4. Structures and Mechanisms
4.6 Structural Analysis
The goal of structural analysis is to aid the structural engineer in designing, evaluating, and verifying the structural integrity of the structures and mechanisms on the spacecraft. Typical requirements dictate margins of safety for critical structural components that must be proven through testing or finite element analysis. In aerospace engineering, safety is a critical consideration in the design process.
Safety Factors
Factor of Safety = =
The margin of Safety = Factor of Safety – 1.0
The idea of safety can be numerically characterized by the terms factor of safety and margin of safety. The factor of safety is the ratio of failure load to design load, or equivalently, failure stress to design stress as stress is load normalized to the area. The design load is what you anticipate seeing on the structure in realistic conditions; in our analysis, the design load is the critical load. The failure load is how much the structure can withstand before failure, derived from a back-of-the-envelope calculation, finite element analysis, or testing. Structural components are not just designed to bear the critical or design load; they are designed to withstand much more than the intended critical load. For bridges, the factor of safety is 10, meaning that if the bridge anticipates 1 car’s weight in a footprint, the bridge was designed and built to withstand 10 cars in that same footprint: a very conservative and safe design. For aircraft and other aerospace engineering applications, the factor of safety is very common 2. The factor of safety is a user-defined threshold that the structure design must meet, typically imposed by the end-user, customer, or structural engineer. This number is defined by how uncertain you are of the load or structure or how safe you want to be; more uncertainty and more safety both lead to higher factors of safety. When in doubt, crank that factor of safety up. The trade-off to imposing too high of a safety factor is that could lead to significant mass accumulation as stronger parts are usually achieved with more mass.
The NASA Structural Design and Test Factors of Safety for Spaceflight Hardware document specify for various factors of safety that must be met for various materials. There are two different failure loads that are used in the definitions: 1) Ultimate Design Load: The product of the ultimate factor of safety and the limit load and 2) Yield Design Load: The product of the yield factor of safety and the limit load. These loads correlate with the ultimate strength and yield strength of the material structure. “Structural designs generally should be verified by analysis and by either prototype or proto flight strength testing. For metallic structures only, it may be permissible to verify structural integrity by analysis alone without strength testing” [NASA STD].

Artemis Kit Specific
Load Equations
In the Structural Loads section of this chapter, we discussed the driving critical loads (design loads) but how do we relate these loads to factors of safety? In this section, we will cover some key structural formulas for back-of-the-envelope calculations, valid for simplified geometries/models. The following sections describe 1 degree-of-freedom problem but structures reside in 3 dimensions. Make sure to repeat calculations for all degrees of freedom or axes.
Ultimate and Yield Loads
We talked about estimating critical loads or design loads but to get a factor of safety, we need to also find the failure loads. The failure load comes in two flavors: ultimate load and yield load. To find ultimate load and yield load, we refer to the structure’s material properties to extract the ultimate strength in yield strength in units of Pascal or .

Stresses come from different directions of loading: compression, tension, and shear. Material sheets will typically specify the strength associated with each direction as the yield or ultimate strength values are different. The direction of loading matters so make sure you use the correct strength number! The area that the load travels across also matters. The stress formula is:
where F is the force and A is the cross-sectional area. If we plug in yield or ultimate strength in and we know the cross-sectional area of the piece we are analyzing, we have yield/ultimate force as our one unknown to solve for.
Buckling Load

Buckling is a failure mode of compressive loading in which the two ends of a beam are constrained and the beam fails by bending, as seen in the figure below. This loading scenario describes a slender member bolted at two ends experiencing a compressive load, like the Artemis CubeSat frame corner posts under launch acceleration. The equation to find the critical buckling load, , depends on Young’s modulus, E, the moment of inertia that resists the direction of buckling, I, and the length of the slender member. As the length of the slender member is likely constrained, the slender member’s strength can be scaled by varying the moment of inertia in that direction. One of the edge lengths affects the moment of inertia to the cubic power, which could be taken advantage of to quickly reinforce a beam that is facing critical loading.

