Spacecraft Materials and Structures هيئاضفلا تابكرملا لكايهو ......Spacecraft Materials and Structures هيئاضفلا تابكرملا لكايهو داوم

Spacecraft Materials and Structuresمواد وهياكل المركبات الفضائيه

Code 494Instructor: Mohamed Abdou Mahran Kasem

Aerospace Engineering Department

Cairo University, Egypt

Contact details

Email: [email protected]

Office hours: Monday and Wednesday.

Site link: https://scholar.cu.edu.eg/?q=mohamedabdou/classes/

https://scholar.cu.edu.eg/?q=mohamedabdou/classes/

Course details

Main text Book:

• Reddy, “An introduction to the finite element method”• Hughes, “The finite element method-linear static and dynamic finite element analysis”• Sarafin, and Larson, “Spacecraft Structures and Mechanisms-From concept to lunch”

Grades:

➢ Attendance – 5% points➢ Assignments – 5% points➢ Midterm – 15% points➢ Final Project– 5% points➢ Final exam – 70% points

Course Contents

• Spacecraft structure design considerations

• Introduction to Finite Element Method

• One dimensional elements (Trusses)

• One dimensional elements (beams and frames)

• Two dimensional Plates

Spacecraft Structure

• The spacecraft structure is the physical platform that supports and integratessubsystems and payload.

• The spacecraft structure supports, protects and provides a house for everysingle component of the spacecraft system such as electronic components,batteries, and instruments.

• In this course, we concentrate on structural analysis and design of spacecraftstructures, however the concepts mentioned in this course can be applied toany other aerospace structure.



Spacecraft Configuration

Spacecraft configuration

• A spacecraft consists of a payload in addition to a collection ofsubsystems.

• We distinguish between the payload and the rest of the spacecraftcomponents, because the payload is typically unique for a givenmission.

• Payloads represent the mission main purpose.

• The payload may gather, process, encode, receive, transmit, or recordinformation.

• Payloads include optical telescopes, radiometers, radars,spectrometers, and sensors.

Spacecraft Subsystems

• A subsystem is a group of components that supports a common function.

Subsystem Function Key components

Attitude control (ACS)Determine and control the attitude

(orientation) and orbital position. Sensors and actuators

Propulsion (PS) Changing spacecraft orbit Propellent, tanks, pipes, and thrusters

Communication (CS)Communicate with ground control for

tracking.Receiver, transmitter, and antenna

Command and data

handling (C&DH)Distributes and processes commands Data recorder and computer

Electrical power (EPS)Generates, stores, regulates, and

distributes electrical power.Solar arrays, batteries, electronics and cables.

Thermal control (TCS) Monitors and controls temperature Heaters, radiators, heat pipes, and insulation.

Structures, and

mechanisms (SMS)

Physically support all the other

subsystems in addition to the payload,

and moves them as needed.

Primary, secondary and tertiary structures and

mechanisms.

Spacecraft Subsystems

Structure Function

• Supports spacecraft’s key components in desirable locations.

• Protects the spacecraft’s components from dynamic environmentsduring ground operations, launch, and mission operations.

• Structure vibration should not interface with the vehicle controlsystem or harm any spacecraft component.

• The structure material must survive ground, launch, and on-orbitenvironments.

Structure requirements

• The structure material must have the right strength to stand for the appliedload (material selection).

• The structure should be stiff enough to support, and protect spacecraftcomponents (static analysis).

• The structure modes should be higher than any surrounding modes (Modalanalysis).

• The structure vibration responses must be acceptable (Dynamic analysis).

• The structure must stand for the number of loading cycles during its whole life(Fatigue analysis).

• The structure should be stable or has accepted stability (Buckling analysis).

Support, protect, vibration, material

An optimum structure should satisfy all these requirements with minimum weight, and minimum cost.

Types of an spacecraft structure

• Primary structure – is the backbone, ormajor load path, between the spacecraft’scomponents and the launch vehicle.

• Secondary structure – is the supportingmembers in the spacecraft such as booms,and solar panels.

• Tertiary structure – includes the non-fetalstructure elements such as boxes that houseelectronic components.

