Pod

● Braking System: The Eddy current brake system and friction brake system are

used to generate a total deceleration force of 6000N to stop the pod safely without

crashing.

● Levitation System: The magnetic levitation system will be placed on the skis and

connected to the chassis to lift the pod from the ground, thus decreasing the friction

force.

● Electronics System: Electronics system will collect the sensor data to controll and

monitor the system. Electronics system will be also used to transfer the data to the

laptop and receive the orders from laptop remotely.

● Control and Navigation System: The navigation and control system will report

the current state of the pod and the performance of all components.

In Figure 7, it demonstrates the chassis with some other systems fixed on it. There

is one battery box placed on the top of the chassis, where the electronics system and

control and navigation system will be fixed on the battery box. On the right side in the

figure is the front face of the chassis and the rear face is on the left side. There are one

friction braking system and one Eddy current braking system fixed on the sides of the

chassis in both front and rear parts. Two groups of linear induction motor are fixed in

the central of the chassis. Each group will attach to one side.

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Figure 7. Chassis with some other systems

The exploded-view drawing of the KTH Hyperloop pod design in figure 6 shows

more information about the position of different components.

From the top-down version, the first one is the carbon fiber shell, following by the

electronic system and battery box, chassis with braking systems and motor and skis

with magnetic levitation system. Two components not mentioned in last paragraph are

the shell and skis with magnetic levitation system. The shell acts like a cover to reduce

the drag force on the whole pod. The skis are on the two sides of the chassis and they

will be connected with the beams and the sides of the chassis. There will be some

springs between the beams and skis, like the shock absorb to exclude the vibration on

the chassis.

Figure 8. Exploded-view drawing of KTH Hyperloop pod design

There are three loading cases to be conducted. The first one is lifting. Before

starting up the pod, four group members need to lift the pod to the tunnel and then run

it. The second one is braking. To finish the competition, all pods should stop

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successfully without crashing in the tunnel. Two friction braking systems and two Eddy

current braking systems are placed on the chassis. There will exist normal and friction

forces applied on the chassis. To check whether these forces will cause the failure on

the chassis, braking process should be analyzed. The third loading case is acceleration.

At the beginning of the competition, the pod will accelerate to the peak velocity.

Similarly, the forces from the motor should also be analyzed.

The masses of different subsystems are listed in Table 2.

Table 2. Masses of subsystems

Subsystem Mass (kg)

DSLIM 68.00

Ski (2x) 55.99

Eddy current braking (2x) 47.38

Friction braking (2x) 21.48

Chassis 23.104

Battery system 73.95

Lateral stability module (2x) 5.212

Shell 6.1

Inverter 15

Low voltage battery (2x) 1.656

Electronics and sensors 5.1

After understanding the structure of the pod and how it works, chassis can be modeled

in the Hypermesh.

First, the STEP file of the chassis should be imported to the Hypermesh and

click the function that splits the component by body. Then we can get the 3D model of

the whole chassis as shown in Figure 9.

Figure 9. CAD file of the chassis part

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Second, midsurface of all components will be constructed. Since the chassis is

made of sheet aluminum, it can be modeled with shell elements, which is 2D elements.

Using 2D elements instead of 3D element can save huge amounts of time. Moreover,

since the chassis is symmetrical with XZ plane, we can keep only half of the model and

add some so-called “symmetric constraints” to make the half model perform as the

whole model. As shown in Figure 10, all the nodes on the symmetric axis should be

constrained on DOF 2,4,6 to make it perform as the whole model.

Figure 10. Chassis model with symmetric constraints

Contact surfaces and type of contact will be used to define the relationship

between the components to unit all the components as a whole pod. Since the goal is to

assess the performance of the current chassis design, tie contact is chosen, which

simplifies the model and saves quite a lot time. The contact relationship is shown in

Figure 11.

Figure 11. Contact relationship between surfaces

Next, mass nodes should be used to represent the components attached to the

chassis as shown in Figure 12. Components including two braking systems, skis, battery

box, electronic system and motor will all be connected to the chassis to get as close as

possible to the reality world. 1D element, RBE3, is used to connect the nodes of

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connection parts and mass nodes because RBE3 will not affect the stiffness of the

structure. The light blue parts are all RBE3 elements.

