Franz-Josef FALKNER

Numerical assessment of complete load-displacement curves of geometric
nonlinear structures

In this thesis numerical procedures for the computation of stability points and the post-buckling
behaviour of slender structures are presented.
The Finite-Element equations for plane beam structures are derived from the principle of virtual
displacements. Thereby no restrictions are made on the magnitude of the displacements.
The arc-length method is used to compute unstable parts of the equilibrium path. The iterative
load changes are calculated utilizing a quadratic constraint condition.
Extented equation systems, containing the equilibrium equations and additional equations describing
the stability point, are formulated for the direct computation of critical points. These
equation are solved by means of the Newton-Rapson method and a bordering algorithm. At bifurcation
points a branch switching algorithm is employed to compute a equilibrium point on the
secondary path. The remaining part of this path is calculated by means of the arc-length method.
With the above mentioned procedures the complete structural response of spatially trusses, plane
beam structures and a cylindrical panel are successfully computed.

 

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