I’ve been trying to understand theory behind BeamDyn, I find myself a bit confused after reading about GEBT and LSFE, which lead me to ask these questions.
1- Is the difference between GEBT and Euler-bernoulli beam theory is that GEBT uses 6*6 mass and stiffness matrices?
2- How is LSFE more accurate than FEM ?
I would appreciate it if you can guide me into the right direction.
Here are my answers to your questions:
Yes. A generalized Euler-Bernoulli beam model would essentially use 4x4 mass and stiffness matrices (neglecting the transverse shear terms). GEBT effectively uses a generalized Timeshenko beam model using 6x6 mass and stiffness matrices (including the transverse shear terms).
LSFE is also a FEM. Standard FEM uses low-order shape functions and the solution is refined by increasing the number of nodes and elements. In LSFE FEM, the solution is refined by increasing the order of the shape function (by adding nodes within a given element) rather than be increasing the number of elements. (Within BeamDyn, we typically use one finite element with a shape function on the order of 5-8.) For a “smooth solution”, it can be shown that an LSFE converges quicker to the “true” solution with fewer nodes than standard low-order FEM e.g. see: onlinelibrary.wiley.com/doi/abs/10.1002/we.2101.
I hope that helps.
Brilliant, thank you Dr. Jonkman.
It helped greatly to clear my head.