FEM please help!
FEM please help!
(OP)
I'm struggling to grasp the "finite element method".
Can anyone help explain it in simple terms?
Can anyone help explain it in simple terms?
When was the last time you drove down the highway without seeing a commercial truck hauling goods?
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RE: FEM please help!
RE: FEM please help!
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RE: FEM please help!
Well, think of this as a 2 node finite element.
You can also develop stiffness/force relationships between 3 node, 4 node, etc. elements. Essentially the same thing except that you now have to make assumptions as to how the forces distribute between the "other" nodes. For a 2 node element - the force simply reacts to the other singular node.
Because of the multiple nodes and the assumption as to how the stiffness and forces relate, you find that you can only satisfy one of the two following aspects of the structure:
1. Force equilibrium
2. Boundary condition compatibility (i.e. - the nodes from one element deflect the same way as the adjacent element sharing the same node).
Since you can't satisfy both, and you really don't want a disjointed structure after you apply the forces (i.e. you want to satisfy no. 2 above). You allow for approximation in the force equilibrium.
So using many smaller elements reduces the error in force equilibrium and you get a pretty close answer.
RE: FEM please help!
Areaway wall analyzed as a plate with pinned bottom, fixed sides and a free top. I apply a triangular earth load to it (plus a uniform surcharge if adjacent to traffic or parking).
Concrete mat foundation with multiple column loads
Concrete balcony supported on 3 sides
I am sure there are many other examples. With today's software programs, most of these problems can be modeled and solved within 5 minutes.
Good luck!
RE: FEM please help!
The interpolation functions are built in to the type of element you want. For the constant strain triangle, strain is assumed to be constant across the element from node to node. With the linear strain triangle, strain varies linearly across the triangle. Now we know that in many cases, the strain is not constant nor does it vary linearly through an element, but if you make each increment small, so that you have more nodes where the solution is better, then your results will also become better.
FEM is used for heat transfer analysis as well as fluid dynamics, among other things. What's important to remember is that it is a method to solve differential equations, and it is an approximate solution.
RE: FEM please help!
A simple explanation is that each element is discretized (that is broken down into smaller elements that are determinate). The forces, strains, and stresses are then solved for each discretized element. The discretized elements are then reassembled to give results through compatibility. The more discretized elements that are made (the more pieces that the original element is broken up in) the more convergence on the the "real" solution, i.e. the more accurate the solution.
This method can only be accomplished by a computer because the computations are immense.