Closing out the course on the Finite Element Method, an introductory master's level course open to all disciplines at Aalto University and a part of the basic requirements of a master's degree in mechanical engineering at Aalto University, was a project to conduct displacement analysis on a structure erected in the engineering building in response to a point load. A simplification of the structure follows the image of the structure itself.

Applying the concepts learned in class, it was necessary to simplify the structure into a set of constitutive elements for analytical purposes. As such, we modeled elements 1, 2, and 3 as beams in bending, with elements 4 and 5 being represented as bars in compression, as they are connected to the structure by cylindrical joints. The simplification of the geometry to a 2D problem was due to the natural symmetry present in the structure and the level of complexity of our calculations. 

With enough degrees of freedom for the Mathematica script to run, we were able to arrange our inputs as seen below for the program to be able to recognize the specific geometry of the structure. 

Our analytical results were closely matched by the experimental measurements we took of the displacement of the structure as we loaded a rigid bar mounted at the apex of the structure with metal plates of measured weight. After each addition of load, the structure was struck with not a small amount of force to help the joints overcome the large amount of internal friction in the structure to reach their proper equilibrium point. In fact, we had to repeat these measurements as we were too gentle with the structure the first time around. Interestingly, the displacement measurement device was so sensitive, that if anyone in the room even shifted their weight between their feet, the stiff and elastic concrete floor would flex enough to be visible in the output of the sensor. 

Finally, we estimated an equivalent stiffness value for the structure between the analytical and experimental results, coming to the final estimation error of just under 10%, which, once compared to the results of the class, was more than satisfactory for the experimental setup we used. 

This was a great chance to put into practice simplifying a structure into a geometry more suited to FEA implementation. A big takeaway would be that when making structures in 3D modeling software and importing them into FEA enviornments, it can be useful and necessary to simplify the geometry of the part, replacing welded joints with fully constrained surfaces, and replacing flanges with similarly simplified connections to speed up calculations for large assemblies and structures. It will come with experience exactly which simplifications will have the most impact on performance and how they will effect the calculation of error in the resultant calculations.