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Curved panels are structural elements that form the skin of wings, fuselages and tail booms in aircraft. Buckling of these structures would adversely affect aircraft performance. Due to this, the problem of buckling has been extensively researched in the past. Most of the research has been restricted to the analysis of flat composite panels and analysis of curved panels through simplifications involving geometry, material properties and boundary conditions. The present study aims to develop an analytical solution that can predict the critical buckling load for a wider range of problems. An analytical solution was developed in order to obtain the critical buckling load for a doubly-curved composite laminate under compression, shear, moment or any combination of the three loads. The assumptions of the classical laminate plate theory were used in order to obtain the displacement fields as well as strains of the laminate. The energy method was employed in order to obtain the critical buckling load for various load cases. The values obtained through the analytical solution are compared to the critical buckling loads obtained through finite element analysis (FEA). The highest deviation of critical buckling load from FEA was calculated to be 16.55%. Variation of the critical buckling load with respect to the radius of curvature, boundary conditions and stacking sequence was analyzed. The developed solution was also found to be valid for cases when radii of curvatures are unequal as well as when the length and breadth of laminate are unequal. [ABSTRACT FROM AUTHOR]

The article presents the seismic evaluation and retrofit of a 10-storey steel building located in Vancouver, British Columbia, designed following the provisions of the 1980 NBCC and the CSA-S16.1-M78 steel design standard. Lateral resistance is achieved by tension-only X-bracing with back-to-back double angle members. Seismic evaluation is first performed in accordance with the recommendations of the User's Guide to NBCC 2010 using response spectrum analysis. A Tier 3 systematic evaluation according to ASCE 41-13 is then carried out using both linear and nonlinear dynamic analysis procedures. The performance objectives are set same as those implied in NBCC 2010. The ASCE 41 approach results in much less corrections to the structure. Using the mean results from 10 ground motions is also less stringent than using the maximum of three records. For this structure, nonlinear dynamic analysis permitted to identify the concentration of inelastic deformations demands on the braces along the frame height. This behaviour induced considerable bending moment demands on the columns not captured by linear dynamic analysis. Finite element analysis of the structure columns showed that columns of braced steel frames can exhibit higher ductility compared to acceptance criteria specified in ASCE 41. [ABSTRACT FROM AUTHOR]

• A numerical scheme is developed based on fibre element discretisation. • Application to predict the collapse strength of cylindrical shell under longitudinal bending. • Comparison with equivalent finite element analysis shows the rationality of the proposed method. • Comparison with design guidance demonstrates the conservatism of codified methods. Cylindrical shell is a fundamental building block of many engineering structures. They are usually designed to be the primary load-carrying components to withstand different combinations of environmental loads. This paper presents a fibre-based approach to modelling the progressive collapse of cylindrical shells under combined axial compression and bending moment. In this method, the progressive collapse behaviour of cylindrical shells is incrementally evaluated by accounting for the local response of each fibre element. This approach offers a computationally efficient and robust scheme to compute the ultimate strength of cylindrical shells. Moreover, it enables the modelling of load-shedding between the buckled and intact shell elements on the compressive side, and the yielding failure on the tensile side, which appears to be ignored in existing design codes. Analyses are performed on cylindrical shells with a wide range of design parameters. Validation using the finite element method demonstrates a reasonably well performance of the proposed fibre-based modelling technique. [ABSTRACT FROM AUTHOR]

The lateral buckling analysis of cold-formed thin walled beams subjected to pure bending moments has been performed. The critical buckling loads are estimated based an optimization criteria. The estimated critical buckling stresses are compared with the published results, they show excellent agreement. The effect of the beam length, radius and thickness of the flanges and the length of the extended open flanges, on the critical buckling stresses have been studied for several combinations of the geometric parameters of the beam. Among the three beams, the critical buckling moments for the beam with the extended open flanges are found to be the maximum. However, considering the material and manufacturing costs, beams with rounded cross section are efficient in resisting the buckling loads. [ABSTRACT FROM AUTHOR]