Figure 12. Chassis model with all mass nodes

After that, forces can be applied on the mass node of the components. For

example, since the friction force occurs at the connection point between I-beam and

friction braking pad, the friction force should be added on the mass node of friction

braking system.

Finally, material and property should be assigned to the whole chassis in

Hypermesh. The thickness of all shell elements is 3 mm according to the structure group

in KTH Hyperloop. Necessary inputs of aluminum property from chosen supplier is

listed in Table 3.

Table 3. Material property of aluminum

Young’s Modulus 75000 MPa

Poisson’s Ratio 0.33

Density 2790 kg/m3

Yield Stress 240 MPa

Yield Strain 0.2%

Shell Modeling

Since the shell from the CAD file designed by the aerodynamic group in KTH

Hyperloop is just the combination of some surfaces, we can mesh these surfaces directly

after importing the STEP file.

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Figure 13. Shell model of 2D elements

The shell is made of composite material, carbon fiber. For carbon fiber, some

plies are first to be created and then construct the laminate with these available lies

created before.

The laminate should be quasi isotropic, balanced and symmetric, or the laminate

will suffer some twisting torque even though there are no external forces applied on it.

The laminate is shown in Figure 14 as [0/45/90/−45]𝑠.

Figure 14. Laminate of the shell

The thickness of all plies is 0.3 mm because of the minimum thickness that the chosen

supplier can manufacture is 0.3 mm. The zero-direction of ply is along z-axis in

Figure 15.

Figure 15. Laminate with fiber direction

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The type of carbon fiber is T700s, whose property is shown in Figure 16. The density

of this type of carbon fiber is 1540 kg/m3.

Figure 16. T700s carbon fiber property [13]

3.3 Overall Concept Generation

To increase the stiffness and reduce the weight of the chassis, structure analysis and

optimization analysis are integral. There are some steps to conduct the simulation for

chassis made of aluminum. One thing to keep in mind is to make the simulation as close

to the reality as possible.

The first step is to understand how the current pod work. All other components

including battery box, electronic and control system, ski and magnetic levitation system,

friction braking system, Eddy current braking system and pod stability system will be

fixed on the chassis, so the connection parts between the chassis and these components

must be maintained. Meanwhile, the loading cases and corresponding boundary

conditions like forces from these components and constraints will be clear.

The second step is to run the simulation of structure analysis on the HyperWorks

with all loading cases. After checking the displacement, strain and stress from the

simulation results, the performance of the current chassis design can be resolved.

The third step is to run the optimization on the HyperWorks. With structure

optimization results, we can check the how different components contribute to the

whole stiffness. The parts with higher element density implies that they contribute more

to the stiffness and should not be removed. Also, the size optimization gives the

optimized thickness for each component with the given constraints.

According to the structure analysis and optimization results, some unnecessary

parts that contribute almost nothing to the whole stiffness can be removed and the

thickness of the components can be reduced for some non-critical parts, thus reducing

the mass as much as possible.

28

For shell part, the procedure is quite similar to the chassis part. Since the shell is

made of carbon fiber that is a composite material, the failure mode and criteria are

totally different from the isotropic materials like aluminum and steel. In this sense, the

first step is to do some information research.

The second step is to run the structural simulation on the HyperWorks with given

loading cases. By checking different composite failure criteria, the performance of the

current shell design can be figured out.

The third step is to do the optimization to reduce the weight of the shell part.

Through free size optimization, size optimization and shuffle optimization, new design

can be finalized. After understanding the most efficient way to do composite material

optimization, some noncritical parts in the chassis can be replaced by carbon fiber to

reduce more weight.

Except for the changes from the structure analysis and optimization analysis

results, alternative material and structure can also be taken into consideration.

For chassis, using carbon fiber sandwich with an aluminum honeycomb core

instead of solid aluminum can reduce the weight a lot. This honeycomb sandwich

material has high stiffness with low density. The drawback of this honeycomb structure

is that it needs specific mounting parts different from the traditional ones as shown in

Figure 2. Moreover, the whole chassis can be manufactured by carbon fiber. Carbon

fiber is really expensive and its fault tolerance is really low that once some parts of the

carbon fiber chassis are broken, it’s not possible to repair them. However, the weight

of chassis can be reduced enormously due to the low density and high stiffness of

carbon fiber. Besides, some high-stiffness materials like high strength steel can be used

on critical parts so that other parts’ thickness can be decreased.

