An analytical solution for buckling of plates with circular cutout subjected to non-uniform in-plane loading

Abolghasemi, Saeed; Eipakchi, Hamidreza; Shariati, Mahmoud

doi:10.1007/s00419-019-01592-3

Cited by 16 publications

(15 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The application of the four boundary conditions yielded a system of four homogeneous equations -Equations (30), (31), (34) and (35) in terms of the four integration constants. Further simplification of the system of homogeneous equations using Equations (32) and (33) yielded the system of two homogeneous equations -Equations (36) and (37) which is expressed in matrix form as Equation (38). The characteristic elastic buckling equation is obtained from the condition for nontrivial solution as Equation (39) which is a determinantal equation.…”

Section: Discussionmentioning

confidence: 99%

“…Several other seminal research papers on the theme of elastic and inelastic buckling of plates of various shapes, subjected to different boundary and loading conditions are reported in the literature. Some of these research works are reported by Batford and Houbolt [27], Wang et al [28], Ullah et al [29], Xiang et al [30], Ullah et al [31], Abolghasemi et al [32], Ezeh et al [33] and Ibearugbulem and Eze [34].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Galerkin – Kantorovich Method for the Elastic Buckling Analysis of Thin Rectangular SCSC Plates

Onyia¹,

Rowland-Lato²,

Ike³

2020

International Journal of Engineering Research and Technology

View full text Add to dashboard Cite

This paper presents the elastic buckling analysis of thin rectangular plates using the Galerkin-Kantorovich method. The plate has two opposite simply supported edges x = 0 and x = a, and two clamped edges y = 0 and y = b where the origin is a corner and the uniform compressive load is applied at the simply supported edges. Mathematically, the problem is a boundary value problem (BVP) represented by a domain differential equation and boundary conditions. The buckling deflection function is assumed as an infinite series of an unknown function of y coordinate (G(y)) and a known function (of the x coordinate) that satisfies all the Dirichlet boundary conditions along the simply supported edges. The Galerkin-Kantorovich formulation of the BVP is an integral equation that further simplified to a homogeneous fourth order ordinary differential equation (ODE) in the unknown function G(y). The general solution of the ODE was achieved using trial function methods. The enforcement of the boundary conditions along the clamped edges resulted in a system of homogeneous equations in terms of the four integration constants. The condition for nontrivial solution is used to obtain the characteristic buckling equation as a transcendental equation which is solved for the elastic buckling load for each buckling mode using computer software based iteration methods. The critical elastic buckling load is found to correspond to the first buckling mode. The characteristic elastic buckling equation obtained is found to be the exact buckling equation for the problem and is identical with previously obtained equations. The elastic buckling loads obtained agree with the previous results from the literature.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Galerkin – Kantorovich Method for the Elastic Buckling Analysis of Thin Rectangular SCSC Plates

Onyia¹,

Rowland-Lato²,

Ike³

2020

International Journal of Engineering Research and Technology

View full text Add to dashboard Cite

show abstract

“…This article has illustrated the application of the single finite Fourier sine integral transform method to the elastic stability problem of rectangular thin SSCF and SSSS plates. The problem is governed by BVP given for SSCF plates as Equations (17), (18), (19) and (20), where Equation 17is the domain equation and Equations (18), (19) and (20) are the boundary conditions. The application of the one-dimensional finite sine integral transform to the governing domain equation converted the problem to an integral equation expressed as Equation (21).…”

