Buckling of skew plate structures using <i>B</i>‐spline functions

Mizusawa, T.; Kajita, Tateo; Naruoka, Masao

doi:10.1002/nme.1620150108

Cited by 57 publications

(16 citation statements)

References 24 publications

(1 reference statement)

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“…The maximum kinetic energy is where pl is the mass density of the Ith layer. Clearly the strain energy (equations (6), (7)) comprises distinct contributions from bending and through-thickness shearing actions whilst the kinetic energy (equation (8)) comprises distinct contributions associated with translation and with rotation.…”

Section: Discussionmentioning

confidence: 99%

Vibration of shear‐deformable rectangular plates using a spline‐function Rayleigh‐Ritz approach

Wang¹,

Dawe²

1993

Numerical Meth Engineering

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SUMMARYThe prediction of the natural frequencies of vibration of rectangular plates or. orthotropic laminates is described, through the use of B-spline functions as trial functions in a Rayleigh-Ritz approach. Throughthickness shear deformation effects are included in the analysis and hence assumptions have to be made for the spatial variation over the plate middle surface of each of the lateral deflection and the two rotation components. Two versions of the splinc-function Rayleigh-Ritz approach are described: in one of these the deflection and rotations are represcnted by functions of the same polynomial order, whilst in the other a lower-order representation is used for cach rotation component in one of the co-ordinate directions. It is shown in a number of applications that the former version leads to shear-locking behaviour whilst the latter version avoids this behaviour and is suitable for the analysis of both thick and thin plates.

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Section: Discussionmentioning

confidence: 99%

Vibration of shear‐deformable rectangular plates using a spline‐function Rayleigh‐Ritz approach

Wang¹,

Dawe²

1993

Numerical Meth Engineering

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“…The order of the matrices is given by r x (k + MRl), in which k -1 is the degree of B-spline functions, and MR is the number of strips and r is the number of series terms in the basic functions. If the two opposite radial edges are simply supported, the basic functions in equation (2) can be expressed by (18) Y,(E) = sin(rn?rf); (rn = 1,2, ..., r ) Y,([) = sin(p?rE); (p = 1,2, ..., r )…”

Section: A2w/aq2((1/a)aw/aq + (1/42)(1/a2)a2w/at21 + 2(1 -~) ( 1 / 9 mentioning

confidence: 99%

Vibration of annular sector plates using spline strip method

Mizusawa

Kajita

1992

Commun. appl. numer. methods

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SUMMARYThis paper presents the vibrations of annular sectorial plates with two opposite radial edges simply supported using the spline strip method. To demonstrate the convergence and accuracy of the present method, several examples are solved, and results are compared with those obtained by the analytical method and by other numerical methods. Stable convergence and excellent accuracy are obtained using the high-order spline strip models. Accurate frequencies of annular sector plates with different sector angles, radii ratios and tapered thickness in the angular direction are shown in tabular form.

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“…Aircraft wings and skew bridges are well-known direct applications of these kinds of plates. The elastic buckling of skew plates has been studied by some researchers [1][2][3]. However, to the best of author's knowledge, the plastic buckling of skew plates is not available in open literature.…”

Section: Introductionmentioning

confidence: 97%

Elastic/plastic buckling analysis of skew plates under in-plane shear loading with incremental and deformation theories of plasticity by GDQ method

Maarefdoust

Kadkhodayan

2014

J Braz. Soc. Mech. Sci. Eng.

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The present study is concerned with the elastic/ plastic buckling analysis of a skew plate under in-plane shear loading. The governing equations for moderately thick skew plates are analytically derived based on firstorder shear deformation theory, whereas the incremental and deformation theories of plasticity are employed. Two types of shear loads, i.e. rectangular shear (R-shear) and skew shear (S-shear) have been investigated. The buckling coefficient values are significantly affected by the direction of stresses. Since the problem is geometrically and physically nonlinear, the generalized differential quadrature method as an accurate, simple and computationally efficient numerical tool is adopted to discretize the governing equations and the related boundary conditions. Then, a direct iterative method is employed to obtain the buckling coefficients of skew plates. To demonstrate the accuracy of the present analytical solution, a comparison is made with the published experimental and numerical results in literature. The influences of the aspect and thickness ratios, skew angle, incremental and deformation theories and various boundary conditions are examined for R-shear and S-shear buckling coefficients. Finally, some mode shapes of the skew thick plates are illustrated. The present results may serve as benchmark solutions for such plates.

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Buckling of skew plate structures using B‐spline functions

Cited by 57 publications

References 24 publications

Vibration of shear‐deformable rectangular plates using a spline‐function Rayleigh‐Ritz approach

Vibration of shear‐deformable rectangular plates using a spline‐function Rayleigh‐Ritz approach

Vibration of annular sector plates using spline strip method

Elastic/plastic buckling analysis of skew plates under in-plane shear loading with incremental and deformation theories of plasticity by GDQ method

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