This paper presents a theoretical approach to analyze the eccentric bending and buckling of laminated cantilever beams actuated by embedded pre-stretched SMA wires. Two mechanisms are involved: phase transition of the SMA wires and the nonlinear bending of the laminated beam. On the basis of material model for shape memory alloy during the phase transition in thermal field proposed by Brison, constitutive relations of the SMA hybrid laminated beams are established to interpret the relationship among the recovery stress, the internal stress, the thermal temperature and the thermal expansion. Governing equations in terms of the slope function and the horizontal displacement are derived according to von-Kaman geometrically nonlinear relationships. The nonlinear bending deformation of the SMA hybrid laminated beams is analyzed by considering the deflection due to eccentric bending moment as an initial imperfection and is solved using perturbation approach. A compatible condition is proposed to ensure consistent deformation between the SMA wires and the laminated beams. By developing Matlab program, parametric studies are carried out to investigate the effect of the pre-strain, the volume fraction and the location of the SMA wires on the deflection, the critical temperature, the recovery stress and the internal stress of the SMA hybrid laminated beams. The efficiency and accuracy of the analytical solutions were expounded by comparing with the results from finite element analysis. It is found that buckling may or may not occur in the SMA hybrid laminated beam relying on the value of the pre-strain of the SMA wires. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigated the bending strength of girth-welded stainless steel circular hollow sections by numerical method. At first, finite element simulation of girth welding process was carried out to obtain the weld-induced residual stresses and deformations employing sequentially coupled three-dimensional thermo-mechanical finite element formulation. Then, nonlinear finite element analysis in which the moment versus end-rotation response, the ultimate moment resistance and the failure mode of the girth-welded circular hollow sections under pure bending were explored incorporating the residual stresses and depressions along with the initial global geometric imperfections was performed. Feasibility of adopting the current codified provisions (Eurocode 3) for stainless steel circular hollow sections in bending as the cross-section slenderness limit for girth-welded stainless steel circular hollow section flexural members was also examined. Results showed that the flexural behavior of girth-welded stainless steel circular hollow sections always involves local buckling near the girth weld on the compression side, which significantly affects the moment versus end-rotation behavior. Moreover, the results demonstrated that the Class 3 slenderness limit of 280 from Eurocode 3 for stainless steel circular hollow sections in flexure may be applied to girth-welded stainless steel circular hollow sections subjected to bending. [Copyright &y& Elsevier]

Cylindrical shell is a common structural design solution in many engineering fields, such as the foundation supporting structures and buoyant column of the offshore wind turbine in the maritime sector. Operating in an ocean environment, these cylindrical shell structures need to withstand a combination of axial compression, bending moment, torsion and external pressure. This study contributes a parametric investigation for unstiffened cylindrical shells subjected to axial compression. Emphasis is placed on the ultimate strength characteristics and their relation with the initial geometric imperfection. The nonlinear finite element method is adopted by considering geometric and material nonlinearities in conjunction with an arc-length incrementation to solve the governing equilibrium equation. The numerical prediction is compared with the prevailing code-based approach, i.e. DNV, ABS, API and Eurocode. This study shows that the ultimate strength of unstiffened cylindrical shells in axial compression is highly sensitive to initial geometric imperfection. The code-based formulae appear to be overly conservative for predicting the ultimate compressive strength of cylindrical shells. • Numerical collapse test of unstiffened cylindrical shell under axial compression. • Different imperfection shapes in longitudinal and circumferential directions are analysed. • Comparison is completed between the numerical prediction and code formulae. [ABSTRACT FROM AUTHOR]

This work presents an investigation on the compressive strain capacity of resisting buckling on an X80 steel corroded pipeline subjected to a bending moment using nonlinear finite element analysis (FEA) validated by full-scale tests. The modelling results indicate that the existing strain-based assessment method is not suitable for pipelines with deep corrosion and has certain application limitations. Consequently, a new evaluation method based on far-field strain was developed to predict the buckling failure of corroded pipelines subjected to bending loads. The influence of the corrosion shape type, corrosion size (i.e., depth d , length L , and width w), pipe geometry, and internal pressure on the critical buckling strain capacity and critical buckling moment of the pipeline were studied using parameter sensitivity analysis to verify the proposed strain criteria. The results illustrate that the variation trends between the critical buckling strain and the critical buckling moment with each factor were consistent, indicating that the proposed novel strain-based evaluation method is effective and applicable. In addition, the buckling resistance of a pipeline with rectangular corrosion is relatively weaker than that with a semi-spherical corrosion pit or cylindrical grooved corrosion under the same defect size. Further, the critical compressive strain capacity of a corroded pipeline is primarily affected by the depth and width of the corrosion, whereas the effect of the corrosion length is relatively insignificant. Moreover, the critical length and width of the corrosion defect affecting the bending capacity of resisting buckling were determined as L / D t = 20 and w / π D = 0. 5 , respectively. • A novel strain-based assessment method of local buckling of corroded pipelines. • Determined the effect of defect geometry on critical compressive strain capacity. • Determined the critical defect size that affect the pipe buckling strain capacity. [ABSTRACT FROM AUTHOR]

