What is the Balance of Linear Momentum in Continuum Physics?

[Ihsan]

Homework Statement

1- Find the body force b that acts on this continuum so that Cauchy’s first equation of motion.
2-Find the body forces at the reference point ( 1, 2, 1) where ρ0(rho nod)= 2

Relevant Equations

Balance of Linear Momentum or Cauchy first equation of motion -->b+div σ =ρ x ( x here div x and again div x two time)

Hi,

unfortunately, I am not getting anywhere with the following task
and I try solve it

 

[Mark44]

This isn't my area of expertise, so I can't offer any help with this problem. However, I do have several comments about the problem and your work.

1. The first problem statement is confusing. "Find the body force b that acts on this continuum so that Cauchy’s first equation of motion." So that Cauchy's first equation of motion does what? Is satisfied? Whoever wrote this problem didn't provide a complete sentence or complete thought.
2. The second problem statement is also confusing. The last part of the problem text (in one of your attachments says "... where $0 \rho = 2$. What does this mean? In the problem statement you wrote, you have "... where ρ0(rho nod)= 2" I don't understand either of these.
3. For your relevant equations you have "Balance of Linear Momentum or Cauchy first equation of motion -->b+div σ =ρ x ( x here div x and again div x two time)" Is this the divergence of σ? What does "x here div x and again div x two time" mean?
4. The work you show in the attachments is not as clear as it could be. It looks like ink from one side of the page shows through on the other side of a couple of the pages, making them hard to read. Also, you have crossed out some of the stuff, which again makes your work less legible.

 

[Ihsan]

Thanks you for your note .and Sorry for this .I am new to English language. and this is my first time to use this page .So for your comment ρ0 it mean density in reference configuration and x is acceleration I am very sorry for this .and Sorry for the photo, I did not notice the low resolution of the photo and the ink behind the paper I will try to correct my mistake .and I will take your comments in my mind . Thank you again