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The problems of inelastic instability (buckling) and dynamic instability (resonance) have been the subject of extensive investigation and have received wide attention from the structural mechanics community. This paper aims to tackle these problems in thin-walled structures, taking into account geometrical and/or material non-linearity.

The inelastic buckling mode interactions and resonance instabilities of prismatic thin-walled columns are analysed by implementing the semi-analytical finite strip method (FSM). A scalar damage parameter is implemented in conjunction with a material modelling named rheological-dynamical analogy to address stiffness reduction induced by the fatigue damage.

Inelastic buckling stresses lag behind the elastic buckling stresses across all modes, which is a consequence of the viscoelastic behaviour of materials. Because of the lag, the same column length does not always correspond to the same mode at the elastic and inelastic critical stress.

This paper presents the influence of mode interactions on the effective stresses and resonance instabilities in thin-walled columns due to the fatigue damage. These mode interactions have a great influence on damage variables because of the fatigue and effective stresses around mode transitions. In its usual semi-analytical form, the FSM cannot be used to solve the mode interaction problem explained in this paper, because this technique ignores the important influence of interaction of the buckling modes when applied only for undamaged state of structure

This study aimed to overcome the challenging issues involved in providing high-precision eigensolutions. The accurate prediction of the buckling load bearing capacity under different crack damage locations, sizes and numbers, and analysing the influence mechanism of crack damage on buckling instability have become the needs of theoretical research and engineering practice. Accordingly, a finite element method was developed and applied to solve the elastic buckling load and buckling mode of curved beams with crack damage. However, the accuracy of the solution depends on the quality of mesh, and the solution inevitably introduces errors due to mesh. Therefore, the adaptive mesh refinement method can effectively optimise the mesh distribution and obtain high-precision solutions.

For the elastic buckling of circular curved beams with cracks, the section damage defect analogy scheme of a circular arc curved beam crack was established to simulate the crack size (depth), position and number. The h-version finite element mesh adaptive analysis method of the variable section Euler–Bernoulli beam was introduced to solve the elastic buckling problem of circular arc curved beams with crack damage. The optimised mesh and high-precision buckling load and buckling mode solutions satisfying the preset error tolerance were obtained.

The results of testing typical examples show that (1) the established section damage defect analogy scheme of circular arc curved beam crack can effectively realise the simulation of crack size (depth), position and number. The solution strictly satisfies the preset error tolerance; (2) the non-uniform mesh refinement in the algorithm can be adapted to solve the arbitrary order frequencies and modes of cracked cylindrical shells under the conditions of different ring wave numbers, crack positions and crack depths; and (3) the change in the buckling mode caused by crack damage is applicable to the study of elastic buckling under various curved beam angles and crack damage distribution conditions.

This study can provide a novel strategy for the adaptive mesh refinement for finite element analysis of elastic buckling of circular arc curved beams with crack damage. The adaptive mesh refinement method established in this study is fundamentally different from the conventional finite element method which employs the user experience to densify the meshes near the crack. It can automatically and flexibly generate a set of optimised local meshes by iteratively dividing the fine mesh near the crack, which can ensure the high accuracy of the buckling loads and modes. The micro-crack in curved beams is also characterised by weakening the cross-sectional stiffness to realise the characterisation of locations, depths and distributions of multiple crack damage, which can effectively analyse the disturbance behaviour of different forms of micro-cracks on the dynamic behaviour of beams.

A new approach to the problem of minimum‐weight design of stiffened compression panels is presented. It is predominantly based on the plate instability mode in which the sheet and stiffeners, having been stressed to the same degree, simultaneously buckle over a long wavelength with the length of a buckle equal to the pin‐ended length of a panel. Charts to determine the buckling stresses of the modes required for the minimum‐weight design are given. Formulae and charts are presented to compute the effective moment of inertia of a stiffener, a most important quantity, over a wide range of panel proportions, for Z‐section and integrally machined unflanged stiffeners. The principles of minimum‐weight design are discussed and illustrated by the lightest Z‐stiffener panels selected from extensive test data. Comparison of the theoretical stresses of the optimum panels and many other panels of different proportions with those obtained by tests shows good agreement. The principle of dimensional similarity, which is implicit in the buckling mode referred to above, eliminates the effects of size. Results obtained either from theory or tests can therefore be applied to different size panels of like proportions.

