A variational analysis for large deflection of skew plates under uniformly distributed load through domain mapping technique

Das, Debabrata; Sahoo, Prasanta; Saha, Kashinath

doi:10.4314/ijest.v1i1.58056

Cited by 5 publications

(8 citation statements)

References 26 publications

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“…Comparison of the results with those obtained by Das et al (2009) shows that the simple HP-cloud results are very close to the results obtained by domain mapping technique.…”

Section: Large Deflection Of Isotropic Platessupporting

confidence: 73%

Geometrically nonlinear analysis of thick orthotropic plates with various geometries using simple HP-cloud method

Jafari

Azhari

2016

Engineering Computations

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Purpose – The purpose of this paper is to present a simple HP-cloud method as an accurate meshless method for the geometrically nonlinear analysis of thick orthotropic plates of general shape. This method is used to investigate the effects of thickness, geometry of various shapes, boundary conditions and material properties on the large deformation analysis of Mindlin plates. Design/methodology/approach – Nonlinear analysis of plates based on Mindlin theory is presented. The equations are derived by the Von-Karman assumption and total Lagrangian formulations. Newton-Raphson method is applied to achieve linear equations from nonlinear equations. Simple HP-cloud method is used for the construction of the shape functions based on Kronecker-δ properties, so the essential boundary conditions can be enforced directly. Shepard function is utilized for a partition of unity and complete polynomial is used as an enrichment function. Findings – The suitability and efficiency of the simple HP-cloud method for the geometrically nonlinear analysis of thin and moderately thick plates is studied for the first time. Large displacement analysis of various shapes of plates, rectangular, skew, trapezoidal, circular, hexagonal and triangular with different boundary conditions subjected to distributed loading are considered. Originality/value – This paper shows that the simple HP-cloud method is well suited for the large deformation analysis of Mindlin plates with various geometries, because it uses a set of a few arbitrary nodes placed in a plate of general shape. Moreover the convergence rate of the proposed method is high and the cost of solving equations is low.

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“…Comparison of the results with those obtained by Das et al (2009) shows that the simple HP-cloud results are very close to the results obtained by domain mapping technique.…”

Section: Large Deflection Of Isotropic Platessupporting

confidence: 73%

Geometrically nonlinear analysis of thick orthotropic plates with various geometries using simple HP-cloud method

Jafari

Azhari

2016

Engineering Computations

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“…It is to be noted here that geometric nonlinearity, i.e., the nonlinear strain-displacement relationship is taken into consideration through in-plane stretching. The expressions of b U and m U are not given here to maintain brevity and can be obtained in Das et al (2009).…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…The present paper is an extension of the earlier work by Das et al (2009) to analyse the large deflection static behaviour of isotropic skew plates under uniform pressure loading. As compared to the earlier work which deals with the skew plates of clamped and simply supported boundaries, the present work deals with the same with all possible combinations of clamped and simply supported boundaries.…”

Section: Introductionmentioning

confidence: 95%

“…Singh and Elaghabash (2003) developed a numerical method for geometrically nonlinear static analysis of thin plates having quadrangular boundary with four straight edges. Recently, Das et al (2009) investigated the static behaviour of clamped and simply supported skew plates under pressure loading through a numerical domain mapping technique.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Large deflection analysis of skew plates under uniformly distributed load for mixed boundary conditions

Das¹,

Sahoo²,

Saha³

2010

Int. J. Eng. Sci. Tech

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The present paper deals with large deflection static behaviour of thin isotropic skew plates under uniformly distributed load for various mixed flexural boundary conditions. A variational method based on the principle of minimization of total potential energy has been used through assumed displacement fields. The results are generated for different possible combinations of clamped and simply supported boundary conditions and presented in normalized load-deflection plane. Individual effects of skew angle, aspect ratio and boundary condition on normalized load-deflection behaviour are separately shown.

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“…For smoothen the elements, Xuan et al (2007) have used boundary integral method. Das et al (2009) have developed a quite general method which can be applied to any classical boundary conditions. Jain (2009) presented analysis of stress concentration and deflection in isotropic and orthotropic rectangular plates with central circular hole under transverse static loading.…”

Section: Introductionmentioning

confidence: 99%

Static analysis of an isotropic rectangular plate using finite element analysis (FEA)

Vanam¹,

Rajyalakshmi²,

Ramu³

2012

J. Mech. Eng. Res.

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This research work aims to analyze the static analysis of an isotropic rectangular plate with various boundary conditions and various types of load applications. In this paper, finite element analysis has been carried out for an isotropic rectangular plate by considering the master element as a four noded quadrilateral element. Numerical analysis (finite element analysis, FEA) has been carried out by developing programming in mathematical software MATLAB and the results obtained from MATLAB are giving good agreement with the results obtained by classical method-exact solutions. Later, for the same structure, analysis has been carried out using finite element analysis software ANSYS. This job is helpful for obtaining the results not only at node points but also the entire surface of the rectangular plate. Finally, comparison has been done between the results obtained from FEA numerical analysis, and ANSYS results with classical method-exact solutions. Numerical results showed that, the results obtained by finite element analysis and ANSYS simulation results are in close agreement with the results obtained from exact solutions from classical method. During this analysis, the optimal thickness of the plate has been obtained when the plate is subjected to different loading and boundary conditions.

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A variational analysis for large deflection of skew plates under uniformly distributed load through domain mapping technique

Cited by 5 publications

References 26 publications

Geometrically nonlinear analysis of thick orthotropic plates with various geometries using simple HP-cloud method

Geometrically nonlinear analysis of thick orthotropic plates with various geometries using simple HP-cloud method

Large deflection analysis of skew plates under uniformly distributed load for mixed boundary conditions

Static analysis of an isotropic rectangular plate using finite element analysis (FEA)

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