For different boundary conditions and pin constraints, the modified critical load equation is scaled by , where K is defined by the effective length of the slender member:
You’ll notice that by minimizing K, the critical load will increase. Decreasing K involves constraining the beam or slender member along the length, “breaking up” the effective length. For spacecraft support members, “breaking up” the effective length could involve bolting a strut to the main member.
Beam Stiffness
A cantilever beam is a slender structure with a fixed constraint on one end and no constraints on the other end (free end), like a deployed solar array or boom. A cantilever beam deflects if a load is imparted along the length of the beam or the beam experiences a load if a deflection is forced. There are various loading cases seen in the figure below with corresponding formulas, where is the maximum beam deflection, P is the load, L is the length of the beam, E is Young’s modulus, I is the moment of inertia in the loading direction, and M is a moment or torque.

These formulas may be useful to convert between beam deflection and force. If we know the acceleration profile acting on the beam, we can calculate the deflection along the beam, important for missions like SMAP, which has a spinning large flexible reflector/structure that points toward the Earth. The spinning motion produces centrifugal force and the mass at the end of the beam accentuates the centrifugal loading.

A cantilever beam’s yield and ultimate load differ from the buckling load in that the buckling load is parallel with the length of the beam whereas the cantilever beam’s load is perpendicular to the length. The failure load may be calculated by calculating the intermediate variable, bending moment. An example of the moment calculation for the simple point source force at the end of a cantilever beam is = -FL, where F is the magnitude of the force and L is the length of the beam. The critical bending moment occurs at the fixed end of the beam, or the joint between the beam and primary structure. The stress in a bending beam can be expressed as σ = y
where σ is stress, y is the distance to point from the neutral axis, M is the bending moment, and I = moment of Inertia. This stress value may then be used in the yield and ultimate factor of safety.

Beam Natural Frequencies

Structures under dynamic loads (vibration or acoustic loads) can exhibit resonance at the natural frequencies and cause failure. The cantilever beam, like a diving board, can deflect and vibrate once the load suddenly disappears.
Artemis Kit Specific
The structure deflects or displaces with a load, like a spring, and upon release, the beam oscillates around the unloaded equilibrium, like a spring. The natural frequency of the beam in units of rad/s may then be calculated with the following formula [Meirovitch, 1967]:
where is the natural frequency, m is the mass of the beam, L is the length of the beam, E is Young’s modulus, I is the moment of inertia in the loading direction, and
are coefficients describing the first, second, and third natural frequencies. The first natural frequency is the fundamental frequency.
The natural frequency,
may be converted to units of Hz with a
conversion factor:
.
Random Vibe and Acoustic Equivalent g’s
A structure experiences a load due to random vibrations and can be approximated by a number of g’s, an acceleration unit. Developed by John Miles in 1954, GRMS is Root Mean Square Acceleration in G’s (sometimes given as ÿRMS) that relates natural frequency , transmissibility Q at
where
is the critical damping ratio, and input acceleration spectral density
at
[Simmons]:
The expected stress as a result of from random vibration loads is then:
where m is the mass of the beam and I is the moment of inertia in that vibration axis.
Thermal Load
Materials expand at different rates, dictated by their coefficient of thermal expansion (CTE) and their temperature difference. If these structures of differing CTE are bonded together and undergo a temperature difference, the structure will change in length and experience stress. The structural change could result in a deflection (load perpendicular to the length of the beam) or shrinkage/elongation (load parallel to the length of the beam). The change in length is calculated by the total length L, change in temperature T, and CTE
.
The resultant stress from deflection may be calculated with a previous Beam Stiffness section and the axial stress, , can be found with the following formula:
where E is Young’s modulus and L is the length change calculated previously.
Simple Pressurized Shell

Pressurized vessels are rounded sheets that experience tension if the vessel is in positive pressure or compression if the vessel is under negative pressure. Think of blowing up a balloon as positive pressure and sinking a submarine for negative pressure. We care about this stress when dealing with propulsion systems that store propellants. These walls can burst if the cylinder walls experience more stress than the tensile ultimate strength. The thin walls of the vessel experience hoop stress and longitudinal stress, related to pressure p, radius R, and thickness t:

