A seminar by J. Renaudeau at ENSG, Nancy, room G201

On Monday 22nd of May, 1:00 pm.

There exists two different approaches to solve the implicit structural modeling problem that have been proven sufficiently efficient to be widely used. The first one is a mesh based approach consisting in solving both smoothness and data constraints, while the second one is a meshless approach consisting in solving only data constraints. The presence or not of the mesh radically changes the problem at hand. In the first case, data information is reverberated to its surroundings by the mesh connectivity and the smoothness constraint, resulting in a sparse system. In the second
case, data information is perceived everywhere in the studied domain thanks to globally defined shape functions, and which generates a dense system. Therefore, while avoiding the mesh creation in the second approach, we still have to deal with the problematic dense system, making a strong argument of efficiency for the first approach.
In this article, we suggest a third alternative: a meshless approach consisting in solving both smoothness and data constraints, but with locally defined shape functions. Our goal is not to demonstrate a perfect combination but to show that the local meshless concept in structural modeling enables to avoid the creation of a complex mesh while solving a sparse system and still obtaining comparable results. Moreover, we use the variational minimization of the bending energy in order to constrain the smoothness, which is new in structural modeling.