Rigid Body Concept for Geometric Nonlinear Analysis of 3D Frames, Plates and Shells Based on the Updated Lagrangian Formulation
Resource
Computer Methods in Applied Mechanics and Engineering 196 (7): 1178-1192
Journal
Computer Methods in Applied Mechanics and Engineering
Journal Volume
196
Journal Issue
7
Pages
1178-1192
Date Issued
2007-01
Date
2007-01
Author(s)
Abstract
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 updated Lagrangian (UL) formulation, the geometric stiffness matrix [kg] is derived for a 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 [kg] 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 kinds of actions are considered in the stiffness matrices. The robustness of the procedure is demonstrated in the solution of several benchmark problems involving the postbuckling response. © 2006 Elsevier B.V. All rights reserved.
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Type
journal article
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