Difference between analysis and design

• Structural analysis:

A certain structural configuration is given, and it is required to determine thestructure performance (the structure response to certain applied loads).

• Structural design:

A structural performance is given, and it is required to create the structureconfiguration that satisfies this performance, usually with minimum weightand minimum cost.

To do so, first the designer creates an initial sizing for the structure (initialdesign), and then conducts several analyses until reaching to the beststructure configuration (final design).

Structure development/design

We must take steps to avoid failure of structures and mechanisms,but we also must accept some possibility of failure.

There is an important rule in aerospace structure design

Structure development/design process

Structure development/design process

Given structure requirements

(loads, dimensions, …)

Select the appropriate material

for your structure

Construct an initial sizing for

the primary structure

Determine and classify all the

applied loads

Perform stress, displacement,

and fatigue analyses.

Define the primary, secondary,

tertiary structural components

Build an idealized model

Define the safety requirements

for each component

Modify the initial structure sizing

based on the analyses result.

Build and test a prototype

AcceptNo

Yes

Structural Loading

Structural loading

Static loading – are constant or unchanged loads with time such asweight of payloads, steady acceleration.

Dynamic loading – vary with time such as engine thrust, wind gust, andvibration loads.

Most loading applied to any aircraft depends on time and the flight stage (operation events) such as

Launch, on-orbit, and Landing.

Structural loading - Launch

• Launch starts when booster engines ignite (lift-off) and ends with the separation of thepropulsion device that puts the spacecraft in itsfinal orbit.

• A launch vehicle consists of stages, when thepropellent of one stage is used up, the structure,storage tank, and the engine of the stage separatesfrom the launch vehicle.

• Then the engines of the next stage ignite.


• The inertia results from the acceleration of the structureis represented by what call a load factor.

• The load factor is a dimensionless multiple of g’s thatrepresents the inertia force acting on the structure (i.e thehighest acceleration is 4.2 g’s).

• The sign of the load factor is opposite to theacceleration.

• So, the inertia load on a body that results from anacceleration equals the body weight multiplies by theload factor.


• Load factors are determined based on the aircraft category from the user guidesprovided by the governmental agencies.

Structural loading – LaunchExample – 1

Structural loading – Air-loads

• As the vehicle accelerates and approaches the speed of sound the

aerodynamic loads become complex due to the shock waves result from

changing the aerodynamic pressure acting on the vehicle.

• There are other loads such as static air pressure, and wind gusts.

• Anytime a rocket engine ignites or shut down, the launch vehicle

experience a transient loading.

Structural loading – Other loading types

➢ Payloads

➢ Thermal loading

➢ Propulsion loads

➢ Landing loads

Mechanics of MaterialsStress-strain relation

Stress-strain relation

The generalized Hooke’s law is written in the form of a fourth-order tensor:

Where 𝐸𝑖𝑗𝑘𝑙 contains 81 elastic constant coefficients.𝜎𝑖𝑗 = 𝐸𝑖𝑗𝑘𝑙휀𝑘𝑙

In matrix form (Voigt notation),

defines the engineering shear strains.

If 𝐸𝑖𝑗𝑘𝑙 is symmetric matrix, so the number of independent constants reduced to 21.


For isotropic materials in 3D analysis,


For isotropic 2D material, the stress-strain matrix is reduced to

Determination of the Ultimate Strength of a Material

• Materials test can be done in laboratory using theproper material test machines.

• The largest force which may be applied to thespecimen is reached, and the specimen eitherbreaks or begins to carry less load.

• This largest force is called the ultimate load forthe test specimen andis denoted by 𝑃𝑈.

For aluminum

For steel

Determination of the Ultimate Strength of a Material

Factor of safety

• This smaller load is referred to as the (allowable load) and, sometimes, as the (working load) or (design load).

• The ratio of the ultimate load to the allowable load is used to define the factor of safety.

Selection of an Appropriate Factor of Safety

• If a factor of safety is chosen too small, the possibility of failure

becomes unacceptably large;

• If a factor of safety is chosen unnecessarily large, the result is an

uneconomical or nonfunctional design.

