Buckling analysis of rectangular thin plates with two opposite edges free and others rotationally restrained by finite Fourier integral transform method

Zhang, Jinghui; Lu, Jiale; Ullah, Salamat; Gao, Yuanyuan; Zhao, De Hong

doi:10.1002/zamm.202000153

Cited by 11 publications

(8 citation statements)

References 53 publications

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“…On this basis, displacements expressed in terms of ∑ ∞ m=1,2,3,••• κ1 m sin(α m x) and ∑ ∞ m=1,2,3,••• κ2 m sin(α m x) are applied to the y = 0 and y = b sides of the plate in subproblem (1), respectively; displacements expressed in terms of ∑ ∞ n=1,2,3,••• κ3 n sin(β n y) and ∑ ∞ n=1,2,3,••• κ4 n sin(β n y) are applied to the x = 0 and x = a sides of the plate in subproblem (2), where α m = mπ/a, β n = nπ/b, κ1 m , κ2 m , κ3 n and κ4 n are the parameters to be determined (m = 1, 2, 3, . .…”

Section: Analytic Buckling Solutions Of Rectangular Thin Plates Suppo...mentioning

confidence: 99%

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Analytic Solution for Buckling Problem of Rectangular Thin Plates Supported by Four Corners with Four Edges Free Based on the Symplectic Superposition Method

Yang,

Xu,

Chu

et al. 2024

Mathematics

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The buckling behavior of rectangular thin plates, which are supported at their four corner points with four edges free, is a matter of great concern in the field of plate and shell mechanics. Nevertheless, the complexities arising from the boundary conditions and governing equations present a formidable obstacle to the attainment of analytical solutions for these problems. Despite the availability of various approximate/numerical methods for addressing these challenges, the literature lacks accurate analytic solutions. In this study, we employ the symplectic superposition method, a recently developed method, to effectively analyze the buckling problem of rectangular thin plates analytically. These plates have four supported corners and four free edges. To achieve this, the problem is divided into two sub-problems and solve them separately using variable separation and symplectic eigen expansion, leading to analytical solutions. Finally, we obtain the resolution to the initial issue by superposing the sub-problems. The current solution method can be regarded as a logical, analytical, and rational approach as it begins with the basic governing equation and is systematically derived without assuming the forms of the solutions. To examine various aspect ratios and in-plane load ratios of rectangular thin plates, which are supported at their four corner points with four edges free, we provide numerical examples that demonstrate the buckling loads and typical buckling mode shapes.

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Section: Analytic Buckling Solutions Of Rectangular Thin Plates Suppo...mentioning

confidence: 99%

“…The mechanics of plates and shells have been studied by many scholars [1,2]. Rectangular plates supported by corner point are commonly used in various engineering applications, including building structures, mechanical components, and aerospace vehicles.…”

Section: Introductionmentioning

confidence: 99%

Analytic Solution for Buckling Problem of Rectangular Thin Plates Supported by Four Corners with Four Edges Free Based on the Symplectic Superposition Method

Yang,

Xu,

Chu

et al. 2024

Mathematics

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“…The steric hardening is structural reconstruction and reorganization at the intermolecular level produced because of temperature variations during the service life. It is also a complex nonrecoverable process that is produced by ultraviolet (UV) light, oxygen, and heating effect due to temperature changes [21][22][23][24]. Numerous analytical techniques have been developed to investigate and link the physical and rheological properties with the performance characteristics of asphalt binders.…”

Section: Introductionmentioning

confidence: 99%

“…Numerous analytical techniques have been developed to investigate and link the physical and rheological properties with the performance characteristics of asphalt binders. For this reason, it is essential to introduce a collaboration among material engineers, pavement specialists, highway agencies, and asphalt industries [24]. Meanwhile, there may be durable adhesion and film between aggregate and asphalt binder in the existence of moisture to decrease stripping that can be achieved through modification of asphalt binders [25,26].…”

