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Stiffened plates have been widely used in civil, marine, aerospace engineering. As a kind of thin-walled structure operating in complex environment, stiffened plates mostly undergo a variety of dynamic loads, which may sometimes result in large-amplitude vibration. Additionally, initial stresses and geometric imperfections are widespread in this type of structure. Furthermore, it is universally known that initial stresses and geometric imperfections may affect mechanical behavior of structures severely, particularly in dynamic analysis. Thus, the purpose of this paper is to study the stress variation rule of a stiffened plate during large-amplitude vibration considering initial stresses and geometric imperfections.

The initial stresses are represented in the form of initial bending moments applying to the stiffened plate, while the initial geometric imperfections are considered by means of trigonometric series, and they are assumed existing in the plate along the z-direction exclusively. Then, the dynamic equilibrium equations of the stiffened plate are established using Lagrange’s equation as well as aforementioned conditions. The nonlinear differential equations of motion are simplified as a two-degree-of-freedom system by considering 1:2 and 1:3 internal resonances, respectively, and the multiscale method is applied to solve the equations.

The influence of initial stresses on the plate, stresses during internal resonance is remarkable, while that is moderate for initial geometric imperfections. (Upon considering the existence of initial stresses or geometric imperfections, the stresses of motivated modes are less than the primary mode for both and internal resonances). The influence of bidirectional initial stresses on the plate’s stresses during internal resonance is more remarkable than that of unidirectional initial stresses. The coupled vibration in 1%3A2 internal resonance is fiercer than that in internal resonance.

Stiffened plates are widely used in engineering structures. However, as a type of thin-walled structure, stiffened plates vibrate with large amplitude in most cases owning to their complicated operation circumstance. In addition, stiffened plates usually contain initial stresses and geometric imperfections, which may result in the variation of their mechanical behavior, especially dynamical behavior. Based on the above consideration, this paper studies the nonlinear dynamical behavior of stiffened plates with initial stresses and geometrical imperfections under different internal resonances, which is the originality of this work. Furthermore, the research findings can provide references for engineering design and application.

The purpose of this paper is to contribute to the solution of the buckling and resonance stability problems in inelastic beams and wooden plane trusses, taking into account geometric and material defects.

Two sources of non-linearity are analyzed, namely the geometrical non-linearity due to geometrical imperfections and material non-linearity due to material defects. The load-bearing capacity is obtained by the rheological-dynamical analogy (RDA). The RDA inelastic theory is used in conjunction with the damage mechanics to analyze the softening behavior with the scalar damage variable for stiffness reduction. Based on the assumed damages in the wooden truss, the corresponding external masses are calculated in order to obtain the corresponding fundamental frequencies, which are compared with the measured ones.

RDA theory uses rheology and dynamics to determine the structures' response, those results in the post-buckling branch can then be compared by fracture mechanics. The RDA method uses the measured P and S wave velocities, as well as fundamental frequencies to find material properties at the limit point. The verification examples confirmed that the RDA theory is more suitable than other non-linear theories, as those proved to be overly complex in terms of their application to the real structures with geometrical and material defects.

The paper presents a novel method of solving the buckling and resonance stability problems in inelastic beams and wooden plane trusses with initial defects. The method is efficient as it provides explanations highlighting that an inelastic beam made of ductile material can break in any stage from brittle to extremely ductile, depending on the value of initial imperfections. The characterization of the internal friction and structural damping via the damping ratio is original and effective.

Current procedures of buckling load estimation for thin-walled structures may provide very conservative estimates. Their refinement offers the potential to use structure and material properties more efficiently. Due to the large variety of design variables, for example laminate layup in composite structures, a prohibitively large number of tests would be required for experimental assessment, and thus reliable numerical techniques are of particular interest. The purpose of this paper is to analyze different methods of numerical buckling load estimation, formulate simulation procedures suitable for commercial software and give recommendations regarding their application. All investigations have been carried out for cylindrical composite shells; however similar approaches are feasible for other structures as well.

The authors develop a concept to apply artificial load imperfections with the aim to estimate as good as possible lower bounds for the buckling loads of shells for which the actual physical imperfections are not known. Single and triple perturbation load approach, global and local dynamic perturbation approach and path following techniques are applied to the analysis of a cylindrical composite shell with known buckling characteristics. Results of simulations are compared with published experimental data.

A single perturbation load approach is reproduced and modified. Buckling behavior for negative values of the perturbation load is examined and a pattern similar to a positive perturbation load is observed. Simulations with three perturbation forces show a decreased (i. e. more critical) value of the buckling load compared to the single perturbation load approach. Global and local dynamic perturbation approaches exhibit a behavior suitable for lower bound estimation for structures with arbitrary geometries.