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.

Experimental mid/large scale testing of ship-like stiffened panels in compression is a quite expensive exercise that is not standard. Numerical simulations are preferred instead. Because of being relatively inexpensive (cost and time wise), most authors perform an exhaustive design space exploration arriving at a significant number of runs. This work demonstrates that the buckling response with respect to the nondimensional slenderness ratios may well be fitted with nine runs per stiffener geometry.

Efficient derivation of buckling strength formulas for stiffened panels through the employment of design of experiments (DoE) and response surface methodology (RSM) combined with numerical nonlinear experimentation over the entire range of practical geometries.

The surrogate model developed for T-bar stiffeners predicts accurately enough the ultimate stress in the practical design area, while the surrogate models for angle bars and flat bars demonstrate difference between 10 and 30% from common structural rules (CSR).

To the authors' best knowledge, the statistical-based formal and rigorous approach of DoE and RSM to obtaining buckling surfaces for stiffened panels is performed for the first time. The number of required observations per stiffener type has not been addressed yet as each work selects its own sampling scheme without formal reasoning. This work comes to frame the number of observations for efficient surrogate model building.

It is generally known that the perforated section such as the castellated section is good to sustain distributed loads but inadequate to sustain highly concentrated loads. Therefore, it is possible to design the opening in a different arrangement of web opening to achieve section efficiency, thus improving the strength and torsional behaviour of the section with web opening. This study aims to focus on the finite element analysis of I-beam with and without openings in steel section dominated to lateral-torsional buckling behaviour.

In this work, the analysis of different sizes, shapes and arrangements of web opening is performed by using LUSAS application to conduct numerical analysis on lateral-torsional buckling behaviour. This involves three diameter sizes of web opening, five types of opening shapes and two criteria of the model.

The section with c-hexagon web opening was placed about 200-mm centre to centre and 100-mm edge distance, contribute to 7.26% increase of buckling capacity. For the section with 150-mm centre to centre and 50-mm edge distance, the occurrence of local buckling contributes to decrease of lateral buckling section capacity to 19.943 kNm, where pure lateral-torsional buckling mostly occurred because of prevented section. Besides that, the web opening diameter was also analysed. The web crippling was observed because of the increase of opening diameter from 0.67 to 0.80 D.

This contributes to a decrease in buckling capacity as figured in the contour of the deformed shape. For Model 1, an increase of buckling capacity (31.46%) is observed when the opening diameter are changed from 0.67 to 0.80 D.

The objective of this paper is to investigate numerically the buckling behavior of submersible composite cylinders.

By means of FEM and golden section method, the search of hoop winding layers, longitudinal winding layers and helical winding layers are studied to optimize the buckling pressure. Considering the mid-strengthening cylinder, the size and distribution of stiffeners are studied systematically.

The results show that laying the hoop winding layers in the two outer sidewalls and the longitudinal winding layers in the middle of the shell is helpful to increase the buckling pressure, and the optimal helical winding angle changes with slenderness ratio.

For mid-strengthening cylinder, the effect of helical winding angle of stiffener on buckling pressure becomes weak gradually with the increase of stiffener thickness. With the increasing of the spacing between stiffeners, the buckling pressure increases first and decreases later. What is more, the mid-strengthening cylinder is less sensitive to the initial geometric imperfections than unstiffened shells.

Due to the enormous increase in economic development, structural steel material gives an advantage for the construction of stadiums, factories, bridges and cities building design. The purpose of this study is to investigate the behaviour of bending, buckling and torsion for I-beam steel section with and without web opening using non-linear finite element analysis.

