How does CAESAR Incore solver works.can any bdy explain the logic behind that.

Sajir,

First, you must understand that the pipe and fittings items are modeled as beams. The system of conected beams is treated mathematically as a stiffness matrice with boundary conditions representing the restraints, or imposed displacements. The solution of the stiffness matrice is done by techniques for simultaneous equations.
If you understand this, then you will also realize there is not a solution for a piping model that does not have enough restraints. Try to solve a piping model with only Y+ vertical supports. The displacements will go to infinity without enough restraints (anchor or guide line stop) for typical sustained plus expansion analysis.