Various load imperfection approaches to buckling load estimation are validated and compared. All investigated methods do not require knowledge of the real geometrical imperfections of the structure. Simulations were performed using a commercial finite element code. Investigations of sensitivity with respect to a single perturbation load are extended to the negative range of the perturbation load amplitude. A specific pattern for a global perturbation approach was developed, and based on it a novel simulation procedure is proposed.

Several experimental and numerical studies were performed in the past to estimate buckling capacity of corroded tubular members. However, the effect of initial imperfections has not been properly considered in most of these earlier proposed formulas. Therefore, the main objective of this paper is to propose an accurate analytical formula to determine the buckling capacity of patched corroded tubular members.

Tubular members with initial geometrical imperfections can be regarded as beam-columns because of the combination of axial load and bending moment. The proposed formula is derived for a rectangular corrosion patch. The proposed formula is verified with results from finite element analysis of corroded tubular members and experimental results. The formula is also applied to an existing offshore jacket structure to highlight its significance and applicability. It is found that the buckling capacity of jacket members in splash zone reduces significantly with ageing. This reduction is around 29 and 14% for the selected brace and leg member respectively, during the design life. Finally, it is concluded that corrosion reduces the buckling capacity significantly and the proposed formula can be easily applied by practicing engineers to give an accurate and slightly conservative estimate the remaining buckling capacity.

The main finding is the new formula which accurately and conservatively estimate the buckling capacity of corroded tubular members. The proposed formula considers the secondary effect of both initial geometrical imperfections and shifting of centroid because of corrosion.

The proposed new formula is unique and original in that it considers both secondary effects from geometrical imperfections, reduction of cross-section from corrosion wastage and shifting of centroid because of corrosion. Finally, it is concluded that corrosion reduces the buckling capacity significantly and the proposed formula can be easily applied by practicing engineers to conservatively estimate the remaining buckling capacity and verify if further, more advanced estimations are needed.

The purpose of this paper is to derive knockdown factor functions in terms of a shell thickness ratio (i.e. the ratio of radius to thickness) for conventional orthogrid and hybrid-grid stiffened cylinders for the lightweight design of space launch vehicles.

The shell knockdown factors of grid-stiffened cylinders under axial compressive loads are derived numerically considering various shell thickness ratios. Two grid systems using stiffeners – conventional orthogrid and hybrid-grid systems – are used for the grid-stiffened cylinders. The hybrid-grid stiffened cylinder uses major and minor stiffeners having two different cross-sectional areas. For modeling grid-stiffened cylinders with various thickness ratios, the effective thickness (t_eff) of the cylinders is kept constant, and the radius of the cylinder is varied. Thickness ratios of 100, 192 and 300 are considered for the orthogrid stiffened cylinder, and 100, 160, 200 and 300 for the hybrid-grid stiffened cylinder. Postbuckling analyses of grid-stiffened cylinders are conducted using a commercial nonlinear finite element analysis code, ABAQUS, to derive the shell knockdown factor. The single perturbation load approach is applied to represent the geometrical initial imperfection of a cylinder. Knockdown factors are derived for both the conventional orthogrid and hybrid-grid stiffened cylinders for different shell thickness ratios. Knockdown factor functions in terms of shell thickness ratio are obtained by curve fitting with the derived shell knockdown factors for the two grid-stiffened cylinders.

For the two grid-stiffened cylinders, the derived shell knockdown factors are all higher than the previous NASA’s shell knockdown factors for various shell thickness ratios, ranging from 100 to 400. Therefore, the shell knockdown factors derived in this study may facilitate in the development of lightweight structures of space launch vehicles from the aspect of buckling design. For different shell thickness ratios of up to 500, the knockdown factor of the hybrid-grid stiffened cylinder is higher than that of the conventional orthogrid stiffened cylinder. Therefore, it is concluded that the hybrid-grid stiffened cylinder is more efficient than the conventional orthogrid-stiffened cylinder from the perspective of buckling design.

The obtained knockdown factor functions may provide the design criteria for lightweight cylindrical structures of space launch vehicles.

Derivation of shell knockdown factors of hybrid-grid stiffened cylinders considering various shell thickness ratios is attempted for the first time in this study.

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.

