Nonlinear finite elements/Homework11/Solutions/Problem 1/Part 5

Problem 1: Part 5: Consistency condition - 1Edit

Use the consistency condition and the expressions you have derived in the previous parts to derive an expression for   in terms of  ,  ,  ,  , and  .

From the consistency condition

 

From the previous parts

 

Plug into the consistency condition to get

 

Collect terms containing  :

 

Therefore,