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In the nonlinear analysis of elastic structures, the displacement increments generated at each incremental step can be decomposed into two components as the rigid displacements and natural deformations . Based on the updatedLagrangian (UL) formulation, the geometric stiffness matrix k g isderivedfora 3D rigid beam element from the virtual work equation using a rigid displacement field.

Further, by treating the three-node triangular plate element (TPE) as the composition of three rigid beams lying along the three sides, the k g matrix for the TPE can be assembled from those of the rigid beams. The idea for the UL-type incremental-iterative nonlinear analysis is that if the rigid rotation effects are fully taken into account at each stage of analysis, then the remaining effects of natural deformations can be treated using the small-deformation linearized theory. The present approach is featured by the fact that the formulation is simple, the expressions are explicit, and all member actions are considered in the stiffnessmatr ices.

For an incremental -iterative nonlinear analysis, two typical phases can be identified, i.e., the predictor and corrector phases. The predictor relates to solution of the structural displacement increments forgiven load increments based on the incremental structural equation, and the corrector is concerned with recovery of the force increments from the displacement increments for each element and the updating of the element forces 4 . The predictor affects only the speed of convergence of iteration, which therefore is allowed to be approximate to the extent that the direction of iteration is notmidguided. In contrast, the corrector governs primarily the accuracy of solution, which should thus be made as accurate as possible. A common understanding is that if the corrector is not accurateanough, then the unbalanced forces calculated will be incorrect and the iterations performed to remove the unbalanced forces will be meaningless.

Source: ecommons.cornell.edu

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