Analytical solution of the bending problem of free orthotropic rectangular thin plate on two‐parameter elastic foundation

Bai, Eburilitu; Zhang, Chunyu; Chen, Alatancang; Su, Xin

doi:10.1002/zamm.202000358

Cited by 4 publications

(1 citation statement)

References 26 publications

(33 reference statements)

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“…The governing differential equations of the plate were transferred into Hamilton canonical equations, and the analytic solution could be obtained with all edges slidingly supported. Bai et al [30] studied the bending problem of the free orthotropic rectangular thin plate (RTP) on a two-parameter elastic foundation under a concentrated load by using the symplectic superposition method. Tenenbaum et al [31] gave the analytical solutions for the buckling loads of thin rectangular plates with internal supports and different boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Bending Analysis of Stepped Rectangular Plates Resting on an Elastic Half-Space Foundation

Zhang

2023

Buildings

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In this paper, the bending behavior of rectangular plates with stepped thickness resting on an elastic half-space foundation is investigated through an analytic method. Combined with the bending theory of the rectangular thin and moderately thick plate, the stepped rectangular plate is divided into upper and lower plates, and the Fourier series is used to obtain the analytical solution of the deflection of the plate and the interaction force between the plate and foundation. The influence of the elastic modulus of the plate, plate theory, and the dimension of the plate on the deflection of the stepped rectangular plate is also discussed. The results show that the analytical solution is basically the same as the existing research results, and it is also verified by the analysis results of the models established by ABAQUS software. The deflection at the center of the stepped rectangular plate increases with the increase of the elastic modulus of the upper plate and the decrease of the side length of the upper plate, while the plate theory has little effect on the deflection of the plate. This method not only overcomes some of the disadvantages of numerical methods but also eliminates the assumptions of the Winkler foundation model and the two-parameter foundation model, thus obtaining a more reasonable and accurate bending performance of the stepped rectangular plate resting on the elastic half-space foundation.

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Section: Introductionmentioning

confidence: 99%

Bending Analysis of Stepped Rectangular Plates Resting on an Elastic Half-Space Foundation

Zhang

2023

Buildings

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On the Advances of Computational Nonclassical Continuum Theories of Elasticity for Bending Analyses of Small-Sized Plate-Based Structures: A Review

Nuhu

Safaei

2023

Arch Computat Methods Eng

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Mechanical Modeling and Application of Frost Heaving Damage to Assembled Concrete Rectangular Canals in Seasonally Frozen Soil Region

Chang,

Wang,

et al. 2024

Advances in Civil Engineering

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In the design and upkeep of canals in areas of seasonal permafrost, resistance to frost heave is a critical factor for ensuring the stability of water conveyance canals. Mechanical modeling is the key to frost heaving‐resistant design. In this study, the theory of elastic thin plates was used to build a mechanical model of frost heaving damage to rectangular canals. The model’s plausibility was confirmed using a prototype canal as an example, and the canal’s deformation, internal force, and stress distribution were examined. The findings demonstrate that, compared to beam theory, the internal forces and deformations computed by the model are not evenly distributed along the plate width; the base slab and side walls both saw their greatest deformations in the middle portion and two‐fifths from the canal’s top, respectively; at the junction of the two, the bending moments and tensile stresses are maximum and distributions are consistent; transverse moments should be used as control moments in the structural design of canals, and stick feet should be placed at junctions to stop damage. In addition, the maximum normal frost heaving force and optimal thickness that four various canals can withstand were estimated, and the results were biased in favor of safety. The calculation’s results can serve as a theoretical guide for antifreeze design concrete rectangular canals in places that experience seasonal freezing.

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Analytical solution of the bending problem of free orthotropic rectangular thin plate on two‐parameter elastic foundation

Cited by 4 publications

References 26 publications

Bending Analysis of Stepped Rectangular Plates Resting on an Elastic Half-Space Foundation

Bending Analysis of Stepped Rectangular Plates Resting on an Elastic Half-Space Foundation

On the Advances of Computational Nonclassical Continuum Theories of Elasticity for Bending Analyses of Small-Sized Plate-Based Structures: A Review

Mechanical Modeling and Application of Frost Heaving Damage to Assembled Concrete Rectangular Canals in Seasonally Frozen Soil Region

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