Fracture and Fatigue Analysis

Load cycle modeling examines the periodic nature of loads throughout a spacecraft’s lifetime. These loads may incite fatigue and failure in components; think of it like wear and tear in structural components. Load cycles can occur from thermal cycling due to periodic exposure to the sun or dynamic maneuvers (like SMAP’s constant rotation deflecting a slender member or Curiosity’s wheels running over sharp rocks).
Briefly mentioned in the materials section, fatigue limit is correlated with the material’s endurance limit, the component’s mean load, and ultimate tensile strength. It’s hard to know when a component will break under fatigue due to the stochastic nature of the cracks and failures. Fatigue S-N curves, fatigue prediction models, and tests can offer validation that a structural component will not fail under fatigue. For metallic structures, if the number of cycles stays below 10^4 with loading reasonably far away from yield or ultimate loads, the component will likely survive the mission lifetime. Components undergoing higher cycles should be more carefully scrutinized or replicated for fatigue testing.
Finite Element Analysis
Finite element analysis is the use of computer-generated geometries, numerical methods, and the first principles of loads described above. The finite element model breaks down computer geometries into smaller elements and approximates the transfer of loads, cumulative deflection, and distribution of stress for static analysis. Finite element analysis software is complementary and commonly built into CAD software, like Autodesk Inventor, Solidworks, and OnShape.
The entire spacecraft model may be designed and analyzed within one of these software packages.
- By defining material properties for each component in the spacecraft model, ultimate strength, yield strength, CTE, Young’s modulus, and density are all embedded in the model.
- The primary structure, secondary structure, and all supporting component interfaces must be defined and constrained in motion.
- Finite element analysis assists in identifying critical loads on each part of the spacecraft model by applying load conditions on the primary structure and probing the resultant stress on the rest of the spacecraft structure.
- The stress can then be converted to margins or factors of safety. The software will identify the location of the minimum safety factor. The load acting on this component at this location is the critical load.
- If this minimum safety factor does not satisfy the requirements, there must be a redesign of the critical component so that the minimum safety factor is achieved. This process must be iterated from step 3 until all components meet the minimum safety factors for all potentially critical loading scenarios.
Artemis Finite Element Analysis Results
To meet requirements set by launch service providers, the Artemis project completed a finite element analysis for static loads using Solidworks. Graphs are shown below to detail the load conditions, von mises stress, and factor of safety. By taking the calculated minimum factor of safety and design load (1,200 N), the max failure load was found to be 6 kN (approximately 2,700 toilet paper rolls).
Suggested Activity
Reference Documents
Launch Services Program Level Dispenser and CubeSat Requirements Document [NASA LSP-REQ-317.01] & [CubeSat Design Specifications Rev 14]
2.2 CubeSat Mechanical Specifications
CubeSat dimensions and features are outlined in the CubeSat Specification Drawings
Note: The CubeSat Inspection and Fit-check Procedure (CIFP) can be used to aid in verifying that the CubeSat meets the dimensional requirements specified in Appendix B. The CIFP can be found on cubesat.org.
These requirements are applicable for all dispensers not utilizing the tab constraint method. CubeSats designed with tabs can find those specific requirements at the PSC website (planetarysystemscorp.com).
2.2.1 The CubeSat shall use the coordinate system as defined in Appendix B. The origin of the CubeSat coordinate system is located at the geometric center of the CubeSat.
2.2.1.1 The CubeSat configuration and physical dimensions shall be per the appropriate section of Appendix B.
2.2.1.2 Note: Extra volume may be available for 3U, 6U, and 12U CubeSats. This extra volume is shown in Figure 3, sometimes referred to as the “Tuna Can” volume. The availability and volume dimensions are dispenser-dependent.
2.2.2 The –Z face of the CubeSat will be inserted first into the dispenser.