Figure 17. carbon fibre sandwich with an aluminum honeycomb core [14]

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Figure 18. Mounting for carbon fiber sandwich with an aluminum honeycomb core [15]

From the aspects of structure, uniting the components as a whole body can be

practical. Since there are a lot of components in the current design of chassis, the weight

of connection parts and weld material occupies quite a large percentage of the total

weight. Hence, uniting some of these components is a possible solution. Alternatively,

components like battery box can be made as part of the chassis to increase the stiffness.

30

31

4 RESULTS

In the results chapter the results that are obtained with the process/methods described

in the previous chapter are compiled, and analyzed and compared with the existing

knowledge and/or theory presented in the frame of reference chapter.

4.1.1 Lifting case

Since there are many components connected to the chassis, mass nodes are used to

represent these components and they are connected to the nodes of the corresponding

connection areas by 1D element, RBE3. However, since the forces from the battery box

and electronic system contribute uniformly on that area, pressure should be applied on

that area instead of mass node.

The areas where people hold the pod should be constrained in z-axis (DOF 3) as

shown in Figure 19 and gravity field should be applied to the whole system. The

thickness of the whole chassis is 3 mm and the material is aluminum.

Figure 19. Chassis model with constraints in lifting case

Since the yield stress for the aluminum is 240 MPa and the safety factor should

be over 2 according to the competition rule, the maximum von-Mises stress in the

chassis should be less than 120 MPa.

According to the simulation, the displacement and von-Mises stress of the lifting

loading case are shown in Figure 20 and Figure 21. The part with red color implies that

the stress there will be over 120 MPa and displacement is over 2 millimeters, which

will cause failure. Since there are no red points in Figure 20 and 21, there won’t exist

failure in the chassis. The maximum stress in lifting case is 72.26 MPa.

Thus, current chassis design’s performance in lifting case is good enough.

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Figure 20. Displacement of chassis in lifting case

Figure 21. Stress of chassis in lifting case

4.1.2 Braking case

Similar to lifting case, mass nodes are used to represent the components and connected

to the nodes of the corresponding connection areas by 1D element, RBE3. The only

difference is that we use the mass node and apply the gravity to it to represent the battery

box instead of pressure force because we use the inertia relief analysis, where the

applied loads will be balanced by a set of translational and rotational accelerations, and

if we apply the pressure force to represent the weight of battery box, the total mass will

be smaller than that in the reality, thus making the acceleration in the simulation larger

than in the reality.

The areas where skis support the chassis should be constrained in z-axis (DOF

3) as in lifting case and gravity field should be applied to the whole system. The normal

forces from four braking systems are 750 N for each and braking forces are 500 N for

each. All of them will be applied on the node where the forces occur in the reality. For

example, the friction force in the reality will occur in the area where friction braking

33

pad contacts the I-shape beam and the friction force will be placed on the node in the

center of that area.

According to the simulation, the displacement and von-Mises stress of the

braking loading case are shown in Figure 22 and Figure 23. The red color implies that

the stress there will be over 120 MPa and displacement is over 2 millimeters, which

will cause failure. Apparently, there are many red points in these two figures, which is

the connection parts between the chassis and two braking systems. The maximum stress

in braking case is 200.6 MPa, much higher than 120 MPa.

Thus, the performance of the current chassis design in braking case is bad and

must be improved.

Figure 22. Displacement of chassis in lifting case

Figure 23. Stress of chassis in braking case

4.1.3 Acceleration case

Similar to braking case, mass nodes are used to represent all the components and

connected to the nodes of the corresponding connection areas by 1D element, RBE3.

34

The areas where people hold the pod should be constrained in z-axis (DOF 3) and

gravity field should be applied to the whole system. The acceleration force from one

linear induction motor are 3000 N, which will be applied on the node where the forces

occur in the reality as in braking case.