Section: Ivi Imposition Of Boundary Conditions For Ssss Platesmentioning

confidence: 99%

“…Considerable research works have been presented on the stability of plates of various shapes, types and boundary conditions. Some significant contributions to the research on plate stability are reported by: Gambhir [2], Bulson [3], Chajes [4], Timoshenko and Gere [5], Shi [8], Shi and Bezine [9], Ullah et al [10,11,12,13], Wang et al [14], Abodi [15], Yu [16], Abolghasemi et al [17], Xiang et al [18] and Bouazza et al [19] Contemporary research work on the plate stability problems have used various numerical methods such as the differential quadrature method (DQM), discrete singular convolution (DSC) method, harmonic differential quadrature method, ordinary finite difference method (FDM), meshfree method, generalized Galerkin method, finite strip method, B-spline finite strip method, exact finite strip method, hp-cloud method, modified Ishlinskii's solution method, meshless analog equation method, finite element method (FEM), extended Kantorovich method (EKM) and pb2-Ritz method. Very recent research work on the subject of plate stability using various numerical and analytical techniques have been reported by Lopatin and Morozov [20], Ghannadpour et al [21], Jafari and Azhari [22], Zureick [23], Seifi et al [24], Li et al [25], Wang et al [26], Mandal and Mishra [27], Shama [28], and Yao and Fujikubo [29].…”

Section: Introductionmentioning

confidence: 99%

Elastic Buckling Analysis of SSCF and SSSS Rectangular Thin Plates using the Single Finite Fourier Sine Integral Transform Method

Onyia¹,

Rowland-Lato²,

Ike³

2020

International Journal of Engineering Research and Technology

View full text Add to dashboard Cite

The analysis of the stability problem of plate subjected to inplane compressive load is important due to the relatively poor capacity of plates in resisting compressive forces compared to tensile forces. It is also significant due to the nonlinear, sudden nature of buckling failures. This study presents the elastic buckling analysis of SSCF and SSSS rectangular thin plates using the single finite Fourier sine integral transform method. The considered plate problems are (i) rectangular thin plate simply supported on two opposite edges, clamped on one edge and free on the fourth edge; (ii) rectangular thin plate simply supported on all edges. The plates are subject to uniaxial uniform compressive loads on the two simply supported edges. The governing domain equation is a fourth order partial differential equation (PDE). The problem solved is a boundary value problem (BVP) since the domain PDE is subject to the boundary conditions at the four edges. The single finite sine transform adopted automatically satisfies the Dirichlet boundary conditions along the simply supported edges. The transform converts the BVP to an integral equation, which simplifies upon use of the linearity properties and integration by parts to a system of homogeneous ordinary differential equations (ODEs) in terms of the transform of the unknown buckling deflection. The general solution of the system of ODEs is obtained using trial function methods. Enforcement of boundary conditions along the y = 0, and y = b edges (for the SSCF and SSSS plates considered) results in a system of four sets of homogeneous equations in terms of the integration constants. The characteristic buckling equation in each case considered is found for nontrivial solutions as a transcendental equation, whose roots are used to obtain the buckling loads for various values of the aspect ratio and for any buckling modes. In each considered case, the obtained buckling equation is exact and identical with exact expressions previously obtained in the literature using other solution methods. The buckling loads obtained by the present method are validated by the observed agreement with results obtained by previous researchers who used other methods.

show abstract

“…Muc et al (2018b) described the stability loss in composite structure focusing on buckling and post-buckling behaviour with cutout and reinforcement. Narayana et al (2014); Rajanna et al (2017Rajanna et al ( , 2018; Abolghasemi et al (2019) studied the effect of linearly varying edge loads on the stability of composite plates with a circular or square cutout. Aydin Komur et al (2008) and Chandra et al (2020aChandra et al ( , 2020bChandra et al ( , 2021 analysed the buckling behaviour of composite laminate under non-uniform varying in-plane compressive loads with circular cutouts.…”

Section: Introductionmentioning

confidence: 99%

A Parametric study on the effect of elliptical cutouts for buckling behavior of composite plates under non-uniform edge loads

Chandra¹,

Rajanna²,

Rao³

2020

Lat. Am. j. solids struct.

View full text Add to dashboard Cite

An analytical solution for buckling of plates with circular cutout subjected to non-uniform in-plane loading

Cited by 16 publications

References 39 publications

Galerkin – Kantorovich Method for the Elastic Buckling Analysis of Thin Rectangular SCSC Plates

Galerkin – Kantorovich Method for the Elastic Buckling Analysis of Thin Rectangular SCSC Plates

Elastic Buckling Analysis of SSCF and SSSS Rectangular Thin Plates using the Single Finite Fourier Sine Integral Transform Method

A Parametric study on the effect of elliptical cutouts for buckling behavior of composite plates under non-uniform edge loads

Contact Info

Product

Resources

About