Abstract: The durability of thermal barrier coatings (TBCs) employed in most turbine engines is limited by delamination, both within the coating and at the coating–substrate interface. A test used for evaluating the mixed-mode toughness pertinent to such delaminations has been fully-analyzed by determining the steady-state energy release rate, the mode mixity and the critical length for buckling. An analytic solution based on beam theory establishes basic estimates and scaling relationships. Selected finite-element calculations have been used to affirm the fidelity of the results. The energy release rate attains steady-state, but the phase angle changes throughout because of a small (but significant) bending moment induced at the supports. The coating buckles at a critical delamination length, whereupon the energy release rate increases rapidly and violates steady state. The solutions are used to re-interpret measurements reported in the literature for an electron beam physically deposited TBC. [Copyright &y& Elsevier]

Abstract: The problem of buckling of the Euler–Bernoulli and Timoshenko beams is analyzed by the finite element method. Significant improvement in accuracy of the method is obtained by replacing the discontinuous function of the bending moment related to the approximation of the eigenfunction obtained by FEM by a “smoothed” function in the Rayleigh quotient. The smoothed function is obtained by fitting the discontinuous one using the least square technique. [Copyright &y& Elsevier]

Tubular steel towers are the most common design solution for supporting medium-to-high-rise wind turbines. Notwithstanding, historical failure incidence records reveal buckling modes as a common type of failure of shell structures. It is thus necessary to revisit the towers' performance against bending-compression interactions that could unchain buckling modes. The present investigation scrutinises buckling performances of a cylindrical steel shell under combined load, by means of the energy method. Within the proposed framework, the differential equations to obtain dimensionless expressions showed the energy-displacement relations taking place along the shell surface. Furthermore, shell models integrated with initial imperfection have been embedded into finite element algorithms based on the Riks method. The results show buckling evolution paths largely affected by bending moments lead to section distortions (oval-shaped) that in turn change the strain energy dissipation routine and section curvature. The shell geometrical parameters also show a strong influence on buckling effects seemingly linked to a noticeable reduction of the shell bearing capacity during the combined loading scenarios. [ABSTRACT FROM AUTHOR]

The current slenderness limits are significantly different in international design codes for cold-formed Circular Hollow Sections (CHS) under pure bending. This paper aims to use the Finite Element (FE) method to understand the behaviour of cold-formed CHS under pure bending and to propose new design rules. The model is calibrated by comparing its predicted load-deflection curves with previously published experimental data. In total, 21 specimens were modelled with diameter-to-thickness ratios ranging from 13 to 122. The current slenderness limits in the present international steel specifications were examined using the FE model and their suitability for cold-formed CHS is discussed. The effect of section slenderness on rotation capacity has been examined where the predicted variation of rotation capacity against section slenderness has been compared to the experimental results. A new equation for the amount of initial geometrical imperfection as a function of section slenderness has been developed and proposed for design purposes. The ovalisation deformation ratio and the critical strain at local buckling were determined and compared for compact, non-compact and slender sections. The progressive bending deformations of CHS at 10 critical steps have been presented and compared for the three cross sectional types, in particular at the maximum moment and bending rotation. In general, a good agreement has been obtained between the predicted strengths and ductilities using the current FE models and those of the experimental data of cold-formed CHS. • Using finite element method to determine the slenderness limit of cold-formed steel tubes and compared to the previous experimental results. • The effect of geometrical imperfections on the deformation cold-formed CHS has been examined. • The rotation capacity has been presented for CHS. • The ovalisation of compact, non-compact and slender section has been analysed. • The buckling mechanism has been analysed by using strain analysis, the critical strain at maximum moment has been determined and compared to the theoretical results. [ABSTRACT FROM AUTHOR]