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The purpose of this paper is to analyze the inelastic buckling of a rectangular thin flat isotropic plate subjected to uniform uniaxial in-plane compression using a work principle, a deformation plasticity theory and Taylor–Maclaurin series formulation.

The non-loaded longitudinal edges of the rectangular plate are clamped, whereas the loaded edges are simply supported (CSCS). Total work error function is applied to Stowell’s plasticity theory in the derivation of the inelastic buckling equation. Mathematical formulation of the Taylor–Maclaurin series deflection function satisfied the boundary conditions of the CSCS rectangular plate. The critical inelastic load of the plate is then derived by applying variational principles.

Values of the plate buckling coefficient are calculated using various values of moduli ratio for aspect ratios ranging from 0.1 to 1.0, in intervals of 0.1. The accuracy of the proposed technique is validated by comparing the results obtained in the present study with solutions from a previous investigation. The percentage differences in the values of the buckling coefficient ranged from −0.122 to −4.685 per cent.

The results indicate that the work principle approach can be used as an alternative approximate method for analyzing inelastic buckling of rectangular thin flat isotropic plates under uniform in-plane compressive loads.

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.

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.

Concrete arch structures are commonly constructed for various civil engineering applications. Despite their frequent use, there is a lack of research on the response and performance of concrete arches when subjected to fire loading. Hence, this paper aims to investigate the response and in-plane failure modes of shallow circular concrete arches subjected to mechanical and fire loading.

This study is conducted through the development of a three-dimensional finite element (FE) model in ANSYS. The FE model is verified by comparison to a non-discretisation numerical model derived herein and the reduced modulus buckling theory, both used for the non-linear inelastic analysis of shallow concrete arches subjected to uniformly distributed radial loading and uniform temperature field. Both anti-symmetric and symmetric buckling modes are examined, with analysis of the former requiring geometric imperfection obtained by an eigenvalue buckling analysis.

The FE results show that anti-symmetric bifurcation buckling is the dominant failure mode in shallow concrete arches under mechanical and fire loading. Additionally, parametric studies are presented which illustrate the influence of various parameters on fire resistance time.

Fire response of concrete arches has not been reported in the open literature. The authors have previously investigated the stability of shallow concrete arches subjected to mechanical and uniform thermal loading. It was found that temperature greatly reduced the buckling loads of concrete arches. However, this study was limited to the simplifying assumptions made which include elastic material behaviour and uniform temperature loading. The present study provides a realistic insight into the fire response and stability of shallow concrete arches. The findings herein may be adopted in the fire design of shallow concrete arches.

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.

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 is given. The bibliography at the end of the paper contains 1,726 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 1996‐1999.

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

The main function of the castellation process is making I-sections stiffer by increasing the height of web and supplying a higher moment capacity of primary axis than plain-webbed members of the same weight. In addition, it optimizes the use of heavy, costly constructional steel material and provides good services accessibility. The purpose of this study was to investigate the strength and buckling behavior of axially loaded castellated cruciform steel columns using finite element analysis. Although a significant body of research exists on the failure of different columns, there is no proper criterion introduced to determine the point of buckling in the equilibrium path of an imperfect column.

This paper considers a wide range of practical geometric dimensions and various end conditions using ANSYS software. Findings are reported for about 224 samples of castellated cruciform I-shaped sections, and a simplified approach to evaluate buckling capacity of castellated columns, using the slenderness-load curve, is developed. In addition, the axial compressive capacities of those steel sections are investigated numerically in the current study.

The results of nonlinear analyses of these columns revealed that the load-carrying capacity of castellated cruciform steel columns far outweighs and is more appropriate than that of the traditional cruciform steel columns. In the present paper, new geometric criteria have been introduced having the ability to cover different types of columns. It shows the critical load of columns in the range of elastic and inelastic behavior.

This study can provide a background for practical engineering applications and design specifications for steel structures with castellated sections. In the present paper, new geometric criteria have been introduced having the ability to cover different types of columns. It shows the critical load of columns showing both elastic and inelastic behavior. Because this method showed reliable performance, it can be used during experimental tests for detecting buckling point.

This study can provide background for practical engineering applications and design specifications for steel structures with castellated sections; also, a physical criterion has been defined for calculating the buckling load of real columns.

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.

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.