Stability analysis of simply-supported rectangular plates under non-uniform uniaxial compression using rigorous and approximate plane stress solutions

Jana, Prasun; Bhaskar, K.

doi:10.1016/j.tws.2006.04.009

Cited by 59 publications

(23 citation statements)

References 10 publications

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“…To satisfy the stress-free constraints, the admissible functions X p (ξ), Y q (η) in function Φ 1 (ξ, η) are expanded using Legendre polynomials and are given as [16,26,27],…”

Section: Legendre Polynomialsmentioning

confidence: 99%

Buckling analysis and optimisation of variable angle tow composite plates

Wu¹,

Weaver²,

Raju³

et al. 2012

Thin-Walled Structures

251

143

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Variable Angle Tow (VAT) placed composite laminates, where the fibre orientations continuously varying over the plane of each ply, generally exhibit variable stiffness properties. The stiffness tailoring of VAT plates through the design of fibre orientation distributions can substantially improve the buckling resistance, which is mainly due to the benign, non-uniform, in-plane load redistribution. In this work, a new mathematical definition is proposed to represent the general variation of fibre-orientation in the VAT plate. In this definition, the coefficients of polynomials are directly equal to the designed fibre angles at pre-selected control points. A Rayleigh-Ritz approach is used to determine the prebuckling loads distributions and critical buckling load of VAT plates. It provides a more efficient means to evaluate the buckling load of VAT laminates, compared with other numerical solutions. Subsequently, preliminary optimisation of VAT plates for maximum buckling load is done using the proposed definition of nonlinear variation of fibre angles. Results obtained for simply supported square VAT plates are compared with optimal results reported in the literature. Finally, long VAT plates with one free edge and others simply supported are studied to demonstrate the viability of the proposed modelling strategy

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“…To satisfy the stress-free constraints, the admissible functions X p (ξ), Y q (η) in function Φ 1 (ξ, η) are expanded using Legendre polynomials and are given as [16,26,27],…”

Section: Legendre Polynomialsmentioning

confidence: 99%

Buckling analysis and optimisation of variable angle tow composite plates

Wu¹,

Weaver²,

Raju³

et al. 2012

Thin-Walled Structures

251

143

View full text Add to dashboard Cite

show abstract

“…Similarly, it can be observed that the shear stiffness coefficient (K s ) exerts a greater influence on the critical buckling load factor in comparison with the transverse stiffness coefficient (K w )whereas increasingK s can increase the critical buckling mode. (2) 34.748 (2) 34.748 (2) 27.768 (2) 8.261 (1) 8.261 (1) 5.488 (1) 5.488 (1) 2.667 (1) α = 0.5 60.533 (2) 47.878 (2) 44.591 (2) 36.866 (2) 13.649 (1) 9.217 (1) 8.709 (1) 6.292 (1) 3.523 (1) α = 1 88.873 (2) 75.085 (2) 61.305 (2) 53.538 (2) 37.655 (1) 10.403 (1) 20.246 (1) 7.346 (1) 4.949 (1) α = 1.5 150.318 (3) 145.003 (2) 92.943 (2) 87.759 (2) 144.343 (2) 11.904 (1) 86.820 (2) 8.770 (1) 7.200 (1) α = 2 253.816 (3) 253.810 (3) 155.088 (2) 154.265 (2) 253.740 (3) 13.843 (1) 153.966 (2) 10.750 (1) 10.116 (1) The superscript numbers within the parenthesis indicate the mode of buckling (2) 191.473 (3) 135.334 …”

Section: Sss Fmentioning

confidence: 99%

“…Also, Kang and Leissa [9] extended their analysis to buckling of thin rectangular plates having two opposite edges simply supported subjected to linearly varying in-plane load. Jana and Bhaskar [10] studied buckling of a simply supported rectangular plate with various types of non-uniform compressive edge loads using Galerkin method. Buckling analysis of simply supported symmetric cross-ply composite rectangular plates under a linearly varying edge load was investigated by Zhong and Gu [11] in the framework of first-order shear deformation plate theory (FSDT).…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of functionally graded rectangular plates under nonlinearly varying in-plane loading resting on elastic foundation

Bodaghi

Saidi

2010

Arch Appl Mech

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In this research work, an exact analytical solution for buckling of functionally graded rectangular plates subjected to non-uniformly distributed in-plane loading acting on two opposite simply supported edges is developed. It is assumed that the plate rests on two-parameter elastic foundation and its material properties vary through the thickness of the plate as a power function. The neutral surface position for such plate is determined, and the classical plate theory based on exact neutral surface position is employed to derive the governing stability equations. Considering Levy-type solution, the buckling equation reduces to an ordinary differential equation with variable coefficients. An exact analytical solution is obtained for this equation in the form of power series using the method of Frobenius. By considering sufficient terms in power series, the critical buckling load of functionally graded plate with different boundary conditions is determined. The accuracy of presented results is verified by appropriate convergence study, and the results are checked with those available in related literature. Furthermore, the effects of power of functionally graded material, aspect ratio, foundation stiffness coefficients and in-plane loading configuration together with different combinations of boundary conditions on the critical buckling load of functionally graded rectangular thin plate are studied.

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“…Yan and Young [9] presented a numerical Finite Element study to investigate buckling of fixed-ended cold-formed steel channel columns with various lip profiles subjected to axial load. Jana and Bhaskar [10] used superposition techniques for buckling analysis of plates under nonuniform compressive stress. Wang, et al [11] employed the differential quadrature method to compute the buckling load of plates under non-uniform compression.…”

Section: Introductionmentioning

confidence: 99%

A Simplified Procedure for Prediction of Ultimate Strength of Beam-Column Channel Sections

Bedair¹

2011

ENG

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A design procedure is presented to estimate the load carrying capacity of beam-column channel sections. A reduced cross-section is used to compensate for the reduction in the post-buckling stiffness. The non-linear stress distribution acting on the entire channel width is replaced by simplified linear distributions. Using this simplified concept, the maximum stress in the post-buckling state, is assumed to be carried entirely by both edges while the central region of the channel remains unstressed. Thus a fraction of the channel section is considered in resisting the applied loading. This approximation enables the structural engineer to deal with a simplified stress distribution to compute the ultimate strength instead of the non-linear one.

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Stability analysis of simply-supported rectangular plates under non-uniform uniaxial compression using rigorous and approximate plane stress solutions

Cited by 59 publications

References 10 publications

Buckling analysis and optimisation of variable angle tow composite plates

Buckling analysis and optimisation of variable angle tow composite plates

Stability analysis of functionally graded rectangular plates under nonlinearly varying in-plane loading resting on elastic foundation

A Simplified Procedure for Prediction of Ultimate Strength of Beam-Column Channel Sections

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