SDTlib is based on the TITOP (Two-Input Two-Output Port) formalism. The TITOP model of a flexible body (a solar panel, for example) describes its dynamics independently of the rest of the system. By assembling TITOP models, we can build a model of a complex structure while retaining physical parameters for each substructure.
The following figure shows a flexible structure, L_i, connected to a parent structure L_(i-1) at point P, and to a child structure L_(i+1) at point C.
The TITOP model of this structure is the 12×12 transfer between the inputs (in red):
W_(L_(i+1)/L_i,P) the torsor containing the force and torque applied by L_(i+1) on L_i at point C,
- W_(L_(i+1)/L_i,P) the torsor containing the force and torque applied by L_(i+1) on L_i at point C,
- u ̈_P the accelerations (translation and rotations) imposed on L_i at point P,
And the outputs (in blue):
- u ̈_C the resultant accelerations at point C (with rigid and flexible components),
- W_(L_i/L_(i-1),P) the torsor applied by L_i to L_(i-1) in reaction to point P.
Here, the flexible body is embedded in P – free in C; but the SDTlib performs the necessary inversion operations to obtain any boundary conditions (and for any number of connection points).
The TITOP model is built from the mechanical data of the structure. In SDTlib, analytical models are implemented for simple shapes (plates and beams), as well as finite element models for plate assemblies; for more complex structures, it is also possible to directly enter resonance frequencies and modal participation factors, obtained by any external software, or to directly enter the f06 file supplied by Nastran.
The TITOP model can then be connected to the structure, both for simple configurations (such as a solar panel embedded in the central body at one point) and complex ones (open kinematic chains representing a robotic arm, plate assembly in a closed kinematic chain to model a solar panel, etc.). It is compatible with LFT (Linear Fractional Transformation) representation of uncertainties to produce a fully parameterized model.
