ANALYSIS OF PHYSICALLY NON-LINEAR THIN-WALLED CROSS-SECTIONS BY NON-LINEAR OPTIMISATION

Thin-walled cross-sections are usually calculated by the theory of VLASOV, which takes into account the warping of the cross-section and the twist of the element. This theory is applied to structures made of linear-elastic material only. Using the method proposed in the paper, the physically non-linear behaviour of the material is also taken into account. The mechanical modelling is based on the LAGRANGE principle of total potential energy using an integral description of the stress-strain relations. In this way, a non-linear optimisation problem is formulated. This approach has the advantage that the strains and stresses are directly calculated without needing to pre-calculate any characteristics of the cross-section. The application of the proposed method is demonstrated by means of an example. The numerical problem can be solved by standard software, for instance by using spreadsheet programmes.