Numerical solution techniques for structural instability problems

ABSTRACT Purpose: The purpose is to overcome numerical problems arising in structural instability numerical computations for equilibrium configurations corresponding to increasing loads on structures having points of instability or more generally large non linearity.Design/methodology/approach: The used numerical methodology was the finite element method with the particular technique of non linear transient dynamic analysis. In such way dynamic equilibrium paths, which are able to lead to required corresponding static ones, can be obtained.Findings: A methodology to develop this kind of analyses as well as a procedure to set some initial parameters and to check the accuracy of the solution have been investigated and pointed out.Research limitations/implications: In the future it will be possible to apply the investigated numerical procedure to other practical cases.Originality/value: We have overcome the limitations in the use of the Newton-Raphson classical method when load control conditions are considered. We also emphasise the practical limits of the Arc Length technique, which requires consistent formulations of the element stiffness matrix in non-linear field; this kind of high precision is often not available in the common FE codes.Keywords: Arc-length; Buckling; Post-buckling; Quasi-static analysis

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