New approximate analytical solution of the large deflection problem of an uniformly loaded thin circular plate with edge simply hinged

Yun, Yin-shan; Hui, Liu

doi:10.1016/j.aej.2021.04.033

Cited by 5 publications

(2 citation statements)

References 25 publications

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“…Based on the new estimation of the convergence and approximation error of the Adomian decomposition method derived by Cherruault and Adomian [36], to characterize the accuracy of the approximate solution, we define the following two error functions as follows [8,9]:…”

Section: Discussionmentioning

confidence: 99%

“…It is di cult to obtain exact solutions to these large de ection problems, so people mainly study their numerical solutions and approximate analytical solutions by various methods and theories. Vincent [1] applied the perturbation method to solve the bending problem of a circular thin plate under a uniformly distributed load; Qian [2] used the central de ection as the perturbation parameter to solve the large de ection problems by the perturbation method; Nguyen-Van et al [3] studied the large de ection problems of plates and cylindrical shells with an e cient four-node at element with mesh distortions; Madyan et al [4] proposed an automated Ritz method for the large defection problem of plates with mixed boundary conditions; Yu et al [5] studied the nonlinear analysis for the extreme large bending de ection of a rectangular plate on nonuniform elastic foundations; Wang et al [6] proposed a wavelet method for the bending of circular plate with large de ection; Sladek et al [7] gave an iterative solution of large de ection problem of thin plates by the local boundary integral equation method; Yun et al [8] used the homotopy perturbation method to solve the large de ection problem of a circular plate; Yun et al [9] obtained new approximate analytical solution of the large de ection problem of a uniformly loaded thin circular plate with edge simply hinged by the Adomian decomposition method; Gbeminiyi et al [10] considered free vibration analysis of thin isotropic rectangular plates submerged in uid by the Adomian decomposition method and so on.…”

Section: Introductionmentioning

confidence: 99%

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New Analytical Solution of the Large Deflection Problem of a Circular Thin Plate with Edge Clamped but Sliding Freely Under a Combined Loading

Zhao

Yun

2022

Mathematical Problems in Engineering

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This paper intends to study the large deflection problem of a circular thin plate with an edge clamped but sliding freely under the combined action of uniformly distributed load and centrally concentrated load by the Adomian decomposition method. If the uniformly distributed load is not decomposed, the parameters obtained by the Adomian decomposition method are the same as the perturbation solution studied by scholars before. If the uniformly distributed load is decomposed into a finite series, a new analysis solution can be obtained through the Adomian decomposition method. From the error comparisons between the new solution in this paper and the perturbation solution, one can see that the result in this paper is better. Finally, the internal stress and deflection are discussed through the graphics based on the new analysis method.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

New Analytical Solution of the Large Deflection Problem of a Circular Thin Plate with Edge Clamped but Sliding Freely Under a Combined Loading

Zhao

Yun

2022

Mathematical Problems in Engineering

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An explicit nonlinear model for large spatial deflections of symmetric slender beams

Chen,

Yao,

Liu

et al. 2024

International Journal of Non-Linear Mechanics

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Chained Spatial Beam Adomian Decomposition Model: A Novel Model of Flexible Slender Beams for Large Spatial Deflections

Chen,

Chen

2024

Journal of Mechanisms and Robotics

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The main element of compliant mechanisms and continuum robots is flexible slender beams. However, the modeling of beams can be complicated due to the geometric nonlinearity becoming significant at large elastic deflections. This paper presents an explicit nonlinear model called the spatial beam Adomian decomposition model (SBADM) for intermediate spatial deflections of a slender beam with uniform, bisymmetric sections subjected to general end-loading. Specifically, the elongation, bending, torsion, and shear deformations of the beams are modeled based on Timoshenko's assumptions and Cosserat rod theory. Then, the quaternion transformation and Adomian decomposition are used to solve the nonlinear governing differential equations for the beam by truncating the higher-order terms, yielding an explicit expression for spatially deflected beams within intermediate deflection ranges. Simulations demonstrate the accuracy and time-wise efficiency of the SBADM, as well as its advantages over the state-of-the-art. In addition, this paper also introduces a discretization-based scheme called the chained SBADM (CSBADM) for large spatial deflections of flexible beams. Real-world experiments with two different configurations have also been performed to validate the effectiveness of the CSBADM. The results indicate that the CSBADM can accurately calculate the load-displacement relations for large deformed beams.

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New approximate analytical solution of the large deflection problem of an uniformly loaded thin circular plate with edge simply hinged

Cited by 5 publications

References 25 publications

New Analytical Solution of the Large Deflection Problem of a Circular Thin Plate with Edge Clamped but Sliding Freely Under a Combined Loading

New Analytical Solution of the Large Deflection Problem of a Circular Thin Plate with Edge Clamped but Sliding Freely Under a Combined Loading

An explicit nonlinear model for large spatial deflections of symmetric slender beams

Chained Spatial Beam Adomian Decomposition Model: A Novel Model of Flexible Slender Beams for Large Spatial Deflections

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