• Smart Structures and Systems
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• v.25 no.4
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• pp.447-457
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• 2020

In this study, a simple two-dimensional shear deformation model is employed for buckling analysis of functionally graded (FG) plates. The proposed theory has a kinematic with integral terms which considers the influence of shear deformation without using "shear correction factors". The impact of varying material properties and volume fraction of the constituent on buckling response of the FG plate is examined and discussed. The benefit of this theory over other contributions is that a number of variables is reduced. The basic equations that consider the influence of transverse shear stresses are derived from the principle of virtual displacements. The analytical solutions are obtained utilizing the "Navier method". The accuracy of the proposed theory is proved by comparisons with the different solutions found in the literature.

• Advances in aircraft and spacecraft science
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• v.5 no.6
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• pp.615-632
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• 2018

Mechanical buckling of a rectangular functionally graded plate is obtained in the current paper using a refined higher-order shear and normal deformation theory. The impact of transverse normal strain is considered. The material properties are microscopically inhomogeneous and vary continuously based on a power law form in spatial direction. Navier's procedure is applied to examine the mechanical buckling behavior of a simply supported FG plate. The mechanical critical buckling subjected to uniaxial and biaxial compression loads are determined. The numerical investigation are compared with the numerical results in the literature. The influences of geometric parameters, power law index and different loading conditions on the critical buckling are studied.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.689-696
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• 2006

This paper deals with the geometrical non-linear analyses of the buckled columns. Differential equations governing elasticas of the buckled columns are derived, in which both effects of taper type and shear deformation are included. Three kinds of taper types such as breadth, depth and square tapers are considered. Differential equations are solved numerically to obtain the elasticas and buckling loads of such columns. End constraint of both clamped ends and both hinged ends are considered. The effects of shear deformation on the elastica of the buckled column and buckling load of column are investigated extensively. Experimental studies are presented that complement theoretical results of non-linear responses of the elasticas.

• Smart Structures and Systems
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• v.21 no.4
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• pp.397-405
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• 2018

In this paper, a novel simple shear deformation theory for buckling analysis of single layer graphene sheet is formulated using the nonlocal differential constitutive relations of Eringen. The present theory involves only three unknown and three governing equation as in the classical plate theory, but it is capable of accurately capturing shear deformation effects, instead of five as in the well-known first shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). A shear correction factor is, therefore, not required. Nonlocal elasticity theory is employed to investigate effects of small scale on buckling of the rectangular nano-plate. The equations of motion of the nonlocal theories are derived and solved via Navier's procedure for all edges simply supported boundary conditions. The results are verified with the known results in the literature. The influences played by Effects of nonlocal parameter, length, thickness of the graphene sheets and shear deformation effect on the critical buckling load are studied. Verification studies show that the proposed theory is not only accurate and simple in solving the buckling nanoplates, but also comparable with the other higher-order shear deformation theories which contain more number of unknowns.

• Steel and Composite Structures
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• v.46 no.1
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• pp.75-92
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• 2023

The novel composite cold-formed steel (CFS)/engineered cementitious composites (ECC) beams have been recently presented. The new composite section exhibited superior structural performance as a flexural member, benefiting from the lightweight thin-walled CFS sections with improved buckling and torsional properties due to the restraints provided by thinlayered ECC. This paper investigated the shear performance of the new composite CFS/ECC section. Twenty-eight simply supported beams, with a shear span-to-depth ratio of 1.0, were assembled back-to-back and tested under a 3-point loading scheme. Bare CFS, composite CFS/ECC utilising ECC with Polyethylene fibres (PE-ECC), composite CFS/MOR, and CFS/HSC utilising high-strength mortar (MOR) and high-strength concrete (HSC) as replacements for PE-ECC were compared. Different failure modes were observed in tests: shear buckling modes in bare CFS sections, contact shear buckling modes in composite CFS/MOR and CFS/HSC sections, and shear yielding or block shear rupture in composite CFS/ECC sections. As a result, composite CFS/ECC sections showed up to 96.0% improvement in shear capacities over bare CFS, 28.0% improvement over composite CFS/MOR and 13.0% over composite CFS/HSC sections, although MOR and HSC were with higher compressive strength than PE-ECC. Finally, shear strength prediction formulae are proposed for the new composite sections after considering the contributions from the CFS and ECC components.

• Structural Engineering and Mechanics
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• v.87 no.3
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• pp.283-296
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• 2023