One big difference from the braking case is that one extra force will be applied

on the ski to balance the weight of the skis. During the process of acceleration, the

magnetic levitation system will work and the whole pod will be suspended. At this

moment, the skis actually support the whole pod in z-direction, which implies that the

total reaction force in the connection area between chassis and skis is equal to the total

weight of the pod minus the weight of the skis and magnetic levitation system.

According to the simulation, the displacement and von-Mises stress of the lifting

loading case are shown in Figure 24 and 25. The red color implies that the stress there

will be over 120 MPa and displacement is over 2 millimeters, which will cause failure.

Apparently, there are many red points in two figures, which is the connection parts

between the chassis and two braking systems. The maximum stress in acceleration case

is 153.4 MPa, much higher than 120 MPa.

Thus, the performance of the current chassis design in acceleration case is bad

and must be improved.

Figure 24. Stress of chassis in braking case

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Figure 25. Stress of chassis in braking case

4.1 Chassis optimization

Step 1: Increase the thickness

Since the current chassis design will fail in both braking and acceleration processes,

optimization cannot be conducted right now. The first step is to make the maximum

Von-Mises stress in all loading cases within the safety range. In this sense, the thickness

of critical parts where braking systems locate should be increased to increase the

stiffness. As shown in Figure 26, the thickness of the purple parts will be increased

from 3 mm to 5 mm. The other parts won’t be changed.

Figure 26. Chassis model with different properties

Then the maximum stress in braking and acceleration processes is lower than

120 MPa as shown in Figure 27 and 28, which implies that we can start the optimization

analysis to remove some unnecessary material.

The mass increases from 21.5 kg to 28 kg.

36

Figure 27. Stress of chassis in acceleration case

Figure 28. Stress of chassis in braking case

Step 2: Size optimization

Size optimization is used to determine the proper thickness of components to

achieve the objective under limitations. In Figure 29, the red and blue color components

are designable parts and two beams are non-designable parts. In the optimization

analysis, only designable parts will be included.

By setting the objective as minimizing the total mass and the constraint that the

displacement of all nodes in y-direction cannot exceed 2 millimeters and maximum

Von-Mises stress cannot exceed 120 MPa, the thickness of blue parts and red parts are

1.845 mm and 3.832 mm respectively.

The total mass is reduced from 28 kg to 20.1 kg.

37

Figure 29. Size optimization result of chassis

Step 3: Topology optimization

The constraints and objective of topology optimization is the same as size

optimization analysis. The element density is a scale to assess how different parts

contribute to the whole stiffness. For parts with higher value of element density, they

contribute more to the stiffness. In Figure 30, the parts in the center of the chassis are

most blue, implying that some parts can be removed without influencing the whole

stiffness a lot.

Figure 30. Topology optimization result of chassis

According to the topology result, the chassis is redesigned and the new design

is shown in Figure 31. Compared with the original design, some holes and squares are

made on the chassis and some components with low element density are removed. After

that, the mass decreases from 20.1 kg to 17.06 kg.

38

Figure 31. Chassis new design

Step 4: Second round of size optimization

In the first round of size optimization, the thickness of the whole designable

component will be changed completely. However, there is an alternative way to just

increase the thickness of some critical areas in one component while maintaining the

thickness of the other areas in same component that one extra sheet aluminum can be

welded to the critical area to increase its stiffness.

In this sense, different properties are assigned more detailed to the chassis as

shown in Figure 32. Yellow area implies the critical parts that contribute a lot to the

whole stiffness.

Figure 32. Chassis with different properties for critical and noncritical parts

39

Final result is listed in Table 4

Table 4. Result of chassis optimization

Optimized Thickness (mm) Manufacturable Thickness (mm)

Gray parts 2.022 2

Blue parts 1.988 2

Orange parts 4.574 4.5

Green parts 2.501 3

Step 5: Reanalyze the new design

After determining the thickness of new chassis design, structural analysis

should be done again to ensure that new design fits all requirements.

The results of stress, strain and displacement are shown below. In Figure 33,

red color implies that the stress in the chassis is larger than threshold value, 120 MPa.

In Figure 34, red color implies that the strain in the chassis is larger than threshold value,

0.2%. In Figure 35, red parts imply that the displacement in the chassis is larger than

threshold value, 2 mm. Since there are no red parts, the new design meets the

requirements perfectly.

