Question

can anyone help me with finite element analysis?
stress-displacement relation? use of partial differentials in this subject

Answer 1

What is your question?

Answer 2

how can we practically prove the analysis of different elements in mesh gives the final stresses in the entire body???? because there will be many parts in the boundary which are left without considering the stress there

Answer 3

First of all, Finite Element Analysis will give you the displacements in a mesh. The stresses are calculated based on the strains (which are obtained from the displacements) and Young's Modulus. As you refine the mesh you will find that the stresses asymptotically converge to a constant value. You can determine how accurate you want the answer to be by chosing the change in value as a function of mesh refinement.

Not all the elements will need to be the same size. Some areas of the mesh will have a small change, some will have a large change (around a hole or at a corner). You need smaller elements in areas where the change is large. Try to make the sizes of the elements so that the strain-energy density is about the same in all of them. Also, try not to have an aspect ratio (length/width) larger than 20, preferably not larger than 10.

The type of elements also makes a difference, but since I don't know what problem you are solving I can't comment on that.