Free-vibration and buckling analyses of plate problems are investigated with the aid of the strain gradient notation finite element method (SGN-FEM). As SGN-FEM employs physically interpretable polynomials in developing finite elements, parasitic shear sources, which are the cause of shear locking, can be precisely identified and subsequently eliminated. This allows two mutually complementary objectives to be defined in this work, namely, evaluate the efficiency of free-vibration and buckling results provided by corrected models, and study the severity of parasitic shear effects on plate models performance. Parasitic shear are flexural terms erroneously present in shear strain polynomials. It is reviewed here that six parasitic shear terms arise during the formulation of the four-node Mindlin plate element. Two parasitic shear terms have been identified in the in-plane shear strain polynomial while other two have been identified in each of the transverse shear strain polynomials. The element is corrected a-priori, i.e., during development, by simply removing the spurious terms from the shear strain polynomials. The computational implementation of the element in its two versions, namely, containing the parasitic shear terms (PS) and corrected for parasitic shear (SG), allows for assessments of the accuracy of results and of the deleterious effects of parasitic shear in free vibration and buckling analyses. This assessment of the parasitic shear effects is a novelty of this work. Validation of the SG model is done comparing its results with analytical results and results provided by other numerical procedures. Analyses are performed for square plates with different thickness-to-length ratios and boundary conditions. Results for thin plates provided by the PS model do not converge to the correct solutions, which indicates that parasitic shear must be eliminated. That is, analysts should not rely on refinement alone. For thick plates, PS model results can be considered acceptable as deleterious effects are really critical in thin plates. On the other hand, results provided by the SG model converge well for both thin and thick plates. The effectiveness of the SG model is established via high-accuracy results obtained in several examples. It is concluded that corrected SGN-FEM models are efficient alternatives for free-vibration and buckling analysis of Mindlin plate problems, and that precise elimination of parasitic shear is a requirement for sound analyses.

• Structural Engineering and Mechanics
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• v.9 no.5
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• pp.417-432
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• 2000

A comprehensive analytic study has been conducted to investigate the instability problems of metal-plate-connected (MPC) joints in light frame trusses. The primary objective in this study is to determine the governing factors that constitute the buckling of the metal connectors and their effects on the structural response of joints. Another objective is to recommend design curves for the daily structural design of these joints. The numeric data presented in this paper has emerged from a broad base that was founded on over 350 advanced computer simulations, and was supported by available experimental results obtained by others. This basic-to-applied research includes practical engineering parameters such as size of gaps, shear lengths, gauge (plate thickness) of connectors, size of un-braced areas, failure modes, and progressive disintegration of joints. Square-end members have been emphasized though the results cover the custom-made fitted joints. The results indicate that chord shears cause and dominate the buckling of MPC joints, and the shear length has a more pronounced effect than the size of gaps. Further, large gauges and small un-braced areas improve the buckling response. Several practical recommendations have been suggested throughout the paper such as keeping the ratio of gap/shear length below 3/4 for improving the buckling strength. The study reveals that multi-area joints should not be simplified as single web-to-chord MPC joints such as keeping the ratio of gap/shear length below 3/4 for improving the buckling strength, even where one web is in tension and the other in compression. Finally, the results obtained from this study favorably agree with experimental data by others, and the classic buckling theories for other structural components.

• Journal of Korean Society of Steel Construction
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• v.15 no.5 s.66
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• pp.591-601
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• 2003

Because of their high out-of-plane and in-planes strength, trapezoidally corrugated plates have been increasingly used in buildings and bridges. If corrugated plates are used as the web of plate girders or prestressed concrete box girders, the flanges take most of the bending stress. On the other hand, the corrugated plate web supports shear stress due to the accordion effect. The corrugated plate web could fail by three different buckling modes: global, local, or interactive shear buckling. To determine the effects of geometric parameters on the buckling capacity of the corrugated plates, a parametric study was performed using finite dement method. The analysis results showed that the buckling capacity and modes depend on individual parameters as well as combinations of parameters.

• Journal of Korean Association for Spatial Structures
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• v.21 no.4
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• pp.57-64
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• 2021

This paper conducted a comparative analysis of the shear buckling characteristics of trapezoidal and sinusoidal corrugated steel plates considering of their initial imperfection. Initial imperfection refers to the state where the shape of the corrugated plate is initially not perfect. As such, an initially imperfect shape was assumed using the eigen buckling mode. To calculate the buckling stress of corrugated steel plates, the linear buckling analysis used a boundary condition which was applied to the plate buckling analysis. For the comparison of trapezoidal and sinusoidal corrugation, the shape parameters were assumed using the case where the length and slope of each corrugation were the same, and the initial imperfection was considered to be from 0.1% to 5% based on the length of the steel plate. Here, for the buckling analysis, ANSYS, a commercial FEA program, was used. From the results of buckling analysis, the effect of overall initial imperfection showed that the larger the initial imperfection, the lower the buckling stress. However, in the very thin model, interaction or local buckling was dominant in the perfect shape, and in this case, the buckling stress did not decrease. Besides, the sinusoidal model showed higher buckling stress than the trapezoidal one, and the two corrugation shapes decreased in a similar way.

• Structural Engineering and Mechanics
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• v.42 no.6
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• pp.867-882
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• 2012

Analytical (Rayleigh-Ritz method) and numerical studies are carried out and buckling interaction curves are developed for simply supported plates of varying aspect ratios ranging from 1 to 5, under the combined action of in-plane shear and tension. A multi-step buckling procedure is employed in the Finite Element (FE) model instead of a regular single step analysis in view of obtaining the buckling load under the combined forces. Both the analytical (classical) and FE studies confirm the delayed shear buckling characteristics of thin plate under the combined action of shear and tension. The interaction curves are found to be linear and are found to vary with plate aspect ratio. The interaction curve developed using Rayleigh-Ritz method is found to deviate in an increasing trend from that of validated FE model as plate aspect ratio is increased beyond value of 1. It is found that the observed deviation is due to the insufficient number of terms that is been considered in the assumed deflection function of Rayleigh-Ritz method and a convergence study is suggested as a solution.