The control model was simulated via LUSAS software with the four main parameters which included opening size, layout, shape and orientation. The analysis used a constant beam span which is 3.5 m while the edge distance from the centre of the opening to the edge of the beam is kept constant at 250 mm at each end.

The analysis results show that the optimum opening size obtained is 0.65 D while optimum layout of opening is Layout 1 with nine web openings. Under bending behaviour, steel section with octagon shapes of web opening shows the highest yield load, yield moment and thus highest structural efficiency as compared to other shapes of openings. Besides, square shape of web opening has the highest structural efficiency under buckling behaviour. The lower buckling load and buckling moment contribute to the higher structural efficiency.

Further, the square web opening with counter clockwise has the highest structural efficiency under torsion behaviour.

Recently, this steel section has found increasing popularity in residential, industrial and commercial buildings with their high load-carrying capacity due to the nature of high strength to weight ratio properties. However, the rise on the price of steel section should be more emphasized; therefore, the optimization in steel section design is needed to overcome the issue of material cost. As such, tapered steel sections save on material use, while the introduction of web openings allows the placement of mechanical and electrical services, plumbing and also aesthetic design considerations.

The purpose of this study is to investigate the lateral torsional buckling behavior of a tapered steel section with an ellipse-shaped opening by analyzing its structural parameters. To achieve this, the finite element analysis (FEA) of the section is modeled using LUSAS software, which allows for a detailed analysis of the section's behavior under varying loads and conditions. It involves the variation in web opening size, opening layout, opening rotation angle and the tapering ratio. Eigenvalue buckling analysis is adopted to know the parametric effects of each 108 model. The size of opening varies from 0.2 to 0.5 d of the total depth where the opening located. There are three type of layouts applied in this study, which are the layouts A, B and C. There are three types of rotation angles for the ellipse-shaped opening, including the non-rotated vertical opening and two additional types formed by rotating the opening 45 degrees clockwise and counterclockwise around the center-point of the ellipse. A fixed-free boundary condition was applied, resulting in a simulation of a cantilever beam. The models are fixed at one end with a larger depth, and free at the other end with a smaller depth. Loading condition is an application of 10 kN/m uniform distributed load in the direction of gravity along the mid-span of the top flange.

It is observed that the model 82 with Layout A, tapering ratio 0.3, opening size 0.5 d and opening rotated in 45 degree anti-clockwise direction results in the highest structural efficiency among the 108 models. Therefore, the buckling moment of model 82 is 1,013.08 kNm with structural efficiency of 481.26, which shows an increase of 3.17% compared to the controlled model.

The FEA results shows a significant increase in ductility and stiffness of the tapered steel section with elipse shape opening and consequently changes in the behaviour of yield point.

The purpose of this paper is to describe the results of a combined numerical and experimental study into the ability of supersonic particle deposition (SPD) to restore the load carrying capacity of rib stiffened wing planks with simulated stress corrosion cracking (SCC).

In this context the experimental results reveal that SCC can result in a dramatic reduction in the load carrying capacity of the structure and catastrophic failure via cracking that tears the length of the structure through buckling. A combined numerical and experimental study then reveals how this reduction, in the load carrying capacity can be overcome by using SPD.

This paper is the first to show that SPD can be used to restore the load carrying capacity of rib stiffened structures with SCC. It also shows that SPD repairs can be designed to have only a minimal effect on the local stiffness and hence on the load path. However, care should be taken to ensure that the design is such that premature failure of the SPD does not occur.

This is the first paper to show that a thin layer of SPD deposited 7,075 aluminium alloy powder on either side of the SCC-simulated stiffener has the potential to restore the load carrying capability of a rib stiffened structure. As such it represents an important first step into establishing the potential for SPD to restore the buckling strength of rib stiffened wing panels containing SCC.