2.2.3 No components on the yellow shaded sides (see Appendix B CDS drawings) shall protrude farther than 6.5 mm normal to the surface from the plane of the rail.
2.2.3.1 Note: Please refer to the CIFP for the recommended protrusion measurement technique.
2.2.4 Deployables shall be constrained by the CubeSat, not the dispenser. This requirement originates from the requirements of most Launch Providers.
2.2.5 Rails shall have a minimum width of 8.5mm measured from the edge of the rail to the first protrusion on each face.
2.2.5.1 Note: An example is shown in Figure 4.
2.2.6 Rails should have a surface roughness of less than 1.6 µm.
2.2.6.1 Note: This is typically met if the rail material is shown to be properly anodized. Otherwise, if the surface appears rough, more testing may be required.
2.2.7 The edges of the rails should be rounded to a radius of at least 1 mm.
2.2.7.1 Note: This is typically met using engineering drawings and manufacturer certification.
2.2.8 The ends of the rails on the +/- Z face shall have a minimum surface area of 6.5 mm x 6.5 mm contact area with neighboring CubeSat rails (as per drawing in Appendix B).
2.2.8.1 Note: If the CubeSat is not sharing the dispenser with another spacecraft, the Launch Provider may choose to waive this surface area requirement.
2.2.9 At least 75% of the rail should be in contact with the dispenser rails. 25% of the rails may be recessed.
2.2.10 Note: Table 1 shows the typical maximum mass for each U configuration.
Table 1: CubeSat Mass Specifications U Configuration Mass [kg]
1U: 2.00
1.5U: 3.00
2U: 4.00
3U: 6.00
6U: 12.00
12U: 24.00
2.2.10.1 Note: Masses larger than the one presented in Table 1 may be evaluated on a mission-to-mission basis. Verify constraints with your dispenser provider or Launch Provider.
2.2.10.2 Note: Acceptable masses may vary depending on the dispenser’s capabilities. Verify capabilities with your dispenser provider.
2.2.11 The CubeSat center of gravity shall fall within the ranges specified in Table 2.
Table 2: Ranges of the acceptable center of gravity locations as measured from the geometric center on each major axis
X-Axis Y-Axis Z-Axis
1U + 2 cm / -2 cm + 2 cm / -2 cm + 2 cm / -2 cm
1.5U + 2 cm / -2 cm + 2 cm / -2 cm + 3 cm / -3 cm
2U + 2 cm / -2 cm + 2 cm / -2 cm + 4.5 cm / -4.5 cm
3U + 2 cm / -2 cm + 2 cm / -2 cm + 7 cm / -7 cm
6U + 4.5 cm / -4.5 cm + 2 cm / -2 cm + 7 cm / -7 cm
12U + 4.5 cm / -4.5 cm + 4.5 cm / -4.5 cm + 7 cm / -7 cm
2.2.12 The CubeSat structure should be made from aluminum alloy.
2.2.12.1 Note: Typically, Aluminum 7075, 6061, 6082, 5005, and/or 5052 are used for both the main CubeSat structure and the rails. If materials other than aluminum are used, the CubeSat developer should contact the Launch Provider or dispenser manufacturer.
2.2.13 Any aluminum CubeSat external surfaces, such as rails and standoffs that are in contact with the dispenser rails, shall be hard anodized to prevent any cold welding within the dispenser.
2.2.14 If a CubeSat shares a dispenser with another CubeSat(s), each CubeSat shall employ a mechanism to encourage separation from neighboring CubeSats within the dispenser.
2.2.14.1 Note: Any mechanism that will provide separation is acceptable. The common assumption with separation springs is that “stronger is better”. This is not always the case. Stronger separation springs can overpower the CubeSat dispenser deployment spring force during ejection and yield unpredictable separation characteristics, possibly re-contacting neighboring CubeSats. On the other hand, lower force springs may not have sufficient energy to separate the CubeSats from the required amount. The general guideline is to select a separation spring with a max force less than 6.7 N (1.5 lbf) but with a stroke length greater than 2.5 mm (0.1 inches)
2.2.14.2 The separation mechanism shall not extend beyond the level of the standoff in a stowed configuration.
2.2.14.3 Note: The most common placement of the CubeSat separation mechanism is centered on the end of the two standoffs on the CubeSat’s –Z face as per Figure 5.
2.2.14.4 Note: A separation mechanism is not required for CubeSats that do not share a dispenser with another CubeSat(s).
Structural Requirements Excerpt from NanoRacks External CubeSat Deployer (NRCSD-E) Interface Definition Document (IDD) [NR-NRCSD-S0004]
4.1 Structural and Mechanical Systems Interface Requirements
