A small strain, large rotation theory and finite element formulation of thin curved beams
In this thesis a theory for the geometrically nonlinear analysis of thin curved beam-type structures is proposed and an associated displacement finite element formulation developed. An exact two-dimensional large rotation theory, which is based on an intrinsic coordinate system, has been developed. Four alternative Lagrangian formulations of the theory have been presented for comparison. A family of two-dimensional thin curved beam elements has been developed by using the constraint technique to include the convective coordinate system. The elements are relatively simple and the minimum number of degrees of freedom necessary has been used. The Total Lagrangian formulation has been shown to be numerically more effective than the Updated Lagrangian formulation. A new Total Lagrangian formulation that includes the effect of curvature change on axial force in the incremental equilibrium equations has been developed. The formulation is based on the geometric strains and has the capability of predicting true axial force values in large rotation and curvature problems. This approach can be used in the general continuum mechanics largz; d3formation formulations. A large rotation theory for three-dimensional beams and Total Lagrangian formulations of the theory, which are based on the Green strains and the geometric strains, have been developed. The theory correctly describes the large rotation elastic response of a thin eccentric curved beam of rectangular cross-section. Material nonlinearity, which is based an the von-Mises yield function and the Prandtl-Reuss flow rule and in which isotropic hardening is assumed, has been included in the formulation. A family of three-diinensional beam elements, that can accurately accommodate the theory, has been developed by the constraint technique. The elements are suitable for use as stiffeners in the analysis of stiffened shell structures. The elements, which have been developed, have been implemented in the LUSAS finite element system. The accuracy of the results obtained has been demonstrated by comparison with*published results.