Written By: Daniel Asante

Introduction

The purpose of this section is to include  structural analysis simulations to verify that the complete CubeSat structure, including internal and external components such as the satellite bus, solar wing frame, mounting interfaces, and deployables, can withstand the mechanical and thermal loads expected during launch and space operation. The simulations are then verified that they align with the structural verification requirements outlined in the SpaceX Falcon 9 Rideshare Payload User’s Guide [RPUG] and applicable CubeSat design standards.

This document provides an overview of:

• The structural configuration of the CubeSat.

• The design loads and constraints.

• Simulation methodology and software tools used (ANSYS Mechanical).

• Modal, static, thermal, and buckling analysis results.

• Compliance with safety factors and launch provider requirements.

Structural Configuration Overview

• Satellite form factor: 3U CubeSat (100 mm × 100 mm × 340.5 mm).

• Primary structure material: AL6061-T6 (for rails, Shells, and wing frame).

• Mounting interface: Compatible with EXOpod NOVA deployer.

• Subsystems included:

  • Solar wing deployment frame

  • Payload Reflector and Feed Arm

  • Stacked Shells

  • Corner Rails

The following tests will results in the structural finite element analysis performed on the engineering model primary structure of ArcticSat. The primary structure of ARCTICSAT is defined as the structure consisting of corner rails combined with the module shells.   All components/parts under the secondary structure  have been removed and detailed analyses will be conducted in Phase D.

Modal Analysis

Modal Analysis is a form of finite Element Analysis which provides information on the natural frequencies and mode shapes of a structure or component. All structures and components have natural frequencies and its essential to understand these natural frequencies so we can try to predict how a structure or component will behave when exposed to vibrational frequencies in the field.

Typically, a structure or component is constrained and when a modal analysis is executed, it will extract the frequencies at which the component or structure will naturally resonate. By knowing these resonance frequencies of  a structure or component, we can design our parts to ensure that these resonant frequencies are outside the range of operation of our application.

According to the SpaceX Falcon 9 Rideshare Payload User Manual, payloads must have no elastic natural frequencies below 40 Hz. An elastic natural frequency is defined as any frequency response of the payload with any modal participation, as computed by a fixed-base modal analysis.  Based on this Modal Analysis was conducted using Ansys Mechanical on the ArcticSat Model.

• First Analyses consisted of just the primary structure which is essentially just the external body without the interior mechanical/electrical components. The material assigned for this analysis was Aluminum 6061, since the primary structure is made of only AL6061. All contacts were fully defined in the model such as bonded contacts for the interaction between shells and rails. Some boundary conditions were compression-only to simulate the loaded spring in the ExoPod NOVA deployer as well as fixed supports on the rails in contact with the ExoPod. Modal Analyses was then solved for the first six modes as shown below.

From the results it is seen that the first mode resulted in a natural frequency of 1014 Hz which is not below the operating range of the Space X Falcon 9 Rocket of 40 Hz. 

ArcticSat Payload conisits of a Reflector Antenna and a Feed. Both of these components are constrained with a pre-defined burn wire configuration to attain a fully stowed ArcticSat model. This Payload Compartment is added to the model for modal analyses. Adequate connections and boundary conditions were added such as no separation and bonded connections to simulate how both the Reflector Antenna and Feed  is constrained within the CubeSat with respect to the burn wire configuration setup for each paylaod component.

From the results it is seen that the first mode resulted in a natural frequency of 114.02 Hz which is still not below the operating range of the Space X Falcon 9 Rocket of 40 Hz. 

Below are the Total Deformation mode shapes for all six modes zoomed into the payload module.

Harmonic Response

After Modal Analysis was conducted, a Harmonic Response was linked to the Modal Analysis using Mode Superposition Method and a boundary condition of expected acceleration from the launch vehicle was included as indicated in the RPUG – Axial [x] = 10 g and Lateral [Y & Z] = 17 g. From this analysis, a frequency response was generated from the total deformation solution in order to plot how long the CubeSat will continue to oscillate after being excited based from expected launch loads.

The Quality factor Q, was calculated from the frequency Response Graph indicated above.

Q = 𝐹𝜊𝐹𝐻𝑖𝑔ℎ− 𝐹𝑙𝑂𝑊, whereby 𝐹𝜊 is the resonant Frequency [ Highest Peak] and 𝐹𝐻𝑖𝑔ℎ− 𝐹𝑙𝑂𝑊 are the estimated bandwidth of the resonant peak. 𝐹𝐻𝑖𝑔ℎ− 𝐹𝑙𝑂𝑊 could not be found using Half-power Bandwidth method due to the narrow resonant peak hence, the width of the resonance peak was estimated an average amplitude level.

𝐹𝜊 = 0.2351 kHz, 𝐹𝐻𝑖𝑔ℎ = 0.24215 kHz, 𝐹𝑙𝑂𝑊 = 0.22805 kHz.

Hence,  Damping Factor Q = 𝐹𝜊 / (𝐹𝐻𝑖𝑔ℎ - 𝐹𝑙𝑂𝑊).

