Yes, you can.

But it mainly depends on the geometry of your problem. If it is relatively simple, FDM can be very effective, but for more complex shapes, FEM is more suitable.

I am not that expert but I think FDM FEM are just tools to explain the mathematical equations which govern the physics of the phenomena. The method which explains the physics better is usually use dint hat field like for fluids, FDM or more recently FVM is preferred. However, I don't think there may be any issue with using one method in other. I think the best way is to solve some simple heat transfer equation in solids using FDM and FEM and see if there is any difference.Hope this helps. Experts may kindly comment.

The discussion on imechanica.org "Why not use FDM in solid mechanics" will throw more light on your question. In addition go through the excellent book by Boyd on "Chebychev and Fourier Spectral methods" that will detail you on the different approximation techniques and the necessity of these techniques.

Just an issue of solving a set of partial differential equations. FDM/FEM do both based on different constructs.

I think a more appropriate question to ask is to what extent of accuracy you want your solution to be. FEM uses numerical quadrature and basis functions, which can be very accurate for fundamental studies. Finite difference, unless a very fine grid is used, then there might be significant discretization errors involved. As far as I'm aware, for very minute systems where accuracy is of utmost importance, e.g. in droplet formation, finite element is usually used to study the physics. If you do not need high accuracy and are only interested in engineering solutions, then finite difference or finite volume would suffice. A word of caution is that finite element may be computationally more expensive though.

If you search, you can find lot of good references that compare FVM, FDM, FEM, and Spectral methods for solving PDEs. Each of these methods have their pros and cons depending on whether the solution of the problem fits a good global solution (e.g., diffusion operator) or more local variations (e.g., convective operator). If local conservation or control is very important, FVM and FDM are favored. However, if weak/global solutions are good enough for your problem, FEM and Spectral methods work very well. However, within FEM one can chose different basis functions to get better local control such as CVFEM. I am generalizing at a very broad level and please take this answer with a pinch of salt. At the end it all depends on ease-of-use, learning curve, development time, accuracy, efficiency, extensibility, etc.

FEM can be used for the complex geometry. If you have those structure in complex geometry then using FDM would not be the convenient one. As per the geometry of your metal you can determine.

Finite difference method is generally used for heat conduction in solid.

FDM can be effectively used if the geometry of your problem is not so complicated. You may want to have a look at ITASCA Software very usefull in Rock mechanics and Soil Mechanics which uses FDM.

http://itascacg.com

you could use FDM when have governing differential equations but you could use FEM even if you don't have governing differential equations else you could use Total Potential Energy ,PI=Strain Energy - External Potential ,

L. Hoskoti: the answer for your question is YES.

You can, but it is easier to produce computer codes for problems with more complex geometry using FEM (Finite Element Method) or FVM (Finite Volume Method) - Pragyan Bhattarai did a similar comment. For dynamical systems, where there is time derivative, the FDM is applied for time discretization, coupled with FEM, FVM, or even FDM for discretizing the space variables.

As already mentioned, the answer is yes. I would say that the main problem in FDM is not in the geometry representation but in the BC (what comes naturally in the FEM), in the FDM just the Dirichlet type are natural to impose.

Just like we used to read more books before the age of the Internet, FDM was more used before the age of FEM. Solving problems of elasticity for example. Books are always good to read and FDM is always helpful, even together with FEA. In structural optimization, for example, certain operations at the local level are much cleaner with finite differencing than with having to go into the bowels of the code (say, finite element formulations) to obtain exact derivatives. While this is a simple example of finite differencing, it is widely used in this context.

Yes for sure you can. You may need to refer to one of my papers in this regard named "Axisymmetric buckling of the circular annular nanoplates using finite difference method"

Thank you. It helped me a lot.