The NRCSD-E is designed to house 6U of payloads in each of its six silos, for a total volume of 36U. It can accommodate any combination of CubeSats from 1U to 6U in length, up to a maximum volume of 6U in the 1x6x1U form factor. The only dimensional requirement that varies between the form factors is the total length (Z-axis dimension), which is specifically noted in the requirements herein. This section captures all mechanical and dimensional requirements to ensure the payloads interface correctly with the NRCSD-E and adjacent CubeSats.
4.1.1 CubeSat Mechanical Specification
1) The CubeSat shall have four (4) rails along the Z-axis, one per corner of the payload envelope, which allows the payload to slide along the rail interface of the NRCSD as outlined in Figure 4.1.1-1.
2) The CubeSat rails and envelope shall adhere to the dimensional specification outlined in Figure 4.1.1-1.
Note: Any dimension followed by ‘MIN’ shall be considered a minimum dimensional requirement for that feature and any dimension followed by ‘MAX’ shall be considered a maximum dimensional requirement for that feature. Any dimension that has a required tolerance is specified in Figure 4.1.1-2. The optional cylindrical payload envelope (the “tuna can”) must be approved for use by NanoRacks and special accommodations may be required if utilizing this feature.
3) Each CubeSat rail shall have a minimum width (X and Y faces) of 6mm.
4) The edges of the CubeSat rails shall have a radius of 0.5mm +/- 0.1mm.
5) The CubeSat +Z rail ends shall be completely bare and have a minimum surface area of 6mm x 6mm.
Note: This is to ensure that CubeSat +Z rail ends can serve as the mechanical interface for adjacent CubeSat deployment switches and springs.
6) The CubeSat rail ends (+/-Z) shall be coplanar with the other rail ends within +/- 0.1mm.
7) The CubeSat rail length (Z-axis) shall be the following (+/- 0.1mm):
-
-
- 1U rail length: 113.50mm
- 2U rail length: 227.00mm
- 3U rail length: 340.50mm
- 4U rail length: 454.00mm
- 5U rail length: 567.5mm
-
- 6U rail length: 681 to 740.00mm
-
-
Note: Non-standard payload lengths may be considered. Any rail length differing from the above dimensions must be approved by NanoRacks and recorded in the payload unique ICA.
8) The CubeSat rails shall be continuous. No gaps, holes, fasteners, or any other features may be present along the length of the rails (Z-axis) in regions that contact the NRCSD-E rails.
Note: This does not apply to roller switches located within the rails. However, the roller switches must not impede the smooth motion of the rails across surfaces (NRCSD-E guide rails, fit gauge, etc.).
9) The minimum extension of the +/-Z CubeSat rails from the +/-Z CubeSat faces shall be 2mm.
Note: This means that the plane of the +/-Z rails shall have no less than 2mm clearance from any external feature on the +/-Z faces of the CubeSat (including solar panels, antennas, etc.).
10) The CubeSat rails shall be the only mechanical interface to the NRCSD-E in all axes (X, Y, and Z axes).
Note: For clarification, this means that if the satellite is moved in any direction while inside the NRCSD, the only contact points of the payload shall be on the rails or rail ends. No appendages or any part of the satellite shall contact the walls of the deployer.
11) The CubeSat rail surfaces that contact the NRCSD-E guide rails shall have a hardness equal to or greater than hard-anodized aluminum (Rockwell C 65-70).
Note: NanoRacks recommends a hard-anodized aluminum surface.
12) The CubeSat rails and all load points shall have a surface roughness of less than or equal to 1.6 µm (ISO Grade N7).
4.1.2 CubeSat Mass Properties
1) The CubeSat mass shall be less than the maximum allowable mass for each respective payload form factor per Table 4.1.2-1.
Note: The requirement driver for the CubeSat mass is the ballistic number (BN), which is dependent on the projected surface area of the payload on-orbit. The mass values in Table 4.1.2-1 assume no active or passive attitude control of the payload once deployed. If the CubeSat has attitude control capabilities or design features, then the operational ballistic number (BN) drives the mass requirement. If applicable, this shall be captured in the unique payload ICA.
2) The CubeSat center of mass (CM) shall be located within the following range relative to the geometric center of the payload: a. X-axis: (+/- 2cm) b. Y-axis: (+/- 2cm) c. Z-axis: i. 1U: (+/- 2cm) ii. 2U (+/- 4cm) iii. 3U (+/- 6cm) iv. 4U (+/- 8cm) v. 5U (+/- 10cm) vi. 6U (+/- 12cm)
4.1.3 RBF/ABF Access