Section: Introductionmentioning

confidence: 99%

Performance Evaluation of Aged Asphalt Pavement Binder through Rejuvenators

Yaseen¹,

Jamal

Almoshaogeh

et al. 2022

Sustainability

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Natural resources are declining due to rising infrastructure, renovation, demolition, and recycling of existing structures that necessitate sustainable development. It urges the researchers to modify the aged asphalt binder in the recycling to enhance the performance life of asphaltic pavements. The aim of this research study is to reutilize recycled materials through rejuvenation. This study utilizes the Cereclor to rejuvenate the aged binder collected from recycling and explore its transformation by comparing it with parent binder of similar grade. Different types of tests, such as basic physical properties, saturates, aromatics, resins, and asphaltenes (SARA) analysis for the fractional composition, bending beam rheometer (BBR), and dynamic shear rheometer (DSR) for rheological properties are applied to investigate these properties and effect on the performance. The results show that rejuvenator improved the fractional composition of the aged asphalt binder. It significantly improved the physical properties of the binder. The asphaltene contents are reduced up to 18% in the fractional composition through the addition of the optimum dosage (7.5%) of the rejuvenator. The colloidal instability index was decreased from 0.74 to 0.43 value by changing its unstable to stable colloidal structure. In addition, rejuvenator improved the rheological properties at a wide range of temperatures. The rejuvenator has the potential to soften the aged binder through optimum dosage (7.5%), as indicated in the results of fractional composition, colloidal structure, and rheological properties. Furthermore, it has been concluded that it can be utilized as a rejuvenator in the recycling industry to resolve the recycled materials disposal issues and lead to promote sustainable development.

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“…Awrejcewicz et al [16] studied on the free vibrations of FG plates and shallow shells with cutout in thermal environment. Zhang et al [17] employed the finite Fourier integral transform technique to examine the buckling treatment of rectangular thin plates with two opposite edges free and the others rotationally restrained.…”

Section: Introductionmentioning

confidence: 99%

Mechanical buckling analysis of functionally graded composite laminated plates reinforced with temperature dependent graphene sheets resting on elastic foundation

2021

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Present study aims to investigate the mechanical buckling including the shear buckling and the in-plane mechanical buckling of composite laminated plates reinforced with graphene sheets with temperature dependent features resting on Winkler-Pasternak elastic foundation in a thermal ambient. The governing equations in the framework of the first order shear deformation theory are attacked by the Ritz method. The plate is subjected to uniaxial, biaxial and shear loads. The innovation of the present paper is considering the temperature dependency and anisotropicity of the material properties of a nanocomposite layer that reinforced with graphene sheets for the purpose of the determination of the mechanical buckling treatment of a graphene reinforced composite (GRC) laminated plate with different boundary condition types. Resorting to the extended Halpin-Tsai micromechanical model, the thermo-mechanical characteristics of a lamina is defined. Numerical outcomes of the present study are confirmed with the presented data in the literature. The effects of the elastic foundation parameter, the temperature, the plate side to its thickness ratio, the layup scheme, the boundary condition type and the distribution pattern of graphene-reinforced composites on the critical buckling load are investigated. It is found that, the impact of elastic foundation incorporation is less visible on the critical shear buckling load rather than the critical uniaxial and biaxial mechanical loads. Moreover, the largest critical buckling load belongs to layup [0] 10 among the all under studied lamination schemes.

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Buckling analysis of rectangular thin plates with two opposite edges free and others rotationally restrained by finite Fourier integral transform method

Cited by 11 publications

References 53 publications

Analytic Solution for Buckling Problem of Rectangular Thin Plates Supported by Four Corners with Four Edges Free Based on the Symplectic Superposition Method

Analytic Solution for Buckling Problem of Rectangular Thin Plates Supported by Four Corners with Four Edges Free Based on the Symplectic Superposition Method

Performance Evaluation of Aged Asphalt Pavement Binder through Rejuvenators

Mechanical buckling analysis of functionally graded composite laminated plates reinforced with temperature dependent graphene sheets resting on elastic foundation

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