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Abstract: This study presents the analytical, numerical, and experimental results of thin hemispherical metal shells into the plastic buckling range illustrating the importance of geometry changes on the buckling load. The hemispherical shell is rigidly supported around the base circumference against horizontal and vertical translation and the load is vertically applied by a rigid cylindrical boss at the apex. Kinematics stages of initial buckling and subsequent propagation of plastic deformation for rigid-perfectly plastic shells are formulated on the basis of Drucker–Shield''s limited interaction yield condition. The effect of the radius of the boss, used to apply the loading, on the initial and subsequent collapse load is studied. In the numerical model, the material is assumed to be isotropic and linear elastic perfectly plastic without strain hardening obeying the Tresca or Von Mises yield criterion. Both axisymmmetric and 3D models are implemented in the numerical work to verify the presence of non-symmetric deformation modes in the case of thin shells. In the end, the results of the analytical solution are compared and verified with the numerical results using ABAQUS software and experimental findings. Good agreement is observed between the load–deflection curves obtained using three different approaches. A secondary bifurcation point is detected in thin shells in which the deformation degenerates from symmetric to non-symmetric behavior. The bifurcation point depends on the (R/t 0) ratio and the material parameters. [Copyright &y& Elsevier]

Abstract: This paper presents and illustrates a GBT formulation to analyse the elastic localized web buckling of thin-walled steel beams under concentrated loads. The theme of localised web buckling is first introduced by describing the parameters that most influence the buckling behaviour of slender plates subjected to edge loads. After that, a GBT formulation to analyse the elastic localized web buckling of thin-walled steel beams under concentrated loads is presented: the GBT equations are derived and the determination of deformation modes is briefly addressed. Then, two illustrative examples are shown and validated by comparison with shell finite element results: (i) cold-formed steel plain channel beams with web crippling configurations and (ii) welded steel I-section beams with patch loading configurations. It is found that both pre-buckling longitudinal normal () and shear () stresses have to be included in the buckling analyses of cold-formed steel beams with External One Flange (EOF) and Internal One Flange (IOF) configurations as well as welded steel beams with Patch Loading Test (PLT) configuration. Furthermore, the pre-buckling transverse normal () stresses have to be included in the buckling analysis of cold-formed steel beams with External Two Flange (ETF) and Internal Two Flange (ITF) configurations as well as welded steel beams with Opposite Patch Loading Test (OPLT) configuration. In beams with EOF, IOF, PLT configurations, the GBT pre-buckling analysis should consider global and shear modes while the GBT buckling analysis may only consider local modes. In beams with ETF, ITF, OPLT configurations, the GBT pre-buckling analysis should consider transverse extension modes while the GBT buckling analysis may only consider local modes. [Copyright &y& Elsevier]

Abstract: The structural behaviour of elliptical hollow sections has been examined in previous studies under several loading conditions, including pure compression, pure bending and combined uniaxial bending and compression. This paper examines the elastic buckling response of elliptical hollow sections under any linearly varying in-plane loading conditions, including the most general case of combined compression and biaxial bending. An analytical method to predict the elastic buckling stress has been derived and validated against finite element results. The predictive model first identifies the location of the initiation of local buckling based on the applied stress distribution and the section geometry. The critical radius of curvature corresponding to this point is then introduced into the classical formula for predicting the elastic local buckling stress of a circular shell. The obtained analytical results are compared with results generated by means of finite element analysis. The comparisons between the analytical and numerical predictions of elastic buckling stress reveal disparities of less than 2.5% for thin shells and, following an approximate allowance for the influence of shear, less than 7.5% for thick shells. [Copyright &y& Elsevier]