Plastic analysis~inelastic analysis-non-linear analysis

[dgkhan]

I am just asking for my own learning. After crossing elastic limit, the stress and strain does not remain linear, I guess, we get more strain or even continuous increase in strain under same load. All three terms to me address same "one' issue or there is difference?

 

[abusementpark]

Non-linear analysis can also refer to geometric non-linearity ( i.e. P-Delta effects).

 

[Denial]

And "plastic" can be seen as a special case of "inelastic".

 

[Tomfh]

These are distinct concepts and should not be lumped in together. Read up a little more on them to clarify the ideas in your mind.

 

[dik]

I found the question a little obscure. The non-linearity of plastic analysis/design is essentially due to the formation of 'plastic' hinges that permits a redistribution of forces, increasing the load capacity as well as establishing an upper limit on the load capacity of a system.

Dik

 

[rb1957]

"non-linear" is just a catch-all for everything that is not, predictably, linear (and elastic). there are two main types of non-linearity ... material and geometry.

material non-linearity is easy ... stress/strain beyond yield, the material is no longer linear elastic.

geometry non-linearity is when the structure stops responding to external load in a linear manner. your example of plastic hinges is one case ... the beam locally yields, goes plastic, but the beam can continue to react additional load ... the analysis of the beam changes for the standard beam to one with a plastic hinge. shear buckling of a web is another ... initially the web reacts the applied shear with in-plane shear stresses, but after it buckles, the sher is reacted by tension loads along the buckles. there are many of examples of non-linearity.

 

[JoshPlumSE]

My statements here are not exactly textbook definitions. But, this is how I tend to define them:

Non-Linear Analysis:
Any form of analysis in which the force displacement relationship is expected to be non-linear. The main sub-categories of non-linear analysis would be Geometrically non-linear analysis and materially non-linear analysis.

Geometrically non-linear analysis:
An analysis where the deformation of the structure changes the stiffness properties of the structure. Normally, this is within the context of a P-Delta analysis. However, there are more complex behaviors that would also fall under this category (large deflection theory, catenary cables, fabric structures, et cetera).

In-Elastic analysis:
A form of material non-linear analysis where material non-linearity is accounted for from within the analysis itself. The material backbone curve in this case could be elasto-plastic, or could be more complex.

Plastic analysis:
To me this is really a sub-set of in-elastic design where the in-elastic behavior is usually associated with the plastic hinging of a moment frame.... Therefore, we're usually talking about an elasto-plastic material curve.