An applicable formula for elastic buckling of rectangular plates under biaxial and shear loads

This paper presents the generalized integral transform method for solving flexural and elastic stability problems of rectangular thin plates clamped along /2 yb = and simply supported along remaining boundaries (x = 0, x = a) (CSCS plate). The considered plate is homogeneous, isotropic and carrying uniformly distributed transversely applied loading causing bending. Also studied, is a plate subject to (i) biaxial (ii) uniaxial uniform compressive load. The method uses the eigenfunctions of vibrating thin beams of equivalent span and support conditions in constructing the basis functions for the plate deflection and the integral kernel function. The transform is applied to the governing domain equation, converting the problem to integral equations for both cases of bending and elastic buckling. The integral equation reduces to algebraic problems for the bending problem, and algebraic eigenvalue problem for the elastic buckling problem. The deflections are obtained as double infinite series with rapidly convergent properties. Bending moments expressions are double series with infinite terms which are rapidly convergent. Maximum deflections and bending moments values occur at the plate centre in agreement with symmetry. The present results gave double series solutions with good convergent properties in closed form for bending problems. The resulting bending solutions were exact. Solving the resulting eigenvalue equation gave closed analytical equation for the buckling loads. Buckling loads are computed for the cases of biaxial and uniaxial uniform compression of square thin plates using one term approximations. The buckling load obtained for one term approximation of the eigenfunction gave results that are 12.23% greater than the exact solution. The use of more terms in the eigenfunction expansion could give more acceptable results for the eigenvalue problem of buckling of CSCS plates.

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“…Other contributions to the knowledge of plates are found in such seminal papers as presented by authors in [44][45][46][47][48][49][50][51].…”

Section: Review Of Solution Methods For Plate Problemsmentioning

confidence: 99%

Generalized Integral Transform Method for Bending and Buckling Analysis of Rectangular Thin Plate with Two Opposite Edges Simply Supported and Other Edges Clamped

Ike¹,

Onyia²,

Rowland-Lato³

2021

Adv. sci. technol. eng. syst. j.

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“…The buckling of plates is a well‐studied and mature field. [ 27–34 ] Under longitudinal compression, a plate will buckle when a critical stress is reached, given by σ c = kπ 2 D [ w 2 t ] –1 , where D is the flexural rigidity of a plate with width w and thickness t , and k is the buckling coefficient, a constant that depends on geometry and how the plate is supported. [ 27 ] Here D = Et 3 [12(1−ν 2 )] –1 , where E and ν are the elastic modulus and Poisson ratio of the plate, respectively.…”

Section: Introductionmentioning

confidence: 99%

Metallic Plate Buckling As a Low Adhesion Mechanism for Durable and Scalable Icephobic Surface Design

Zarasvand

Pope

Mohseni

et al. 2021

Adv Materials Inter

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Ice accretion is significantly detrimental to a range of different industries worldwide. Current methods for reducing ice adhesion include the use of lubricants, hydrophobic coatings, or soft elastomers, all of which exhibit limited durability. As an alternative, here sparsely confined metallic sheets are suspended and the surface buckling instability is tailored, resulting in ice adhesion strengths on par with these prior strategies but without the use of any coatings. These Buckling Elastomer‐like Anti‐icing Metallic Surfaces, or BEAMS, exhibit ultra‐low ice adhesion (<1 kPa) and the mechanical resilience of metals. Results from an icing wind tunnel confirmed the efficacy of BEAMS toward impact ice accreted in realistic conditions via the high‐speed impingement of ≈20 µm droplets at −20 °C. The BEAMS sheet confinement, boundary conditions, and physical dimensions of both the ice and the metallic plates can be altered to minimize ice adhesion via the mechanics of plate buckling. Additionally, BEAMS that detach ice without directly contacting it are designed, the scalability of BEAMS is demonstrated, and their durability is verified using rain erosion, sandblasting, thermal extremes, and repeated icing/de‐icing, both in an icing wind tunnel and on a benchtop system.

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“…Other significant contributions to the formulation and solutions of plate problems include the following publications: Ghannadiasi and Noorzad [43], Bigdoli et al [44], Zargaripoor et al [45], Goodarzi et al [46], Javidi et al [47], Makvandi et al [48], Sayyad and Ghugal [49], Mirzapour et al [50], Shahabian et al [51], Abdollahzadeh and Ghobadi [52], Cuba et al [53] and Jahanpour and Roozbabani [54].…”

Section: Introductionmentioning

confidence: 99%

Single Finite Fourier Sine Integral Transform Method for the Flexural Analysis of Rectangular Kirchhoff Plate with Opposite Edges Simply Supported, Other Edges Clamped for the Case of Triangular Load Distribution

Mama¹,

Oguaghamba²,

Ike³

2020

International Journal of Engineering Research and Technology

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This paper presents the single finite Fourier sine integral transform method for the flexural analysis of rectangular Kirchhoff plate with opposite edges simply supported, and the other edges clamped for the case of triangular load distribution on the plate domain. The finite sine transform method is adopted because the sinusoidal integral kernel function satisfies all the Dirichlet boundary conditions along the simply supported edges. The governing domain equation which is a nonhomogeneous biharmonic equation is converted by the transformation to an integral equation over the solution domain. The integral equation is reduced by the linearity properties of the transformation, Leibnitz rule and boundary conditions along the simply supported edges to ordinary differential equations (ODEs). Classical methods of solving ODEs in closed-form were used to obtain the solutions that satisfy the boundary conditions along the clamped edges. Thus exact solutions to the boundary value problem that satisfy the governing equation at all points in the solution domain as well as at all points along the four edges are obtained. The resulting expression for the deflection is a single infinite series with demonstrated rapidly convergent properties. The bending moments Mxx, Myy expressions were obtained using the bending moment-deflection relations as infinite series with demonstrated rapid convergence. The converged values of the maximum deflection and bending moments Mxx, Myy evaluated at the plate centre are in excellent agreement with the previous exact results to the problem obtained by researchers who used the Kantorovich-Vlasov method; Levy's method; and the superposition method.

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An applicable formula for elastic buckling of rectangular plates under biaxial and shear loads

Cited by 15 publications

References 13 publications

Generalized Integral Transform Method for Bending and Buckling Analysis of Rectangular Thin Plate with Two Opposite Edges Simply Supported and Other Edges Clamped

Generalized Integral Transform Method for Bending and Buckling Analysis of Rectangular Thin Plate with Two Opposite Edges Simply Supported and Other Edges Clamped

Metallic Plate Buckling As a Low Adhesion Mechanism for Durable and Scalable Icephobic Surface Design

Single Finite Fourier Sine Integral Transform Method for the Flexural Analysis of Rectangular Kirchhoff Plate with Opposite Edges Simply Supported, Other Edges Clamped for the Case of Triangular Load Distribution

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