This resulted in a Q value of 16.68 which is between 10 and 50 as required in the RPUG.

Random vibration

Random vibration simulates the broad-spectrum launch environment in which multiple frequencies are excited simultaneously. This better replicates the actual dynamic loads imparted during liftoff, staging, and fairing deployment of the launch vehicle.

To ensure the mechanical survivability and integrity of the ArcticSat structure, random vibration analysis was performed according to the environmental qualification levels outlined in the SpaceX Falcon 9 Rideshare Payload User Guide (RPUG). These levels are provided as a Power Spectral Density (PSD) function, which defines acceleration energy distribution over a specified frequency range, typically in units of g²/Hz.

As shown in Figure 4-4, the MPE curve specifies critical values across the frequency spectrum, with peaks occurring near the 925 Hz region. Table 4-6 details the exact PSD values at each breakpoint. The RMS acceleration (GRMS) for the total environment is 5.57 g, and this value was applied as the reference for analysis.

In this study, the primary structure was first analyzed independently (without interior components), using Aluminum 6061 as the assigned material. Bonded contacts were defined for shell-to-rail interfaces, with compression-only supports applied to simulate the preload from the deployer spring and fixed supports along the rail contact surfaces. The PSD acceleration spectrum was applied along each principal axis (X, Y, Z) as a loading condition, and total deformation and equivalent stress results were extracted from the solution for each axis.

The analyses below includes the payload module components. The boundary conditions highlighted in the modal analyses section is shared with all corresponding simulations. Take note that the payload compartment shells were hidden so the payload primary components could be illustrated. Hence, the shells were not suppressed in the analysis.

Quasi-Static Acceleration

Quasi-static structural analysis is performed to assess the ability of a spacecraft structure to withstand slowly varying inertial loads, which simulate the integrated effects of static, low-frequency, and high-frequency dynamic accelerations experienced during launch. These types of loads, referred to as “combined loads,” are critical in evaluating the mechanical strength of CubeSat-class spacecraft and their deployers under maximum predicted launch environments.

The RPUG which specifies a load factor of 10 g axially (X-axis) and 17 g laterally (root-sum-square of Y and Z axes), as detailed in Table 4-1. These values represent the maximum predicted combined loads for CubeSats in dispensers with total system mass ≥ 20 kg, and they are applicable for structural verification of small satellites.

In this analysis, the  model was constrained using fixed supports on the deployer rail contact points, and inertial acceleration loads were applied in the X, Y, and Z directions according to the defined quasi-static factors. The analysis was conducted using the Static Structural solver in Ansys Mechanical, and the results for total deformation and equivalent stress were extracted to evaluate the structural response of the CubeSat design under worst-case launch loading conditions.

This assessment provides a baseline verification that the ArcticSat structure remains within acceptable deformation and stress limits during the launch phase. Further refinement may include margin of safety checks and material yield/failure analyses in subsequent iterations.

Below is the analyses including the payload module under the same conditions as above.

Thermal Expansion and Contraction

The payload which contains a feed arm and a reflector antenna has a specific position requirement which enables the payload to operate at its optimum performance. Hence, there is a need to ensure that when ArcticSat is in orbit and is subjected to sunlight and eclipse there is no significant change in distance between feed arm and reflector antenna due to thermal expansion and contraction.

For this simulation a transient thermal analyses was performed for a Sunlight scenario. The initial temperature of the satellite was set as 20C . This value was selected based in the thermal analyses performed for detumbling.  A heat flux value of 0.001362 W/mm^2 used and applied on the face of the satellite continuously facing the sun during orbit. Radiation was applied in all external surfaces of the satellite.

After a transient thermal analysis, a static structural analyses was coupled with the transient thermal analysis. Constraints such as cylindrical support was defined for the hinges (solar wings and payload). No further constraints were added as the satellite is orbiting and has been deployed from the ExoPod NOVA and all Hold and Release Mechanisms (HDRM's) have been activated already. Hence, deployables are in deployed state.

 There is total deformation  of max 0.077 mm which occurs on the tip of the reflector and min deformation  on the feed arm of 0.0085 mm.

Radiation Analyses

The image below indicates the orbit set up [3 orbits] for an analyses of three years.  The radiation analyses has been configured for a Sun-Synchronous Orbit.

Deorbiting

A Deorbit analyses was conducted using the DRAMA software tool.  The wetted area of each of the ArcticSat model was measured in SolidWorks and was used as part of the Deorbit analyses. The wetted area's that was used is as follows:

Total Wetted Area per Face

• Front Face = 84395.1 mm^2

• Side face = 60828.5 mm^2

• Top Face = 18006.83 mm^2

Dimension of Wetted Area per  Face

• Front Face = Height [501.07 mm] x Width [303.76 mm]

• Side face =  Height [501.07 mm] x Width [133.6 mm]

• Top Face = Height [133.6 mm] x Width [303.76 mm]

Separation Switches

Roller switches shall not exceed 3.00 N to ensure that the deployment switches do not interfere with or damage the deployer mechanism [Exolaunch] and that they reliably activate without posing a risk to structural integrity or proper ejection.