Analytical Formulation for the Liner and Penetration

Plate AIB.l Gas ducts, cooling pipes, control rods and other penetractions with finite element mesh schemes 

Kd = Post-elastic stiffness (kip/inch) (KN/mm ) = Elastic (unloading) stiffness (kip/inch) 

In any computer package involving 2- and 3D finite-element technique, Table AIB.l giving analytical formulation can be simulated to analyse the liner between the studs, standpipes and cooling pipes. For the global analysis of the pressure and containment vessels, these local effects can form the worst case. The vessel can be analysed with and without the contribution of the liner. Under ultimate conditions the liner local areas must be thoroughly assesed prior to the final decision of the factor safety above the elastic conditions under (pressure + prestress + temperature) the combined loading  

K= elasto-plastic stiffness matrix as a function of the current state of plastic deformation Kg = initial stress geometric stiffness matrix The determinant K + XKa = 0. 

The essential equation is characteristically triangularized for the /th loading step as 

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