Nonlinear geometric and material analysis of shell structures with particular emphasis on tubular joints
Conte, Joel P.
Doctor of Philosophy
Linear and nonlinear analysis of shell structures are performed using finite elements. Shell elements are formulated to capture the linear and nonlinear behavior of shell structures. Although general, the elements are specially suited for tubular joints. An automatic geometric modeling and mesh generation procedure for T, K and DT-joints is first developed. A set of shell elements are then developed and implemented in a general purpose, research oriented finite element analysis program (FEAP) to carry out linear, materially-nonlinear only, geometrically-nonlinear-only and geometric and material nonlinear analyses of thin shell structures with special emphasis on tubular joints which represent essential components of offshore platforms. A six-degree-of-freedom per node (including a true drilling degree of freedom) assembly allows easy modeling of complicated shell structures such as tubular joints or stiffened shells. The displacement interpolation is carefully chosen in order to avoid shear and membrane locking in linear and nonlinear problems. The curvature effects (initial curvature and changes in curvature due to large displacements and rotations) are incorporated by a simple modification of the flat linear shell element. This computationally very inexpensive modification increases the performance of the element by several folds. The total corotational formulation, a Lagrangian formulation, is used to treat geometric nonlinearity. Each point in the thickness of the shell is considered to be under plane stress conditions. Von Mises yield criterion with linear isotropic and kinematic hardening and the associated Prandtl-Reuss flow rule is used to model the plastic flow behavior of the shell material. The flow rule and hardening law are integrated using the return map algorithm. The robustness of the analysis tool developed is demonstrated by solving a range of linear and nonlinear problems of shell analysis. It is demonstrated through examples and comparison with known analytical or reliable numerical solutions that the elements developed are accurate in predicting both displacements and stresses. The ultimate test of the predictive ability of the analysis tool developed is performed by considering three well documented tubular joint examples (T-, K-, and DT-joints) for which experimental results in terms of load deflection curve are available. The prediction of the collapse load and load-deflection curve for the T-joint is in excellent agreement with the experimental results. This agreement between numerical and experimental results for both the K- and DT- joints is also very good considering the complexity of the actual joint structure. Finally, a parametric study of tubular T-joints is conducted to study the effects of the various geometric parameters on the collapse load.