Buckling analysis of orthotropic thin rectangular plates subjected to nonlinear in-plane distributed loads using generalized differential quadrature method

Poodeh, F.; Farhatnia, Fatemeh; Raeesi, M.

doi:10.1080/15502287.2018.1430077

Cited by 9 publications

(6 citation statements)

References 29 publications

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“…DQM is a computationally efficient numerical approach that was introduced by Bellman et al [56] in 1970s. This method was employed by many scholars to find approximate solutions for the linear and nonlinear, partial and ordinary differential equations governing on mechanical characteristics of the structures with various geometrical shapes and boundary conditions [57][58][59][60][61][62][63][64]. DQM is developed based on the idea that all derivatives of a C:…”

Section: Solution Methodologymentioning

confidence: 99%

Frequency response of rotating two-directional functionally graded GPL-reinforced conical shells on elastic foundation

Amirabadi

Farhatnia

Cívalek

2021

J Braz. Soc. Mech. Sci. Eng.

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In this article, a semi-analytical solution is provided to investigate the free vibration characteristics of rotating truncated conical shells surrounded by a Winkler-Pasternak type foundation. It is assumed that the material of the shell is composed of epoxy as matrix and graphene nanoplatelets (GPLs) as reinforcement dispersed in both thickness and length directions of the shell. The shell is modeled based on first-order shear deformation theory and the equivalent mechanical properties are evaluated using the rule of the mixture and the Halpin-Tsai model. The governing equations are derived by implementing Hamilton's principle incorporating centrifugal acceleration, Coriolis acceleration, and the initial hoop tension. Utilizing trigonometric functions, an analytical solution is presented to solve the governing equations in the circumferential direction and a numerical solution is provided in the longitudinal direction by utilizing differential quadrature method. The convergence and accuracy of the present results are examined with those available in the literature. A parametric study is provided to check the influences of boundary conditions, rotational speed, circumferential wave number, mass fraction and dispersion pattern of the GPLs, and Winkler and shear coefficients of the foundation on the natural frequencies of the shell. It is concluded that an increment in the mass fraction of the GPLs increases the natural frequencies and the GPLs scattering near the inner surface and the small radius of the shell have a higher reinforcing effect.

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Section: Solution Methodologymentioning

confidence: 99%

Frequency response of rotating two-directional functionally graded GPL-reinforced conical shells on elastic foundation

Amirabadi

Farhatnia

Cívalek

2021

J Braz. Soc. Mech. Sci. Eng.

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“…Always, Finding the exact solution for governing equations of engineering problems are not feasible; therefore with increasing the capability of personal computers, a variety of numerical methods, i.e. finite element method, boundary element method and finite differences method are available for engineering aims [32]. DQM is a numerical approach for solving partial, linear and non-linear differential equations.…”

Section: Application Of the Differential Quadratic Methods Into Governmentioning

confidence: 99%

Functionally Graded Sandwich Circular Plate of Non-Uniform Varying Thickness with Homogenous Core Resting on Elastic Foundation: Investigation on Bending via Differential Quadrature Method

Farhatnia¹,

Saadat²,

Oveissi³

2019

AJME

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This paper illustrates the effectiveness of two functionally graded (FG) layers on a homogenous circular plate for bending analysis. The classical plate theory (CPT) serves as the basis of the analysis. Differential quadrature method (DQM) as semi-analytical method is employed to solve the governing equations. The material properties is varied to obey power-law in terms of the plate thickness direction. The plate is subjected to uniform transverse loading and resting on Winkler elastic foundation. In this study, the effect of the different profile of the plate thickness, elastic foundation coefficient, the volume fraction FG index, and effect of the boundary conditions, namely, simply supported and clamped edge on static response are demonstrated. The results are compared with finite element method and published literature that observed to be in accordance with each other.

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“…The loading configurations at the plate boundaries can be divided into static and dynamic loads [19]. In addition, post-or pre-buckling state [19] is another way of classification and final method to distinguish is the applying loads type and way of operation [13,[20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

“…The calculations methods to cope with the problem diverse from Rayleigh -Ritz methods [10], numerical methods [22], exact analytic solutions [25] and semi-analytic solution [26][27].…”

Section: Introductionmentioning

confidence: 99%

On the Solution to Pre- Buckling of a Thin Rectangular Plate Subjected to a Thick Strip in-plane Loading

Nagler¹

2021

1790-5044

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The current paper deals with the problem of the simply supported thin rectangular plate subjected to the intermediate strip in-plane loading. Based on the strain energy method (Fourier ansatz), the critical (minimum value) of buckling stress occurrence was determined in a general form dependent only on the strip thickness, strip location, plate width and stress magnitude. Compatible with the classical columns Euler method it was found that the plate stability is decreased with the increasing of the plate width due to larger induced stresses. Also, strip location relative to the support region was found to influence the buckling (same analogy to the Euler buckling theory; consider the strip as a both sides pressed rod). Additionally, the strip width parameter increase is likely to cause larger buckling stress. Moreover, expressions that includes both axial and transverse loads for different extended cases configurations were also derived and examined based on the strain energy method alongside explanation for possible applications (thin aluminum plate welding). In a general view, it was found that the cases of combined axial and perpendicular loading action are less stabilized than cases where only one kind of loading configuration is participated. Finally, the buckling stress was found to agree qualitatively with the cited literature.

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Buckling analysis of orthotropic thin rectangular plates subjected to nonlinear in-plane distributed loads using generalized differential quadrature method

Cited by 9 publications

References 29 publications

Frequency response of rotating two-directional functionally graded GPL-reinforced conical shells on elastic foundation

Frequency response of rotating two-directional functionally graded GPL-reinforced conical shells on elastic foundation

Functionally Graded Sandwich Circular Plate of Non-Uniform Varying Thickness with Homogenous Core Resting on Elastic Foundation: Investigation on Bending via Differential Quadrature Method

On the Solution to Pre- Buckling of a Thin Rectangular Plate Subjected to a Thick Strip in-plane Loading

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