This paper aims to present results from numerical studies on the response of fire exposed composite girders subjected to dominant flexural and shear loading. A finite element-based numerical model was developed to trace the thermal and structural response of composite girders subjected to simultaneous structural loading and fire exposure. This model accounts for various critical parameters including material and geometrical nonlinearities, property degradation at elevated temperatures, shear effects, composite interaction between concrete slab and steel girder, as well as temperature-induced local buckling. To generate test data for validation of the model, three composite girders, each comprising of hot-rolled (standard) steel girder underneath a concrete slab, were tested under simultaneous fire and gravity loading.

The validated model was then applied to investigate the effect of initial geometric imperfections, load level, thickness of slab and stiffness of shear stud on fire response of composite girders.

Results from experimental and numerical analysis indicate that the composite girder subjected to flexural loading experience failure through flexural yielding mode, while the girders under shear loading fail through in shear web buckling mode. Further, results from parametric studies clearly infer that shear limit state can govern the response of fire exposed composite girders under certain loading configuration and fire scenario.

This paper presents results from numerical studies on the response of fire exposed composite girders subjected to dominant flexural and shear loading.

Steel beams composed of cold-formed sections are common in buildings because of their lightness and ability to support large spans. However, the instability phenomena associated to these members are not completely understood in fire situation. Thus, the purpose of this study is to analyse the behaviour of beams composed of cold-formed lipped channel sections at elevated temperatures.

A numerical analysis is made, applying the finite element program SAFIR, on the behaviour of simply supported cold formed steel beams at elevated temperatures. A parametric study, considering several cross-sections with different slenderness’s values, steel grades and bending diagrams, is presented. The obtained numerical results are compared with the design bending resistances determined from Eurocode 3 Part 1-2 and its French National Annex (FN Annex).

The current design expressions revealed to be too conservative when compared with the obtained numerical results. It was possible to observe that the FN Annex is less conservative than the Annex E, the first having a better agreement with the numerical results.

Following the previous comparisons, new fire design formulae are tested. This new methodology, which introduces minimum changes in the existing formulae, provides safety and accuracy at the same time when compared to the numerical results, considering the occurrence of local, distortional and lateral torsional buckling phenomena in these members at elevated temperatures.

Sigma cross-section profiles are often chosen for their lightness and ability to support large spans, offering a favourable bending resistance. However, they are more susceptible to local, distortional and lateral-torsional buckling, as possible failure modes when compared to common I-sections and hollow cross-sections. However, the instability phenomena associated to these members are not completely understood in fire situation. Therefore, the purpose of this study is to analyse the behaviour of beams composed of cold-formed sigma sections at elevated temperatures.

This study presents a numerical analysis, using advanced methods by applying the finite element software SAFIR. A numerical analysis of the behaviour of simply supported cold-formed sigma beams in the case of fire is presented considering different cross-section slenderness values, elevated temperatures, steel grades and bending moment diagrams. Comparisons are made between the obtained numerically ultimate bending capacities and the design bending resistances from Eurocode 3 Part 1–2 rules and its respective French National Annex (FN Annex).

The current design expressions revealed to be over conservative when compared with the obtained numerical results. It was possible to observe that the FN Annex is less conservative than the general prescriptions, the first having a better agreement with the numerical results.

Following the previous comparisons, new fire design formulae are analysed. This new methodology, which introduces minimum changes in the existing formulae, provides at the same time safety and accuracy when compared to the numerical results, considering the occurrence of local, distortional and lateral-torsional buckling phenomena in these members at elevated temperatures.

In the inelastic stability analysis of plated structures, incremental‐iterative finite element methods sometimes encounter prohibitive solution difficulties in the vicinity of sharp limit points, branch points and other regions of abrupt non‐linearity. Presents an analysis system that attempts to trace the non‐linear response associated with these types of problems at minor computational cost. Proposes a semi‐heuristic method for automatic load incrementation, termed the adaptive arc‐length procedure. This procedure is capable of detecting abrupt non‐linearities and reducing the increment size prior to encountering iterative convergence difficulties. The adaptive arc‐length method is also capable of increasing the increment size rapidly in regions of near linear response. This strategy, combined with consistent linearization to obtain the updated tangent stiffness matrix in all iterative steps, and with the use of a “minimum residual displacement” constraint on the iterations, is found to be effective in avoiding solution difficulties in many types of severe non‐linear problems. However, additional procedures are necessary to negotiate branch points within the solution path, as well as to ameliorate convergence difficulties in certain situations. Presents a special algorithm, termed the bifurcation processor, which is effective for solving many of these types of problems. Discusses several example solutions to illustrate the performance of the resulting analysis system.