Inelastic stability of plate structures using the finite strip method
In this thesis, some nonlinear effects associated with the buckling behaviour of plated steel structures are examined using a modified finite strip method. To include the effects of plasticity over parts of the cross-section, a more general stress-strain relationship than previously included has been used. The method is also extended to account for the large deflection behaviour of perfect and imperfect plates in the elastic range. The only restriction on the method presented here is that the buckling mode varies sinusoidally in the .;, longitudinal direction, which implies either that the ends of the structure are simply supported or that the wavelength of the buckled mode is small in comparison with the overall length of the structure. The present study may be divided into three parts. In the first part the small deflection theory is used to determine the stiffness and stability matrices of ~ individual strip and these are assembled to form an overall stiffness matrix, representing a structure which may be under concentric load, eccentric load or pure bending. In some cases a structure with an overall initial imperfection is considered. The Wittrick-Williams Algorithm is used to obtain the smallest critical buckling load. The method is applicable to the analysis of various structures such as isolated plates, stiffened panels, rolled sections and stiffened box-girder bridges. To check the accuracy of the method a comparison with some published theoretical and experimental results is undertaken. Secondly, a parametric study for stiffened panels, columns, and beams is presented. For the stiffened panels, the effect of seven parameters (slenderness ratio, residual stress, dimensions and shape of the stiffener, mode of buckling, the longitudinal boundary conditions, and the yield stress) has been investigated. Approximate design curves for the optimum dimensions of panels stiffened by flat stiffeners are given. The capability of the method for the analysis of a stiffened box-girder in bending is also shown. The effect of seven parameters (dimensions and shape of the cross-section, the slenderness ratio, the material yield stress, the residual stress, the initial overall imperfection and the eccentricity of the applied load) on the inelastic buckling of columns and beams has been studied. All the results are given in nondimensional graphs or tables. Finally large deflection plate theory is applied to study the post-buckling behaviour of both perfect plates and those with initial imperfections. The work in this section is restricted to the elastic state. The longitudinal axial compression is assumed to act on the plate through two rigid bars at the ends, and various in-plane boundary conditions for the longitudinal unloaded edges have been considered. The Newton-Raphson method is used for the solution of the non-linear equations.