Strain energy and energy norm 3

If you are doing a static stress analysis, use of strain energy (density) would be directly related to stress. Consequently, there would be no obvious advantage to using strain energy (density) over stress in a static analysis.

If you are doing a modal analysis, however, there are no applied loads, and as a result, there are no stresses. Analysts use strain energy density, as it will give them insight into what elements on the model have the greatest deformation normalized to the element volume. Optimization of the model could therefore involve an evaluation of the strain energy density for several modes, and removing material from the structure with low strain energy density and adding material to the structure in regions of high strain energy density. This is how a typical optimization/sensitivity analysis is performed on a model.

I am not familiar with the term "energy norm". Can you please elaborate?

pj

Strain energy density still has usefulness in a static analysis, and is in fact a very good indicator of load paths. As strain energy density is effectively "stress squared" (for linear materials), it tends to highlight the critical load paths more than a stress value does.

Stress can also be (and IS) used in modal analysis. pjhyde is correct in stating that stress values for modal analysis are normalized, but then so are the ensuing strain energy densities.

My experience is that if the design criteria is stress-critical, use stress values. If the criteria is stiffness-dominated and it is necessary to understand load paths, strain energy density is often used.

Brad

I think that the elements located on a load path have higher strain energy density. In simple words, these elements work harder than the others (because of the load path). That's why Brad says strain energy density is a good indicator of load paths.

By the way, in topology optimization tools, we use strain energy density to find out the load path. Then, we usually decide to keep elements on the load path and remove the others.

Hope this helps,

AAY

oso,

Element Strain Energy = Integration of (Stress * Strain) over volume or area of your element (3d or 2d)

If I remember correctly, Energy Norm is the same thing divided by the Strain Energy of the whole structure. This norm is very useful for Error Estimating Procedure (Adapting Mesh). Please check following links:




Have a nice day,
AAY

"If you are doing a static stress analysis, use of strain energy (density) would be directly related to stress. Consequently, there would be no obvious advantage to using strain energy (density) over stress in a static analysis."

I disagree. Look at the example I posted in the other thread on strain energy...if you only look at the stress in the two springs you wont see any difference, but the strain energy is much larger in one than in the other which tells you where you should add stiffness.

Erik

Eap2n
"Stress" in spring elements, as cited in your other post, is an artificial construct to begin with. The stress in Nastran springs is calculated via a stress constant, which is not used in the actual stiffness formulation entered into the global matrix. By the time one is using a spring element, the level of abstraction is such that one cannot say in general whether stress is or is not appropriate (it very much depends on how the stress coefficients were calculated).

This doesn't diminish your contention that using strain energy is useful; but neither is it fair ammunition to use against pjhype's statement.

Brad