Computational field of solid mechanics is mostly dominated by FEM. This is a well known topic.
But is it that FDM (finite difference method) has no chance of surviving
in solid mechanics?
What are the present developments in the use of FDM in case of elasticity analysis of solid body?
I would like to mention some of the recent research works on this topic here.....
Recently a new mathematical model has been developed by Prof. S. Reaz Ahmed and his students known as the "displacement potential approach".
This approach shows how very efficiently FDM can be used in solving problems of elasticity. They have solved numerous problems using this method for the case of both monolithic and composite materials. Quite a number of student have completed their M.Sc thesis on this topic. S.K. Debnath has done his PHD on this new approach.
Many of us previously thought that efficiently solving a 3-D problems of elasticity using FDM is almost impossible. But they have proved it otherwise.
One of the idea about FDM is that it is very difficult to use FDM for solving complex geometries. But they have successfully analyzed complex geometries like gear teeth using this approach.
Moreover in most of their work they have claimed superiority over FEM. This is great, isn't it?
i am giving some links below. Please have a look at it.
You can find many other publications by searching "displacement potential function approach"
in google.
I am yet not an expert on applied mechanics (have just started my M.Sc in mechanical engineering). But i am working with Prof S R Ahmed on his new method and I understand the potential of this approach.
I would like to know what others think about this approach.
And also would like to have knowledge about other research developments of the use of FDM in solid mechanics.
(this is my first blog entry...so any mistake is requested to be expressed in comments...this will help me....thanks)