Analysis of Shallow Shells with Rectangular Projection: Theory

Stavridis, L. T.; Armenàkas, Anthony E.

doi:10.1061/(asce)0733-9399(1988)114:6(923)

Cited by 8 publications

(4 citation statements)

References 6 publications

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“…The boundary conditions for the stress function È of the cantilever plate are treated in the papers (Stavridis, 1998, Stavridis andArmenakas, 1988). These boundary conditions are the following…”

Section: Problem Formulation 21 Equations Of the Plate Vibrationsmentioning

confidence: 99%

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Bifurcation behavior of steady vibrations of cantilever plates with geometrical nonlinearities interacting with three-dimensional inviscid potential flow

Аврамов

2014

Journal of Vibration and Control

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Cantilever plates with geometrical nonlinearities interacting with three-dimensional inviscid potential flow are considered. The new method for analysis of stability and bifurcations of the plate self-sustained vibrations is suggested. The basis of this method is the solution of the singular integral equations with respect to aerodynamic derivatives of the plate pressure drop. The Von Karman equations with respect to transversal displacements and a stress function are used to describe the plate vibrations with geometrical nonlinearity. The combination of the shooting technique and the continuation algorithm are used to analyze bifurcations and stability of the plate self-sustained vibrations. The plate aeroelastic self-sustained vibrations lose stability due to the Naimark-Sacker bifurcation. As a result of this bifurcation, almost periodic and chaotic vibrations are observed. It is shown, when it is acceptable to use one-dimensional models of plate self-sustained vibrations and when the plate model must be two-dimensional.

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Section: Problem Formulation 21 Equations Of the Plate Vibrationsmentioning

confidence: 99%

“…Now the trial functions form the expansion (equation ( 10)) F j ðx, yÞ are considered. These functions satisfy the boundary conditions (equation ( 8)) and they take the following form (Stavridis, 1998;Stavridis and Armenakas, 1988) F j ðx, yÞ ¼ j ðxÞ ' ð yÞ;…”

Section: Finite-degree-of-freedom Model Of Vibrations and System Stability Analysismentioning

confidence: 99%

Bifurcation behavior of steady vibrations of cantilever plates with geometrical nonlinearities interacting with three-dimensional inviscid potential flow

Аврамов

2014

Journal of Vibration and Control

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“…There are not many publications studying shell structures in the dynamic regime including shear deformation and large curvatures. For example, Lim (1995, 1996), Stavridis and Armenakas (1988) and Stavridis (1998) propose shallow shell elements also using the degenerated approach. Others, like Aksu (1997) and Kumbasar and Aksu (1995), formulate shell elements valid for moderately thick and really thick shells but assume orthogonal curvilinear coordinates along the lines of curvature of the reference surface of the shell.…”

Section: Introductionmentioning

confidence: 99%

An efficient general curvilinear coordinates finite element method for the linear dynamic study of thickness-independent shells

Valle

Albanesi²,

Fachinotti³

2019

Lat. Am. j. solids struct.

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yyTo date, a large number of finite element methods have been developed to study the dynamics of shell structures. Most of them are generally based on the degenerated solid approach and other less in shell theories, but introducing, in this last case, some assumptions to analyze this problem: some of them refer to shallow shells (slightly curved shells), or consider thin shells neglecting shear deformation, or dispense some terms in their stress-strain developments like the off-diagonal components of the curvature or metric tensors (orthogonal coordinates). In the present work, we present an improved finite element method for the linear dynamic analysis of shells, from thin to moderately thick and thick shells, developed in general curvilinear coordinates, based on a refined shear deformation shell theory and free of the well-known shear locking effect. Exact constitutive equations, including higher order moments-strains relations, are also deduced for the adequate analysis of thick shells. To circumvent the shear locking problems, the mixed interpolation of the tensorial components (MITC) of the linear strain tensor is used. An exhaustive study of different surfaces is performed, especially in doubly curved shells, and interesting conclusions of the higher order modes of vibration and the strain energy of the element are derived. Other desirable features like a low computational effort, a straightforward extension to nonlinear formulation and applications for composite shells are found in this novel and general formulation. Very good results in the proposed practical cases have been found.

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“…For a formulation based on a stress function, the in-plane boundary conditions are satisfied on the average by introducing the following conditions, as justified, for example, in [20,21,22,23,24]…”

Section: Mathematical Formulationmentioning

confidence: 99%

Geometry Effects on the Nonlinear Oscillations of Viscoelastic Cylindrical Shells

Prado¹,

Amabili²,

Gonçalves³

et al. 2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. In this work the influence of geometry, load and material properties on the nonlinear vibrations of a simply supported viscoelastic circular cylindrical shell subjected to lateral harmonic load is studied. Donnell's non-linear shallow shell theory is used to model the shell, assumed to be made of a Kelvin-Voigt material type, and a modal solution with six degrees of freedom is used to describe the lateral displacements. The Galerkin method is applied to derive a set of coupled non-linear ordinary differential equations of motion.Obtained results show that the viscoelastic dissipation parameter has significant influence on the instability loads and resonance curves.

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Analysis of Shallow Shells with Rectangular Projection: Theory

Cited by 8 publications

References 6 publications

Bifurcation behavior of steady vibrations of cantilever plates with geometrical nonlinearities interacting with three-dimensional inviscid potential flow

Bifurcation behavior of steady vibrations of cantilever plates with geometrical nonlinearities interacting with three-dimensional inviscid potential flow

An efficient general curvilinear coordinates finite element method for the linear dynamic study of thickness-independent shells

Geometry Effects on the Nonlinear Oscillations of Viscoelastic Cylindrical Shells

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