A Refined Theory for Laminated Anisotropic, Cylindrical Shells

Whitney, James M.; Sun, Chang

doi:10.1115/1.3423312

Cited by 169 publications

(34 citation statements)

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“…Higher order theories [Whitney ,1974] which include higher order shear modes lead to improved estimates of in-plane stress distributions. However, higher order theories based on assumption of second and higher order polynomial distribution of in-plane displacements over the depth-of the plate, have two critical deficiencies.…”

Section: (A) 6x14 Elementmentioning

confidence: 99%

“…and linear functions for out-of-plane displacement (u 3 ) to represent the first antisymmetric shear mode and non-zero normal strain. Whitney [1974] also presented another higher-order theory, in which linear variation of in-plane displacements and quadratic variation of normal displacement through the thickness were assumed. This was used to analyze laminated cylindrical shells with moderate radius-to-thickness ratio under static loading.…”

Section: Higher Order Theorymentioning

confidence: 99%

See 1 more Smart Citation

Variational Formulation and Finite Element Implementation of Pagano's Theory of Laminated Plates

Sandh

Wolfe²,

Chyou

1995

Mechanics of Composite Materials and Structures

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Section: (A) 6x14 Elementmentioning

confidence: 99%

Section: Higher Order Theorymentioning

confidence: 99%

Variational Formulation and Finite Element Implementation of Pagano's Theory of Laminated Plates

Sandh

Wolfe²,

Chyou

1995

Mechanics of Composite Materials and Structures

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“…A large diversity of high-order theories of multilayered plates [17][18][19][20] and shells [21][22], relies upon the various selection of the degree of approximation of (14).…”

Section: P=omentioning

confidence: 99%

Refined geometrically nonlinear theories of anisotropic laminated shells

Librescu¹

1987

Quart. Appl. Math.

112

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“…Shell theories accounting for transverse shear and normal deformations have been developed, among others, by Hildebrand et al [14], Reissner [15], and Whitney and Sun [16,17]. Bert [18], Leissa [19], Qatu [1,20], and Liew et al [21], among others, have reviewed shell theories.…”

Section: Introductionmentioning

confidence: 99%

Stretching and bending deformations due to normal and shear tractions of doubly curved shells using third-order shear and normal deformable theory

Shah

Batra

2016

Mechanics of Advanced Materials and Structures

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We analyze static infinitesimal deformations of doubly curved shells using a third-order shear and normal deformable theory (TSNDT) and delineate effects of the curvilinear length/thickness ratio, R/a, a/h, radius of curvature/curvilinear length, and the ratio of the two principal radii on through-the-thickness stresses, strain energies of the in-plane and the transverse shear and normal deformations, and strain energies of stretching and bending deformations for loads that include uniform normal tractions on a major surface and equal and opposite tangential tractions on the two major surfaces. In the TSNDT the three displacement components at a point are represented as complete polynomials of degree three in the thickness coordinate. Advantages of the TSNDT include not needing a shear correction factor, allowing stresses for monolithic shells to be computed from the constitutive relation and the shell theory displacements, and considering general tractions on bounding surfaces. For laminated shells we use an equivalent single layer TSNDT and find the in-plane stresses from the constitutive relations and the transverse stresses with a onestep stress recovery scheme. The in-house developed finite element software is first verified by comparing displacements and stresses in the shell computed from it with those from either analytical or numerical solutions of the corresponding 3D problems. The strain energy of a spherical shell is found to approach that of a plate when R/a exceeds 10. For a thick clamped shell of aspect ratio 5 subjected to uniform normal traction on the outer surface, the in-plane and the transverse deformations contribute equally to the total strain energy for R/a greater than 5. However, for a cantilever shell of aspect ratio 5 subjected to equal and opposite uniform tangential tractions on the two major surfaces, the strain energy of in-plane deformations equals 95-98% of the total strain energy. Numerical results presented herein for several problems provide insights into different deformation modes, help designers decide when to consider effects of transverse deformations, and use the TSNDT for optimizing doubly curved shells.

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A Refined Theory for Laminated Anisotropic, Cylindrical Shells

Cited by 169 publications

References 0 publications

Variational Formulation and Finite Element Implementation of Pagano's Theory of Laminated Plates

Variational Formulation and Finite Element Implementation of Pagano's Theory of Laminated Plates

Refined geometrically nonlinear theories of anisotropic laminated shells

Stretching and bending deformations due to normal and shear tractions of doubly curved shells using third-order shear and normal deformable theory

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