The analytical methods described in this paper are designed to handle two classes of problems. The first class is associated with a load history duration of 50 millisec or more (such as light water reactor blowdown transient); the second class is associated with very rapid load application and a response history of about 100 μsec. The first class of problem is solved by using an implicit method of solution, and the second class is solved by an explicit method. The method of solution for both classes of problems is developed with an appropriate consideration of the materials and geometric non-linearities. Material nonlinearities, both for isotropic and kinematic strain hardening, are handled in a novel manner, such that the solution points remain on the materials curve with any degree of accuracy desired. An iterative scheme and a piecewise Lagrangian formulation are used in the analysis.

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