A semi-analytical study on static behavior of thin skew plates on Winkler and Pasternak foundations

Joodaky, Amin; Joodaky, Iman

doi:10.1016/j.ijmecsci.2015.06.025

Cited by 19 publications

(4 citation statements)

References 21 publications

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“…Static analyses of isotropic rectangular plates resting on Pasternak foundation are performed in many studies as in [8][9]. A semi-analytical solution for the static analysis of thin skew plates on Winkler and Pasternak foundations is presented by [10]. In a recent study, a computing method for bending analysis of thin plates resting on Pasternak foundation is developed, [11].…”

Section: Introductionmentioning

confidence: 99%

Convergence studies for static analysis of thin plates on Pasternak Foundations

Çalık-Karaköse

2023

DÜMF MD

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Convergence studies for the static analysis of thin plates resting on Pasternak foundations is performed. The plates are discretized using two different finite elements, the formulations of which are based on the Kirchhoff and Reissner-Mindlin plate theories. The shear locking problem which arises when full integration is used in the finite element implementation of Reissner-Mindlin plate theory is eliminated with selective integration. The Pasternak foundation is accounted for by adding the parameter matrices of an existing soil finite element to the stiffness matrix terms of the plate finite elements corresponding to deflections. Convergence rates for different boundary conditions, plate thicknesses and soil parameters are obtained and given comparatively through numerical examples.

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Section: Introductionmentioning

confidence: 99%

Convergence studies for static analysis of thin plates on Pasternak Foundations

Çalık-Karaköse

2023

DÜMF MD

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“…Singh et al [37] have presented an analytical solution for the bending analysis of axially functionally graded panels. This method has been applied to solve the problem of skew-symmetric plates [38,39], sector plates [40], stepped plates [41].…”

Section: Introductionmentioning

confidence: 99%

2‐D Analytical solutions for the multisegmented panel subjected to arbitrary boundary condition

Kumar

Kumari

2022

Z Angew Math Mech

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A closed-form bending solution of the multisegmented panels is presented for different support conditions. The panels can have multiple no. of segments along the x-axis with varying material properties. The governing equations are formulated using the extended Kantorovich method (EKM) in the mixed-form, and a set of ordinary differential equations have been obtained. The continuity of displacement and stresses are satisfied at the interface of each segment. The panels can have simply-support, clamp, and free types of support conditions. The panel interface at each segment along the x-axis is assumed to be perfectly bonded. In this work, the stress and deformation variations for four types of panel configuration have been studied. Two segmented panels having aluminum and Graphite-Epoxy with equal and unequal segments are considered. A foursegmented Al/SiC panel having gradual material variation is also analyzed. The effect of ply-angles on the longitudinal variables is also studied for the equal segmented Al/GrEp panel. The deflection and stresses are compared with the finite element solution and found in good agreement with the EKM results. The current development will lead to developing the solution for stepped panels, dissimilar plates, and more complex cases used in aerospace applications.

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“…Following is a listing of those articles. Joodaky and co-authors obtained closed-form solution for bending of clamped thin isotropic skew plate (Kargarnovin et al, 2010), clamped thin skew FGM plate (Joodaky et al, 2012) and thin FGM skew plate resting on elastic foundations (Joodaky et al, 2013;Joodaky and Joodaky, 2015). Hassan and Kurgan (2020) compared the single-term EKM to the multi-term EKM for the bending analysis of thin skew plates.…”

Section: Introductionmentioning

confidence: 99%

Buckling of thin skew isotropic plate resting on Pasternak elastic foundation using extended Kantorovich method

Hassan

Kurgan

2020

Heliyon

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The extended Kantorovich method (EKM) is implemented to numerically solve the elastic buckling problem of thin skew (parallelogram) isotropic plate under in-plane loading resting on the Pasternak elastic foundation. EKM has never been applied to this problem before. Investigation of the EKM accuracy and convergence is conducted. Formulations are based on classical plate theory (CPT). Stability equations and boundary conditions terms are derived from the principle of the minimum total potential energy using the variational calculus expressed in an oblique coordinate system. The resulting two sets of ordinary differential equations are solved numerically using the Chebfun package in MATLAB software. In-plane compression and shear loads are considered along with various boundary conditions and aspect ratios. Results are compared to the analytical and numerical solutions found in the literature, and to the finite element solutions obtained using ANSYS software. The effects of the skew angle, stiffness of elastic foundation, and aspect ratio on the buckling load are also investigated. For plates with zero skew angle, i.e. rectangular plates, with various boundary conditions and aspect ratios under uniaxial and biaxial loading resting on elastic foundation, the single-term EKM is found accurate. However, more terms are needed as the skew angle gets bigger. The multi-term EKM is found accurate in the analysis of rectangular and skew plates with various boundary conditions and aspect ratios under uniaxial, biaxial, and shear loading resting on elastic foundation. Using EKM in buckling analysis of thin skew plates is found simple, accurate, and rapid to converge.

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A semi-analytical study on static behavior of thin skew plates on Winkler and Pasternak foundations

Cited by 19 publications

References 21 publications

Convergence studies for static analysis of thin plates on Pasternak Foundations

Convergence studies for static analysis of thin plates on Pasternak Foundations

2‐D Analytical solutions for the multisegmented panel subjected to arbitrary boundary condition

Buckling of thin skew isotropic plate resting on Pasternak elastic foundation using extended Kantorovich method

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