Linear vs. non-linear
Linear vs. non-linear
(OP)
Folks-
How can you tell if a structural problem is non-linear? When you exceed the yield point of an aluminum test specimen in a tension test the specimen goes into plastic deformation. Is non-linear? What kind of linearities are there in solid mechanics? What makes a problem non-linear? It's OK to talk with math!
Thank in advance!
How can you tell if a structural problem is non-linear? When you exceed the yield point of an aluminum test specimen in a tension test the specimen goes into plastic deformation. Is non-linear? What kind of linearities are there in solid mechanics? What makes a problem non-linear? It's OK to talk with math!
Thank in advance!
Tunalover





RE: Linear vs. non-linear
Geometry- large deflections cause secondary effects such as P-Delta (a moment caused by deflection).
Material- Plastic deformation and Cracking (concrete) are nonlinear effects that, in a lot of instances, are considered failures so analysis beyond these effects is not required (cracking in concrete would be an exception as it is often expected).
If you want to go beyond yield (you did in your question) and deflections are large (your call) use non-linear analysis.
RE: Linear vs. non-linear
Linearity is a simple mathematical approximation to simplify real time problems. In linear analysis, the deflections and rotations are very small, stresses are proportional to strain, material is elastic, the equations are written for the initial structual configuration, loads maintain their original directions as the structure deforms, and the global equations (KU=P) are solved in a single step.
No real time problem will satisfy all these conditions.
There are basically 3 kinds of non-linearities. The 1st two are geometric and material non-linearities.Geometric non-linearity is caused due to large deflections in the structure and material non-linearity is where the material properties are dependant on the strain. I need not go into the details of these as they have already been well explained by dfish67.
The 3rd kind is contact non-linearity. This is the case with crash analysis.
Buckling is inherently non-linear.
RE: Linear vs. non-linear
RE: Linear vs. non-linear
RE: Linear vs. non-linear
RE: Linear vs. non-linear
To decide if you should include non-linear affects (material, goemetry etc.) first run a linear analysis. Then look at the results. Usually you can tell if a linear analysis will be enough or not. If stresses exceed yield in area of concern, a non-linear material may be required. If deformations are too large, a non-linear geometry effect may be required.
Gurmeet