An accurate solution method for the static and dynamic deflections of orthotropic plates with general boundary conditions

Khov, Henry; Li, Wen L.; Gibson, Ronald F.

doi:10.1016/j.compstruct.2009.04.020

Cited by 72 publications

(41 citation statements)

References 14 publications

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“…According to its difference in shapes, boundaries and stress conditions, a variety of methods are supposed by researchers to carry on all kinds of research about the plate. For example, OU et al [1] studied the vibration of stiffened plate under the condition of general elastic boundaries; KHON et al [2] put forward the accurate solution to orthotropic plate under general boundary condition; QUINTANA and NALLIM [3] studied natural frequency as well as vibration mode of symmetric laminates of triangle and ladder with Ritz method. There are also many studies about irregular plates.…”

Section: Introductionmentioning

confidence: 99%

Galerkin solution of Winkler foundation-based irregular Kirchhoff plate model and its application in crown pillar optimization

Peng

Yin

et al. 2016

J. Cent. South Univ.

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Irregular plates are very common structures in engineering, such as ore structures in mining. In this work, the Galerkin solution to the problem of a Kirchhoff plate lying on the Winkler foundation with two edges simply supported and the other two clamped supported is derived. Coordinate transformation technique is used during the solving process so that the solution is suitable to irregular shaped plates. The mechanical model and the solution proposed are then used to model the crown pillars between two adjacent levels in Sanshandao gold mine, which uses backfill method for mining operation. After that, an objective function, which takes security, economic profits and filling effect into consideration, is built to evaluate design proposals. Thickness optimizations for crown pillars are finally conducted in both conditions that the vertical stiffness of the foundation is known and unknown. The procedure presented in the work provides the guidance in thickness designing of complex shaped crown pillars and the preparation of backfill materials, thus to achieve the best balance between security and profits.

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Section: Introductionmentioning

confidence: 99%

Galerkin solution of Winkler foundation-based irregular Kirchhoff plate model and its application in crown pillar optimization

Peng

Yin

et al. 2016

J. Cent. South Univ.

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“…A substantial study of such problem for an orthotropic plate in the static and dynamical cases was carried out in [12].…”

Section: Introductionmentioning

confidence: 99%

Study of the stress-strain state of orthotropic shells under the action of dynamical impulse loads

Vetrov¹,

Шевченко²

2012

J Math Sci

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We consider the problem of the construction of fundamental solutions of the dynamic equations of a thin shallow orthotropic shell with arbitrary Gauss curvature. The asymptotic formulas for a dynamical deflection of a shell under the action of an impulse load are obtained. The physical elasticity relations of the dynamical theory of thin shells are determined. The correctness of the use of a model of special orthotropy in calculations is studied.

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“…It should be stressed that these jumps are not inherently related to the displacement function over the solution domain; instead, they are the artifact resulting from the Fourier series representation of the displacement solution. The detailed illustration is given in [43]. More information about the improved Fourier series can be seen in [42].…”

Section: Admissible Displacement Functionsmentioning

confidence: 99%

“…It has been always of great interest for researchers to develop a unified, accurate, and feasible admissible displacement function which can be used to determine the vibration characteristics of a structure with arbitrary boundary conditions. In the present work, an improved Fourier series proposed by Li for the vibration analysis of 1D [42] and 2D [43] structures with general boundary conditions is extended to investigate the …”

Section: Admissible Displacement Functionsmentioning

confidence: 99%

Three-Dimensional Vibration Analysis of Isotropic and Orthotropic Open Shells and Plates with Arbitrary Boundary Conditions

Jin

Shi

2015

Shock and Vibration

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This paper presents elasticity solutions for the vibration analysis of isotropic and orthotropic open shells and plates with arbitrary boundary conditions, including spherical and cylindrical shells and rectangular plates. Vibration characteristics of the shells and plates have been obtained via a unified three-dimensional displacement-based energy formulation represented in the general shell coordinates, in which the displacement in each direction is expanded as a triplicate product of the cosine Fourier series with the addition of certain supplementary terms introduced to eliminate any possible jumps with the original displacement function and its relevant derivatives at the boundaries. All the expansion coefficients are then treated equally as independent generalized coordinates and determined by the Rayleigh-Ritz procedure. To validate the accuracy of the present method and the corresponding theoretical formulations, numerical cases have been compared against the results in the literature and those of 3D FE analysis, with excellent agreements obtained. The effects of boundary conditions, material parameters, and geometric dimensions on the frequencies are discussed as well. Finally, several 3D vibration results of isotropic and orthotropic open spherical and cylindrical shells and plates with different geometry dimensions are presented for various boundary conditions, which may be served as benchmark solutions for future researchers as well as structure designers in this field.

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An accurate solution method for the static and dynamic deflections of orthotropic plates with general boundary conditions

Cited by 72 publications

References 14 publications

Galerkin solution of Winkler foundation-based irregular Kirchhoff plate model and its application in crown pillar optimization

Galerkin solution of Winkler foundation-based irregular Kirchhoff plate model and its application in crown pillar optimization

Study of the stress-strain state of orthotropic shells under the action of dynamical impulse loads

Three-Dimensional Vibration Analysis of Isotropic and Orthotropic Open Shells and Plates with Arbitrary Boundary Conditions

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