Rigid Body Considerations for Geometric Nonlinear Analysis of Structures Based on the Updated Lagrangian Formulation

Abstract

In the nonlinear analysis of elastic structures, the displacement increments generated at each incremental step can be divided into two parts 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 advantageous in that the formulation is simple, the expressions are explicit, and all kinds of actions are taken into account. The robustness of the procedure is demonstrated in the solution of several problems involving the postbuckling response.