what are the advantages of FEA

Visualisation increases
Design Cycle time reduction
No of prototypes required is less
Testing reduced
Optimum Design

What e applications for FEM?

Linear, non linear, Buckling, Thermal, Dynamic & Fatigue analysis

Mass Scaling

Mass-scaling is a term that is used for the process of scaling the element's mass in explicit simulations to adjust its timestep. The primary motivation is to change (usually increase) the global compute timestep which is limited by the Courant's stability criteria. LS-DYNA allows two different types of mass-scaling using the DT2MS parameter from *CONTROL_TIMESTEP with the default set to no mass-scaling. When DT2MS is less than zero, LS-DYNA adds mass of each element whose timestep is below abs(DT2MS) such that the element's updated DT is equal to abs(DT2MS). When DT2MS is greater than zero, LS-DYNA adds mass to elements whose DT is below abs(DT2MS) and "removes" mass from elements whose DT is greater than zero. DT2MS>0 is seldom used while DTM2<0 is frequently used for overcoming the smallest computed timestep. Care must be taken when using DT2MS<0 to ensure that the added mass does not have an adverse effect on the simulation accuracy. It is common practice to limit the percentage of added mass to less than 5% (at part level) in dynamic simulations. Optionally, users can set ENDMASS in *CONTROL_TERMINATION to terminate a simulation based on percentage of added mass based on the total mass of the model. When ENDMAS is greater than zero, LS-DYNA terminates when the percentage of added-mass reaches ENDMAS and a report of up to 20 nodes (sorted in the descending order of its added mass due to mass-scaling) is written to both standard output and D3HSP file. It must be noted that the percentage of added-mass is based on total mass of the model which included rigid body, rigid walls, etc... and could be misleading if looked at the global level. LS-DYNA outputs the percentage of added mass at component level which is a better indicator of amount of added mass due to mass-scaling. The concept of mass-scaling for both options of DT2MS is graphically illustrated below.

Link to the 2nd definition http://blog2.d3view.com/overview-of-mass-scaling/

Strain Energy

The external work done on an elastic member in causing it to distort from its unstressed state gets transformed into strain energy, which is a form of (PE) potential energy.
The strain energy in the form of elastic deformation is mostly recoverable in the form of mechanical work.

Here is a video I found on you tube
1) 

What is hourglass energy?

1st order reduced-integration elements (which happen to be the very type of elements generally used in explicit solvers) suffer from hourglassing. These elements only have one integration point; because of this the elements can shear without introducing any energies. FEA codes which rely on 1st order reduced integration elements counter this by introducing hourglass energy. In situations where these elements would otherwise shear, this augmented energy keeps this from happening. This is reflected in your reported hourglass energy values. High hourglassing energy is often a sign that mesh issues may need to be addressed.

http://www.dynasupport.com/howtos/element/hourglass
This link is from LsDyna which explains hoursglass energy in detail