By: Ana Cincarevic and Matthew Ong
Date: November 11, 2021
<aside> ❗ Will be updated for more theory (such as principal stresses, transformed stresses)
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Factors that affect the structure of the CubeSat are mass, stiffness, and strength of the material chosen. Different materials contain different properties, which is why it’s important to choose the right material for the CubeSat structure based on its properties. Performing FEA on the structure will dispute near-accurate results while avoiding the challenges of building and testing different CubeSats based on structure and materials.
How does FEA work? It breaks down a structure into a finite number of elements, a large number of sections that will each be analyzed by doing advanced math calculations to predict the behaviour of each element. Then, all the calculated behaviours of each element, or section, are added together, using a computer, to determine how the structure as a whole will behave under the same conditions. FEM is very different and requires an advanced background in math. This is why FEA can now be calculated entirely using a computer. It is possible to test these properties on a structure without having to do advanced calculations.
FEM involves the use of partial differential equations. An approximation of these equations can be made based on different types of discretization methods that approximate the Partial Differential Equations using numerical methods. The solution to the PDEs is represented by dependent variables, such as structural displacements. The first step of FEM is weak formulation of the PDE. This form can be obtained from pointwise PDEs by introducing test functions, multiplying the PDEs with these test functions, and then integrating them over the modelled domain.
As stated already, the design of space structural systems is dictated by mass, stiffness, and strength requirements. For the FEA of the CubeSat, three launch loading scenarios must be considered: quasi static analysis, modal analysis, and vibrations analysis.
Quasi-static events are where the loads are independent of time of vary slowly, so the dynamic effect is very small. The system is assumed to be static even though it’s not. This form of analysis ignores the effect of inertia, damping, and frequency. The quasi static loads are normally calculated by combining both static and dynamic load contributions. The maximum amplitude of these loads is generally determined at the end of the first stage burn because of the weaker mass of the launcher for the same amount of thrust. A high stress concentration occurs at the mount area with the satellite launch pad. To perform this analysis, four corners of the CubeSat are used as boundaries and a mesh is created. The point of inertia is set to the centre of the circle. For the load, the boundary conditions are at the top and bottom faces of the corners. This is set using boundary condition manager. The application of loads can be adjusted using the load manager.
Stress analyses for relatively simple strcutures (trusess, beams) can have idealizations applied to make numerical analyses easier, but are approximate solutions
To model a body, it is best to divide it into an equivalent system of smaller bodies interconnected at two or more nodes/points and/or boundaries. You will also need to have a complete static model wherein all external forces and moments in all directions are balanced, unless a forcing function has been applied
There are important mechanical properties and behaviour that bodies exhbit under any load. Taking a normal x-y-z coordinate space, there are (i) normal stresses and (ii) shear stresses