Project Momentum

This project is about the simulation and optimization of dynamic multibody systems. Multibody systems are mechanical assemblies composed of several mechanical components (e.g. beams, rigid bodies, springs, dampers) interconnected via joints (e.g. spherical, welded, sliding, revolute). Below are a few examples.

The systems considered in this project are subject to transient (time-dependent) loads and boundary conditions. The simulation engine is in charge of finding the trajectory (motion) of the system in space and time. In the optimization module, depending on the desired performance criteria, optimum values of design variables are computed such that the given objective function is minimized/maximized and the constraints are satisfied.

As an example, suppose that the goal is to optimize the following lunar lander such that at its landing time on the moon’s surface, given its landing velocity, the lander’s cabin does not crash into the ground. In other words, its displacement is minimal (at least locally). For this example, the design variables are shock-absorbers parameters (spring constants and damping coefficients) and the spatial coordinates of the landing gear joints.

And here is the animation of the lander before and after optimization:

Below is another example. It is a camera stabilizer called Steadicam used in many professional filming projects. One end (left end here) of this stabilizer arm is connected to the cameraman's/camerawoman's body and the other end holds the camera. This arm is meant to dampen the movements of the body as it goes up/down and back/forth so that the final product is a shake-free film. In this example, the objective is to minimize the camera’s displacement, while the left end moves up and down sinusoidally. The design variables are the spring constants and damping coefficients of the red shock-absorbers.

A full description of the simulation and optimization methods is presented in our paper: Design optimization of dynamic flexible multibody systems using the discrete adjoint variable method. For simulation, geometric variational integrators are employed, and the discrete adjoint variable method is used for performing sensitivity analysis for optimization. Here is the list of my publications so far on this topic:

• Ebrahimi, M., Butscher, A. and Cheong, H., 2021. A low order, torsion deformable spatial beam element based on the absolute nodal coordinate formulation and Bishop frame. Multibody System Dynamics, 51(3), pp. 247-278.

• Ebrahimi, M., Butscher, A., Cheong, H. and Iorio, F., 2019. Design optimization of dynamic flexible multibody systems using the discrete adjoint variable method. Computers & Structures, 213, pp. 82-99.

• Ebrahimi, M., Butscher, A. and Cheong, H., Autodesk Inc, 2022. Techniques for designing structures using torsion-deformable spatial beam elements. U.S. Patent Application 16/950,669.

• Ebrahimi, M., Butscher, A., Cheong, H. and Iorio, F., Autodesk Inc, 2023. Efficient sensitivity analysis for generative parametric design of dynamic mechanical assemblies. U.S. Patent 11,620,418.