A numerical method for plastic limit analysis of 3-D structures

Abstract Based on the upper bound theorem of plasticity, the 3-D limit analysis of rigid-perfectly plastic structures is formulated as a discrete nonlinear mathematical programming problem with only equality constraints by means of the finite element technique. The penalty function method is used to deal with the plastic incompressibility condition. A direct iterative algorithm is employed in solving this formulation. At each step of the iteration, the rigid and plastic zones are continually distinguished, the respective constraint conditions are imposed on them, and the goal function is modified appropriately. The numerical difficulties caused by the nonlinearity and nonsmoothness of the goal function and the incompressibility of plastic deformation are overcome. The limit load multiplier and the associated velocity field computed by the iteration procedure converge monotonically to the upper bounds of real solutions. The numerical procedure has been used to carry out the limit analysis for cylindrical shells with part-through slot-type defects under internal pressure. Numerical examples are given to demonstrate the applicability of the procedure.

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