Large deformation, large roation elasto-plastic shell analysis with particular application to tubular members and joints
The ultimate strength assessment of steel tubular members is of the utmost importance to the design and maintenance of many structures including large offshore platforms. Ultimate strength assessments I using numerical solutions must model both nonlinear material and geometric behaviour. The latter must consider large displacements, very often large rotations, and possibly even large strains. These numerical solutions must be computationally efficient and be capable of running on generally available computer hardware, i.e. minicomputers. To achieve this efficiency, attention must be paid to programming considerations, and a new suite of data management modules has been developed and is described in this thesis, which minimise disk storage and speed program development. In addition, the structural modelling was carried out almost exclusively using the Semiiaaf thin shell element. The work described in this thesis considers most of the components which contribute to the numerical ultimate strength analysis of steel tubular members. Theoretically, attention has been focused in two areas, namely the geometric nonlinearity and the automatic solution of the resulting nonlinear equations. A detailed study has been carried out to understand fully the main methods of accounting for geometric nonlinearity from fundamentals of continuum mechanics. The study has considered both the Green-Lagrange and Logarithmic strain measures with a Total Lagrangian, Updated Lagrangian and Eulerian description of motion. These formulations have been included in the Semiiaaf shell element, firstly using a continuum mechanics based approach, and secondly using the more orthodox stress resultant approach. At all stages within the thesis attention is drawn to the effects of the approximations which have been made and their resulting limitations in the respective formulations. The solution of the nonlinear equations is also covered in detail using Newton-type algorithms coupled with line searches. The solution algorithms have been derived for a constrained environment where a modified version of the generalised arc-length constraint has been used. The inclusion of material nonlinearity has been well developed previously but has been included for completeness. To demonstrate the performance and limitations of the theory presented, several carefully chosen numerical examples have been included which include the analysis of tubular steel T and X joints connections and residual strength assessment of a dented pipeline riser. Where possible, results have been compared with experimental tests. The thesis concludes that for general engineering structures, the Total Lagrangian approach based on the stress resultant model gives good engineering results, even in the presence of moderately large rotations. Of the alternative formulations the Updated Lagrangian layered approach is probably the most effective for large rotations and small to moderate strains.