Figure 33. Stress of chassis in braking case

40

Figure 34. Strain of chassis in braking case

Figure 35. Displacement of chassis in braking case

The mass of chassis decreases from 28 kg to 12.55 kg, reducing 55.2% of the

original weight.

4.2 Shell structure analysis

The shell will be fixed on two beams of the chassis. These connection areas should be

constrained on all degrees of freedom. There are three loading forces applied on the

shell, drag force of the air in the test tunnel, gravity and reaction force from the chassis.

It is quite clear that during the braking process, the stress and strain on the shell

will be largest since the directions of drag force and reaction force from the chassis are

the same. From aerodynamic group in KTH Hyperloop, the pressure field file is

available. By using the “linear interpolation” function, Hypermesh can add pressure to

the shell from the data of pressure field file. The reaction force from the chassis is equal

to the acceleration times the mass of the shell. We can accomplish easily by adding a

gravity field to the shell and defining the field vector along the longitude direction as

deceleration value.

With all external forces and constraints defined, structural analysis can be run.

As illustrated before, there are three types of failure theories of composite materials.

41

The results of maximum strain theory, Hsai-Wu failure theory and Hashin failure theory

are shown in Figure 36, 37 and 38.

When the composite failure index is less than 1, there won’t exist failure in the

structure. To meet the requirement of safety factor as 2, the failure index should be less

than 0.5. Since the composite failure index in all three theories are much less than 0.5,

we can conclude that the current shell design is awesome.

Figure 36. Failure index of max strain theory in braking process

Figure 37. Failure index of Tsai-WU theory in braking process

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Figure 38. Failure index of Hashin theory in braking process

4.3 Chassis Optimization with Composite Material

Since carbon fiber is lighter and more rigid than aluminum, there is an alternative

method to reduce the weight of chassis by replacing some parts of the chassis with the

carbon fiber.

From Figure 33, it’s clear that the central part connected with the linear

induction motor is non-critical areas with much lower stress. In this sense, a new model

is constructed with carbon fiber. The laminate is built as shown in Figure 39 as

[0/45/90/−45]𝑠, which is the same as shell laminate. The only difference is that the

zero-direction of fiber is along y-direction.

Figure 39. Laminate of the central part of the chassis

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Figure 40. Fiber direction of the central part of the chassis

All other settings are the same as what we have done in chassis analysis section.

Since the chassis suffers more external forces during the braking process because of

larger deceleration, it is not so necessary to put the failure index results of all loading

cases in this report. The composite failure index results of braking procedure are shown

below

Figure 41. Failure index of Hashin theory in braking process

44

Figure 41. Failure index of Tsai-Wu theory in braking process

Figure 41. Failure index of Max strain failure theory in braking process

Similarly, the red color implies the failure in the structure as before. Thus, it can

be concluded that it’s a good way to use carbon fiber and aluminum together to

construct the

The total mass reduces from 12.55 kg to 11.71 kg.

45

5 DISCUSSION AND CONCLUSIONS

A discussion of the results and the conclusions that the author have drawn during the

Master of Science thesis are presented in this chapter.

5.1 Discussion

At the beginning, the optimization of the shell part is within the scope, which will

contain free size optimization, size optimization and shuffle optimization. However, the

optimization result of free size optimization doesn’t show anything. Insteadly,

Hypermesh just decreases the thickness of all plies to the minimum manufacturable

thickness, which is defined in the manufacturing constraints. When the applied pressure

field is increased by ten times, the result is normal. The possible reason might be that

the pressure that acts on the shell is too low that the software doesn’t consider it is

necessary to remove some material.

It would be the best to redo the CFD analysis of the shell and apply the pressure

field to the shell in Hypermesh. Even though it is possible to use carbon fiber to build

the whole or part of the chassis, there will exist a lot of extra work to redesign the

mounting method and component interfaces since the volume and mounting way are

totally different for composite material from aluminum.

For the new design of the chassis, sheet aluminum will be welded to the

component to increase some critical areas’ stiffness without increasing the thickness of

the whole component. However, the property of a weld part is a bit different from a unit

part, which should be studied in the future.

5.2 Conclusions

In this thesis project, structure analysis is conducted for both shell and chassis. With

the analysis results, the performance of the current can be concluded. Moreover, the

critical areas are figured out so that the improvement ideas are made.