For aerospace structures the factor of safety is usually around 1.5

Selection of an Appropriate Factor of Safety

F.S selection depends on:

• Variations that may occur in the properties of the member under

consideration.

• The number of loadings that may be expected during the life of the structure

or machine

• The type of loadings that are planned for in the design, or that may occur in

the future.

• The type of failure that may occur.

• Uncertainty due to methods of analysis.

• Deterioration that may occur in the future because of poor maintenance or

because of unpreventable natural causes.

• The importance of a given member to the integrity of the whole structure.

Arranging and sizing structural members

Structural design

• The starting point in structural design is a challenge for designers becausethey usually start from zero, and want to create a strong, light and efficientstructure.

• This process starts by structural sizing in which the designer should useanalytical equations to determine and initial sizing for the structure.

• This analytical model can also used for structure optimization.

• Then a numerical method is used for detailed analysis and design.

Spacecraft Structure – Trusses and Frames

• Trusses and frames have a cross-section

dimensions that are relatively small than the

length.

• Trusses can withstand loads applied to its joints

with its members loaded axially.

• Frames can carry shear and bending through its

joints.

Spacecraft Structure – Monocoque cylinders

• Are axi-symmetric shell without stiffeners

or frames.

• Its strength is limited by its buckling

strength.

Spacecraft Structure – Skin-frame structure

Skin-frame structure has skin (sheet or panel)

surrounding a skeletal made of stringers and

lateral frames that strengthen the structure.

Trusses

• The truss members sizing depends on whether members are in tension orcompression.

• For tension members, we must provide enough cross-section area to keep thedesign yield and ultimate stresses bellow the material allowable and yieldstrength.

• For a compression members, we select a cross-section such that the members isstable in addition to allowable stress requirements.

• Most of spacecraft structural loads are reversible because it result from excitedvibration modes that causes additional compression loads.

• Thus, most of spacecraft members should be sized for compression.

Trusses sizing

• The design ultimate compressive stress should be limited to the material proportional limits (equal 80% of yield stress if unavailable).

• First, define the truss arrangement that is stable and satisfy the design requirements.

• Then, calculate the truss cross-section area that will make the design ultimate stress equal to the material proportional limit.

• We also select the cross-section areas that keep the member stable.

Trusses

The truss member strain energy has the form,

𝒰𝑖 =𝑃2

𝑖𝐿𝑖2𝐴𝑖𝐸𝑖

The total strain energy will take the form

𝒰 =

𝑖=1

𝑛𝑃2


So the displacement in the direction of applied load P

𝛿 =2

𝑃𝒰 =

2

𝑃

𝑖=1

𝑛𝑃2


Trusses

Rule: For several structural designs availablethat satisfies the strength and designrequirements, the lightest is the best (stiffer).

Monocoque cylinders

• An outer dimensions should be selected based on the designrequirements.

• A monocoque cylinders must be designed with suitable buckling andstiffness strength under combined compression, shear, and torsion.

Monocoque cylinders sizing

The process for sizing an isotropic sandwich cylinder:

1. Calculate the cylinder moment of inertia𝐼 = 𝜋𝑟3𝑡

Where r is the cylinder radius and t is the shell thickness.

The cylinder bending stiffness will take the form

𝑘𝜃 =𝐸𝐼

𝐿=𝐸𝜋𝑟3𝑡

𝐿



Thus the required thickness for the cylinder based on a given bending stiffness.

𝑡1 =𝑘𝜃𝑟𝑒𝑞𝐿

𝐸𝜋𝑟3



2. Also the skin thickness based on the material proportional limit can be calculated as

The design ultimate compressive strength

𝐴 = 2𝜋𝑟𝑡

𝑓𝑐𝑢 =𝑝𝑒𝑞𝑢

𝐴=𝑝𝑒𝑞𝑢

2𝜋𝑟𝑡⇒ 𝑡2 =

𝑝𝑒𝑞𝑢2𝜋𝑟𝑓𝑝𝑙

Where 𝑓𝑝𝑙 is the proportional limit and 𝑝𝑒𝑞𝑢 is the ultimate equivalent axial load.



