@Rouben Rostamian  

Dear Rouben

Thanks so much for your help.

Best Regards

@Rouben Rostamian  

Thanks. This equation is a general form of elasticity problem and may be used as 1,2 or 3D in plate and shell problems.

Could you please introduce me a refrence for finding procedure to calculate weak form of these terms?

Best

@Rouben Rostamian  

Thanks, Rouben.

I found this document at 

https://math.stackexchange.com/questions/2091901/how-to-derive-weak-form-of-the-poissons-equation

Please see it. My equation is similar to that, but my equation only has additional terms

.and 

I need to apply the same procedure mentioned on that site on these additional terms.

Could you help me with how I can do the same task these terms?

This equation used in the elasticity problem and considering it as 3D lead to accurate results. This is the reason for using 3D.

Thanks for sharing the paper. The content of the paper was difficult for me because my field is not exactly mathematics, I am an engineering student.

Best

@Rouben Rostamian  

Thanks so much, Rouben,

dimension of the space variable is three. In such case please update your comments.

 will we want triangular elements again?

@vv 

Thanks. 

Could you please check my calculations?

I provided them in the new maple file in attachments.

Best.

55555.mw

@vv 

Thanks. How I can change three conditions to have 5  Eigenvectors that I mentioned their conditions and format in my main question?

Thanks

can anyone help me or if other information needed let me know.

@vv Could you please send me your calculation?

I think they are correct!!!

Thanks

@vv 

Thanks so much.

For the Jordan form how I can find those eigenvectors?

@tomleslie 

Thanks so much. How I can plot

 by having W[r]

 functions.

I do not know how I can extract the solutions of xi[r] (r=1..6).

Thanks for helping me.

Best

displacement.mw

@tomleslie 

Thanks. what is the problem in new equations?

I want to repeat the same procedure for functions z1,z3,z5,z7,z9,z11 and plot the results.

Best

FIG_11_PLOT2.mw

@tomleslie 

Thanks so much,

How I can Plot Phase portrait {differential of xi[j] (t)  i.e.,
[diff(xi[j](t),t)] versus xi[j] (t)}?

@Kitonum 

Thanks. for case R<0, there is a problem!!

@Kitonum 

I saw that link. but I want to plot through using relation

in cylinderical coordinate and then change input data to create different shape.

Best

@Carl Love 

This site not work for me!!!