The performance of chassis is not good. There will exist failure in both

acceleration and braking processes. Thus, the thickness of some parts must be increased

to fit the requirement of safety factor.

An iterative process is taken during the optimization process of the chassis to

try to decrease the total weight of the chassis. The total weight of chassis decreases

from 28 kg to 11.71 kg, which is a huge improvement.

For shell part, due to the low internal pressure in the test channel, the drag force

applied on the shell is really small so that the current design is rigid enough. The

optimization process should be conducted in the future.

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47

6 RECOMMENDATIONS AND FUTURE WORK

In this chapter, recommendations on more detailed solutions and/or future work in this

field are presented.

6.1 Recommendations

The material of chassis is aluminum because of its flexibility of manufacturing and high

tolerance of fault. In this thesis project, the weight of chassis is reduced by removing

unnecessary material and replacing some aluminum parts of the chassis by carbon fiber.

However, there is another way to reduce the weight dramatically by using the carbon

fiber to construct the whole chassis.

The difficulty is that the mounting parts of carbon fiber components are totally

different from those of aluminum components and the thickness will be much thicker

than aluminum, which implies that many components must be redesigned completely.

Nevertheless, for other students continue working on this thesis project, chassis

made of carbon fiber is a possible better solution to the problem.

6.2 Future work

Due to the limitation of time and effort, there are a lot of aspects of this thesis project

that can be improved in the future as shown below:

● Redo CFD analysis of the shell part and import the data to the structural analysis

to increase the accuracy of the final results

● Spot weld connection parts should be included in the simulation of the chassis part

● Redo shell optimization part to figure out whether it is possible to decrease the

weight more

● Chassis made of carbon fiber might be a possible solution to decrease the weight

as much as possible

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49

7 REFERENCES

1. Musk, Elon (August 12, 2013). "Hyperloop Alpha" (PDF). SpaceX.

Retrieved August 13, 2013.

2. Gonzalez, Oscar (22 July 2019). "Elon Musk plans trickier Hyperloop test tunnel

after speed record broken". Retrieved 23 July 2019.

3. Daryl L. Logan (2011). A first course in the finite element method. Cengage

Learning. ISBN 978-0495668251.

4. http://www.recoilengineering.com/finite-element-analysis. Retrieved 25 June 2016.

5. Haertel, Jan Hendrik Klaas (2018). Design of Thermal Systems Using Topology

Optimization.

6. Elhajjar, Rani; La Saponara, Valeria; Muliana, Anastasia, eds. (2017). Smart

Composites: Mechanics and Design (Composite Materials). CRC Press.

7. https://www.researchgate.net/figure/Various-types-of-fiber-reinforced-composite-

lamina_fig1_308721666. Rertieved Sep 2016.

8. http://www.aerospacengineering.net/strength-criteria-of-composite-material-

supported-by-fem-analysis/. Retrieved June 2017.

9.https://www.engineering.com/DesignSoftware/DesignSoftwareArticles/ArticleID/1

0938/How-to-Predict-Composite-Failure-Using-Simulation.aspx. Retrieved Sep 2015.

10. Nachiketa Tiwari. Introduction to Composite Materials and Structures. Indian

Institute of Technology Kanpur

11. SpcaeX (2018). SpaceX Hyperloop Test Track and Pod Specifications

12. KTH Hyperloop (2019). Final Design Report for SpaceX.

13. Jian Xiong, Liu Ma (2010). Fabrication and crushing behavior of low density

carbon fiber composite structures.

14. https://www.alibaba.com/product-detail/Carbon-Fiber-Honeycomb-

Panel_60785768160.html. Retrieved 2010

15. https://aerospaceengineeringblog.com/sandwich-panel/. Retrieved June 2013.

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51

APPENDIX A: GANTT CHART

52

APPENDIX B: RISK ANALYSIS

Risk Impact Probability Solutions

Program not running

successfully

Deliverable not

complete

Moderate Keep in contact with

supervisor and ask for help

Boundary conditions

not proper

Deliverable not good Moderate Discuss more with professors

and supervisors

Not enough time Deliverable not

complete

Low Update Gantt chart and push

myself