Finite element buckling analysis of homogeneous and sandwich plates

Cook, Robert D.

doi:10.1002/nme.1620090104

Cited by 9 publications

(2 citation statements)

References 7 publications

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“…(19) q and ft are the independent field parameters with respect to which the functional II must be extremized. Extremizing it with respect to ft and solving the resulting equations, one gets = H~lGq (20) thus paving the way to express the element stress parameters ft in terms of nodal displacements q.…”

Section: Formulationmentioning

confidence: 99%

“…A simple isoparametric finite element formulation based on a displacement model to account for the nonlinear variation of in-plane displacements and constant transverse displacement through sandwich thickness was presented by Pandya and Kant 18 for the flexural analysis of multilayer symmetric sandwich plates. An initial stress stiffness matrix applicable to the plate elements of arbitrary quadrilateral shape with 12 degrees of freedom was formulated by Cook 19 and applied to the study of the buckling behavior of sandwich plates.…”

Section: Nomenclature Amentioning

confidence: 99%

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Analysis of sandwich plates using a hybrid-stress finite element

Rao¹,

Meyer-Piening²

1991

AIAA Journal

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The bending analysis of a generally orthotropic sandwich plate is presented using an accurate hybrid-stress finite element. The computer program necessary for such an analysis is developed, and its accuracy is checked by comparing the results with the three-dimensional elasticity solution of a simply supported three-layered rectangular laminate. The response of a square angle-ply, fiber-reinforced plastic-(FRP)-faced sandwich with simply supported and clamped edges is evaluated. The results show the following: 1) The soft core of an angle-ply FRP-faced thick sandwich supports a comparatively small amount of the shear force, more so with clamped conditions. The faces carry the shear force and are predominantly subjected to bending action about their centroidal axes, and hence, they no longer act as membranes. 2) To achieve the expected economy of the sandwich construction, it is recommended that the width-to-thickness ratio be kept greater than 20 and 50, respectively, in the cases of simply supported and clamped sandwich plates, wherever possible. Nomenclature a = width of the sandwich plate A ni -boundary of /th layer in element n b = length of the sandwich plate B l = strain matrix of /th layer Q»Q = Boolean matrices corresponding to displacements and stresses, respectively, in /th layer E ZZ9 E yy -elastic modulii, Eqs. (24) and (26) G',G = layer [Eq. (lib)] and element [Eq. (18b)] matrices G yz9 G xz = shear modulii, Eqs. (24) and (26) H 1 9 H = layer [Eq. (lla)] and element [Eq. (18a)] matrices h = thickness of sandwich hj(i = 1,2,3,4) = heights of layer boundaries measured from xy plane I /1 = determinant of the Jacobian of coordinate transformation k = stiffness matrix, Eq. (22) L = longitudinal direction of fiber N = number of elements N 1 = layer matrix depending on Nj and normalized coordinate f NJ = shape function of/'th node p = transverse force intensity p l = boundary load vector Po = amplitude of sinusoidal load or uniformly distributed load P( = 6 x 40 polynomial matrix, Eq. (2) q l ,q = layer and element nodal displacement vectors, respectively Q',Q = layer and element nodal force vectors, respectively S = width-to-thickness ratio, = a/h T M,V,M> U 1 9V 1 9W u 1 V ni = compliance matrix of /th layer = half the thickness of /th layer = transverse direction of fiber = normalized displacement components, Eq. (25) = displacement components of /th layer = values of u' 9 v 1 ', w at/th node = displacement vector of /th layer = volume of /th layer in element n = global coordinate axes Xjjj = in-plane global coordinates of/'th node z = normalized value of z, = 2z/h 0,0' = element and layer stress parameter vectors, respectively f?j(i = 1,2,3) = components of 0, Eq. (16) e/ = strain vector of /th layer €z*»€j0> = engineering strains 6 = fiber orientation angle measured from x axis Pyz'Pzx = Poisson's ratios, Eqs. (24) and (25) £,?7,r = normalized coordinates II = hybrid-stress functional ffi = stress vector of /th layer Tzx*Txy -stress components Tzx&xy -normalized stress components

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Section: Formulationmentioning

confidence: 99%

Section: Nomenclature Amentioning

confidence: 99%