Finite element analysis

[PowersPE80]

Hello,
Can someone please explain to me, without getting overly technical, what exactly a finite element analysis is?

Thanks.

 

[dik]

It's difficult to provide a simple explanation for this...

Many engineering materials are part of a group that is a continuum. These groups have common mathematical descriptions of how they behave. This applies to gasses, solids, liquids, electrical patterns/distributions, magnetic fields, heat transfer, etc. These are all examples of continuums.

Finite element method is a mathematical manner of describing what happens to the above based on the properties of the continuum when they are exposed to external actions.

Dik

 

[JAE]

Powers - very tough to do that well without knowing what you do know.

Are you are familiar with frame analysis programs where you have beams and columns represented by "stick" members - a member that has a joint at either end? You connect all these into a frame or other representation of a structure and by knowing the deflection-force relationship between the two joints you can analyze the structure.

These two-joint "sticks" are two-joint finite elements. They are essentially a member/entity that creates a relationship between two joints. If you move one joint, the other responds with a defined force.

Each joint, typically - in 3D models - represents six degrees of freedom - X, Y, and Z direction translation and X, Y and Z direction rotations.

Now if you expand that two-joint member into a three or more joint member, the member now becomes either a planar flat element (triangle or rectangle) or perhaps even a solid element with multiple joints that all are related to each other in terms of displacement and force.

The analysis/solution is similar to the two-joint member except there is a problem. The two-joint beam type members can be analyzed such that both equilibrium and deformation compatibility are satisfied (Sum of forces/moments = 0 and the deflection of element A at a common joint with element B is the same). However, with more than two joints, you can't satisfy both of these - only one. Most all finite element solutions choose to satisfy the deformation compatibility and then by keeping the size of the elements small, minimize the sum of forces error in the model.

 

[PowersPE80]

I am a structural engineer with 9 years experience. (The discipline next to my screen name incorrectly says civil/environmental). I work on mid-size buildings (1-8 stories) and would consider myself very familiar with many materials...steel, concrete, masonry, wood, cold-formed, etc.

Thanks for your responses but it is still not completely clear to me. I hear my peers constantly refer to finite element analysis and I have never completely understood it's meaning. I use RAM Elements on a regular basis. I believe this is a finite element analysis program but still I am not sure what this means.

I was always under the assumption that finite element analysis will provide stresses at any infinitely small portion of a member, rather than a stress at 10', 11', 12', etc. from a support point.

Is this correct? What will a finite element analysis program enable me to do that an analysis program will not do for me?

 

[dik]

Powers... JAE noted the common use of FEA that most structural engineers use. I tried to describe a general type if application. It can be used for small irregular solids under a variety of conditions.

About 40 years ago, I had written a FEA program for structural use, but for one application, I used it for gas bearings.

A person I met at the University Students Union building had a problem with the bearings wearing out due to the high RPM and loads of turbines.

I knew of a material called lead zirconate titanate which was used for piezoelectric cigarette lighters. It's the material that when struck quickly produces the electric spark.

At the coffee table was an electrical engineer, my mentor of sorts, and I asked him if a potential could be applied to this material and effect a deformation. He said it would.

I then modelled the ceramic gas bearing in FEA program and applied an electrical potential to it to effect the deformation. By varying the potential and the location, it was possible to 'customise' the bearing so that it would be a physical bearing at low RPM's and a gas bearing at high RPM's.

In this instance, the FEA was used to model a 3D solid and apply an electrical potential to it (in the model). The model then deformed according to the properties of the material.

Dik

 

[IDS]

Finite Element Analysis is any anlysis method that works on tha basis of constructing a mathematical model of a structure (or other continuum) by subdividing the structure into a series of small connected "elements" that can be analysed mathematically and will behave in approximately the same way as the actual structure.

A frame analysis program is an example of FEA, although usually the term is reserved for programs that use 2D (plate) elements and/or 3D (brick) elements. In all cases the changes in the position of the "nodes" definining the element can be related to the strains, stress and forces in the elements, leading to a set of simultaneous equations that can be solved to determine the deflections and resulting stresses in the structure resulting from any set of applied loads or deformations.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[rb1957]

have you tried wiki ?

simply up, FEA is a mathematical representation of a physical structure. The analysis solves for internal stresses due to applied loads by minimising internal strain energy.