1) The CubeSat shall have a remove before flight (RBF) feature that prevents the CubeSatfrom powering on when the inhibit switches are not depressed. The NRCSD-E has access ports only on the -X face of the dispenser. CubeSats in silos without the access panels should have timers implemented post RBF removal to prevent powering on of the spacecraft. The access port dimensions are defined in Figure 4.1.3-1.
Note: There is no physical access to the payload after integration into the NRCSDE besides what can be accessed from the access ports.
4.1.4 Deployment Switches
1) The CubeSat shall have a minimum of three (3) deployment switches that correspond to independent electrical inhibits on the main power system (see the section on electrical interfaces).
2) Deployment switches of the pusher/plunger variety shall be located on the rail end faces of the CubeSat’s -Z face.
3) Deployment switches of the roller/lever variety shall be embedded in the CubeSat rails (+/- X or Y faces).
4) Roller/slider switches shall maintain a minimum of 75% surface area contact with the NRCSD-E rails (ratio of switch contact to NRCSD-E guide rail width) along the entire Z-axis.
5) The CubeSat deployment switches shall reset the payload to the pre-launch state if cycled at any time within the first 30 minutes after the switches close (including but not limited to radiofrequency transmission and deployable system timers).
6) The CubeSat deployment switches shall be captive.
7) The force exerted by the deployment switches shall not exceed 3N.
8) The total force of all CubeSat deployment switches shall not exceed 9N.
4.1.5 Deployable Systems and Integration Constraints
1) CubeSat deployable systems (such as solar arrays, antennas, payload booms, etc.) shall have independent restraint mechanisms that do not rely on the NRCSD-E dispenser.
Note: Passive deployables that release upon ejection of the CubeSat from the NRCSD are considered on a case-by-case basis.
2) The CubeSat shall be capable of being integrated forward and backward inside of the NRCSD (such that the +/-Z face could be deployed first without issue).
Note: In general, the deployables should be hinged towards the front of the deployer to mitigate the risk of a hang-fire should the deployables be released prematurely while the CubeSat is still inside the NRCSD.
4.1.6 Deployment Velocity and Tip-Off Rate Compatibility
1) The CubeSat shall be capable of withstanding a deployment velocity of 0.5 to 2.5 m/s at ejection from the NRCSD-E.
2) The CubeSat shall be capable of withstanding up to 5 deg/sec/axis tipoff rate.
Note: The target tipoff rate of the NRCSD-E is less than 5 deg/sec/axis. Additional testing and analysis are being completed by NanoRacks to refine and verify this value. If a payload has specific tipoff rate requirements, these should be captured in the unique payload ICA.
4.4.9 Materials
4.4.9.1 Stress Corrosion Materials
Stress corrosion-resistant materials from Table I of MSFC-SPEC-522 are preferred. Any use of stress corrosion-susceptible materials (Table II) shall be pre-coordinated with NanoRacks and documented in the ICA. Any use of Table III materials shall be avoided.
4.4.9.2 Hazardous Materials
Satellites shall comply with NASA guidelines for hazardous materials. Beryllium, cadmium, mercury, silver, and other materials prohibited by SSP-30233 shall not be used.
4.4.9.3 Outgassing/External Contamination
Satellites shall comply with NASA guidelines for selecting all non-metallic materials based on available outgassing data. Satellites shall not utilize any non-metallic materials with a Total Mass Loss (TML) greater than 1.0 percent or a Collected Volatile Condensable Material (CVCM) value greater than 0.1 percent. Since the satellite will be in close proximity to the ISS for anywhere from 21-90 days, a more thorough outgassing analysis is performed. This outgassing analysis, performed by the ISS Space Environments group, uses ASTM 1559 data to characterize any potential material issues.
Note: A Bill of Materials (BoM) must be provided to NanoRacks to verify all materials requirements are met. The BoM shall be provided in the template specified by NanoRacks and must include the vacuum-exposed surface areas of all non-metals. The ISS Space Environments Team screens the BoMs to ensure there are no external contamination concerns due to high-outgassing components. A bake-out is not required. The NASA website linked below is a useful source for obtaining outgassing data for materials. https://outgassing.nasa.gov/