Ujjwal:

I am not a Math person so I looked up what's available in RG that I hope would be helpful for you:

https://www.researchgate.net/search.Search.html?type=publication&query=learning%20Finite%20Element%20Analysis%20Math%20book&tabViewId=573090cded99e10d41529ec1&previous=researcher

Best regards,

Debra

It is important to divide the answer between linear and non linear FEA. Reddy (An introduction for non linear FEA and Introduction to the Finite Element Method) wrote the most comprehensive textbooks of both disciplines and I really recommend his books. Ferreira (Matlab Codes for Finite Element Analysis) is also an excellent introduction with clear examples but only for linear FEA. Kwon (Finite Element Method using Matlab) is a simple textbook but it had good exercises and codes. Kythe (An introduction to linear and non linear FEA) is also a good textbook for both disciplines. Unfortunately there are few examples of non linear FEA thus probably could be a difficult task. Linear FEA is a widely used technique and probably you will find other good books. I only recommend the texts that I know well. Good Luck! 

Thank You Mr. Roberto Avila-Vázquez.

I've found the books of Zienkiewicz illuminating. See for example the following references:

The Finite Element Method: Its Basis and Fundamentals, 7th ed., Butterworth-Heinemann.

The Finite Element Method for Fluidynamics, 7th ed., Butterworth-Heinemann.

The Finite Element Method for Solid and Structural Mechanics, 7th ed., Butterworth-Heinemann.

I hope this information will be of help.