MHB Where can I find info on the partial derivative of elastic energy wrt position?

AI Thread Summary
The discussion revolves around finding resources on the partial derivatives of elastic energy, surfacic energy, and strain with respect to position, particularly in the context of the finite element method. The author seeks accessible references due to limited skills in vector calculus. A specific example is provided, illustrating that the derivative of elastic energy relates to force. There is a request for clarification on the term "surfacic energy." Recommendations suggest that books on material science may cover the derivative of strain with respect to position.
datahead8888
Messages
8
Reaction score
0
I've been studying a version of the finite element method.

The author of a paper I was reading refers to the partial derivative of total elastic energy wrt position, partial derivative of surfacic energy wrt position, and partial derivative of strain wrt position.

Does anyone know of a good resource that explains these concepts?

I'm not as skilled with vector calculus, so a less aggressive reference is good.
 
Mathematics news on Phys.org
If elastic energy is
$$\frac{1}{2} k x^{2},$$
then its derivative w.r.t. position is just the negative of the force:
$$ \frac{ \partial}{ \partial x} \left( \frac{1}{2} kx^{2} \right)= kx = -F.$$

I've never heard of "surfacic energy". Could you define that, please?

As for the derivative of strain w.r.t. position, you could probably find that in a book on material science.
 
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Back
Top