Bending of laminated orthotropic cylindrical shells—An elasticity approach

Varadan, T.K.; Bhaskar, K.

doi:10.1016/0263-8223(91)90067-9

Cited by 182 publications

(85 citation statements)

References 3 publications

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“…They validate the routine on the same rectangular plate as in their first paper, then use the implementation to solve for interlaminar stresses in a simply-supported cylindrical shell, comparing results to the exact solution by Varadan and Bhaskar [32].…”

Section: Methodsmentioning

confidence: 99%

“…Engblom and Ochoa [30] integrate the equation of equilibrium in the transverse direction to find the transverse normal stress. [32]. The authors apply their formulation to the cases of a sinusoidal load and a centrally located uniform load, both loads considering a step and rectangular pulse function in the time domain.…”

Section: Stress Recovery For Geometrically Linear Problemsmentioning

confidence: 99%

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Geometrically Nonlinear Stress Recovery in Composite Laminates

2012

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Composite laminates are increasingly being used as primary load bearing members in structures. However, because of the directional dependence of the properties of composite materials, additional failure modes appear that are absent in homogeneous, isotropic materials. Therefore, a stress analysis of a composite laminate is not complete without an accurate representation of the transverse (out-of-plane) stresses.Stress recovery is a common method to estimate the transverse stresses from a plate or shell analysis. This dissertation extends stress recovery to problems in which geometric nonlinearities, in the sense of von Kármán, are important. The current work presents a less complex formulation for the stress recovery procedure for plate geometries, compared with other implementations, and results in a post-processing procedure which can be applied to data from any plate analyses; analytical or numerical methods, resulting in continuous or discretized data.Recovered transverse stress results are presented for a variety of geometrically nonlinear example problems: a semi-infinite plate subjected to quasi-static transverse and shear loading, and a finite plate subjected to both quasi-static and dynamic transverse loading. For all cases, the corresponding results from a fully three-dimensional stress analysis are shown alongside the distributions from the stress recovery procedure. Good agreement is observed between the stresses obtained from each method for the cases considered. Discussion is included regarding the applicability and accuracy of the technique to varying plate geometries and varying degrees of nonlinearity, as well as the viability of the procedure in replacing a three-dimensional analysis in regard to the time required to obtain a solution.The proposed geometrically nonlinear stress recovery procedure results in estimations for transverse stresses which show good correlation to the three-dimensional finite element solutions. The procedure is accurate for quasi-static and dynamic loading cases and proves to be a viable replacement for more computationally expensive analyses.

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Section: Methodsmentioning

confidence: 99%

Section: Stress Recovery For Geometrically Linear Problemsmentioning

confidence: 99%

Geometrically Nonlinear Stress Recovery in Composite Laminates

2012

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“…(13). In a similar way, considering the transverse strain-stress constitutive behavior of ε zz (α, β, z) expressed in Eq.…”

Section: General Assumptions and Relationshipsmentioning

confidence: 99%

“…The role played by zig-zag effects and interlaminar continuity has been confirmed by many 3-D analysis of layered plates and shells. [9][10][11][12][13][14][15] These amendments become more significant when complicating effects such as high in-plane and/or out-of-plane transverse anisotropy are present. Hence, as referred by Carrera, 8 Koiter's recommendation concerning isotropic shells could be re-written for the case of multilayered shells as "... a refinement of ... unless the effects of interlaminar continuous transverse shear and normal stresses are taken into account at the same time."…”

Section: Introductionmentioning

confidence: 99%

Shells with Hybrid Active-Passive Damping Treatments: Modeling and Vibration Control

Vasques¹,

Rodrigues²

2006

47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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“…Here, subscripts L and T refer to the fiber and transverse directions of the layer. To compare the derived results with the 3D exact solution [10], the following dimensionless variables are utilized:…”

Section: Finite Element Formulationmentioning
confidence: 99%

Sampling Surfaces Formulation for Functionally Graded and Laminated Composite Shells
Куликов¹,
Mamontov²,
Плотникова³
et al. 2016
AM&T
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This paper focuses on a finite element implementation of the sampling surfaces (SaS) method for the three-dimensional (3D) stress analysis of functionally graded (FG) laminated elastic and electroelastic shells. The SaS formulation is based on choosing inside the nth layer n I not equally spaced SaS parallel to the middle surface of the shell in order to introduce the electric potentials and displacements of these surfaces as basic shell variables. Such choice of unknowns permits the presentation of the proposed FG shell formulation in a very compact form. The SaS are located inside each layer at Chebyshev polynomial nodes that improves the convergence of the SaS method significantly. KeywordsFunctionally graded material; laminated piezoelectric shell; sampling surfaces method, exact geometry solid-shell element.

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Bending of laminated orthotropic cylindrical shells—An elasticity approach

Cited by 182 publications

References 3 publications

Geometrically Nonlinear Stress Recovery in Composite Laminates

Geometrically Nonlinear Stress Recovery in Composite Laminates

Shells with Hybrid Active-Passive Damping Treatments: Modeling and Vibration Control

Sampling Surfaces Formulation for Functionally Graded and Laminated Composite Shells

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