3. Select a face sheet thickness equal to half the larger of 𝑡1𝑎𝑛𝑑𝑡2.

4. Calculate the ultimate compressive strength

𝑓𝑐𝑢 =𝑝𝑒𝑞𝑢

𝐴



5. Calculate the thickness of solid skin 𝑡3that will buckle at 𝑓𝑐𝑢

𝑓𝑐𝑟 =0.35 𝐸𝑡3

𝑟, for axial compression

𝑓𝑐𝑟 =0.4 𝐸𝑡3

𝑟, for bending moment



5. Calculate the thickness of solid skin 𝑡3that will buckle at 𝑓𝑐𝑢

𝑡3 =𝑓𝑐𝑟 𝑟

0.35 𝐸, for axial compression

𝑡3 =𝑓𝑐𝑟 𝑟

0.4 𝐸,for bending moment



6. Calculate the correlation factor 𝛾 and then recalculate 𝑡3 and iterate if needed

𝛾 = 1 − 0.901 1 − 𝑒−

1

16

𝑟

𝑡 , for axial compression

𝛾 = 1 − 0.731 1 − 𝑒−

1

16

𝑟

𝑡 ,for bending moment

Then 𝑡3 can be Calculated from the equation 𝑓𝑐𝑟 =0.6 𝜂 𝛾 𝐸𝑡3

𝑟

𝜂 is the plasticity correction factor which equal 1 in our case



7. Calculate the face sheet spacing that will give the sandwich shell the same radius of gyration per unit width as a solid skin of thickness 𝑡3

For unite width solid skin

𝐴 = 𝑡3, 𝐼 =𝑡3

3

12⇒ 𝜌 =

𝐼

𝐴=

𝑡3

12




For flattened sandwich cross-section

𝐴 = 2 𝑡𝑓 , 𝐼 = 2 𝑡𝑓ℎ

2

2

=𝑡𝑓ℎ

2

2⇒ 𝜌 =

𝐼

𝐴=ℎ

2




The sandwich width is ℎ =2 𝑡3

12

8. The sandwich shell required thickness is

𝑡𝑠= ℎ + 𝑡𝑓

Finite Element MethodBasic concepts

Remember, “ the purpose of analysis is to understand the problem and

gain insight – not generate numbers.” Thomass P. Sarafin.

A system mathematical model

• We calls the real system or a structure “the physical model”.

• Usually we cannot solve the real system, instead we solves an approximaterepresentation to this real system that we call “Mathematical Model/Idealizedmodel”.

• The mathematical model for most systems is represented by a differentialequation that we call the government equation

A system mathematical model

Notation

Notation

Notation

Notation

As we discussed earlier, in finite element method we approximate

the solution of the differential equation u by an approximate

function 𝑢ℎ.

Weighting Function

Integration by parts

𝑤𝑣 𝑥 = 𝑤𝑥𝑣 + 𝑤𝑣𝑥

𝑤𝑣 = න𝑤𝑥𝑣 𝑑𝑥 +න𝑤𝑣𝑥 𝑑𝑥

Integrate both sides w.r.t x

Rearrange

න𝑎

𝑏

𝑤𝑣𝑥 𝑑𝑥 = ቚ𝑤𝑣𝑎

𝑏−න

𝑎

𝑏

𝑤𝑥𝑣 𝑑𝑥

Index notation

𝑢,𝑖𝑖

Index notation

𝐱 =

𝑥1𝑥2𝑥3

𝑥𝑖 , 𝑖 = 1: 3

Vector

Tensor

𝛔 =

𝜎11 𝜎12 𝜎13𝜎21 𝜎22 𝜎23𝜎31 𝜎32 𝜎33

, 𝜎𝑖𝑗 , 𝑖 = 1: 3 𝑎𝑛𝑑 𝑗 = 1: 3

Functional

Roughly speaking, a functional is an operator which maps a function into a scalar.

Variation

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Spacecraft Materials and Structures هيئاضفلا تابكرملا لكايهو ......Spacecraft Materials and Structures هيئاضفلا تابكرملا لكايهو داوم