Nonlinear torsion of thin-walled bars of variable, open cross-sections

Wekezer, Jerry

doi:10.1016/0020-7403(85)90045-1

Cited by 10 publications

(1 citation statement)

References 16 publications

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“…Perfect agreement was obtained between their tests and theory. Many years later, Wekezer [8] investigated the same problem using his numerical model, which is based on a "nite element approach in which the middle surface of the cantilever is described by a shell and further The current model developed in this paper was applied to this problem, using the basic Newton}Raphson method with some process modi"cation. The #ow chart for this computer program is shown in Figure 4.…”

Section: Non-linear Torsionmentioning

confidence: 99%

Non-linear analysis of thin-walled members of open cross-section

Ronagh

Bradford

1999

Int. J. Numer. Meth. Engng.

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The paper presents a means of determining the non-linear sti!ness matrices from expressions for the "rst and second variation of the Total Potential of a thin-walled open section "nite element that lead to non-linear sti!ness equations. These non-linear equations can be solved for moderate to large displacements. The variations of the Total Potential have been developed elsewhere by the authors, and their contribution to the various non-linear matrices is stated herein. It is shown that the method of solution of the non-linear sti!ness matrices is problem dependent. The "nite element procedure is used to study non-linear torsion that illustrates torsional hardening, and the Newton}Raphson method is deployed for this study. However, it is shown that this solution strategy is unsuitable for the second example, namely that of the post-buckling response of a cantilever, and a direct iteration method is described. The good agreement for both of these problems with the work of independent researchers validates the non-linear "nite element method of analysis. Figure 8. Flow chart deploying the direct iteration method of the value of to be used. After convergence on and , the results are recorded and a similar process starts again for the next factor.It can be seen that the eigenvector of a stability analysis is needed in order to build the metric matrix [G]. The most accurate eigenvector would be that which resulted from a quadratic stability analysis [2], in which the e!ects of the initial bending curvature are taken into account. The self-weight of the structure may also need to be incorporated into the stability analysis, and 548

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Section: Non-linear Torsionmentioning

confidence: 99%