Nonlinear dynamic buckling of spherical caps with initial imperfections

Kao, Robert

doi:10.1016/0045-7949(80)90093-0

Cited by 30 publications

(4 citation statements)

References 12 publications

(4 reference statements)

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“…The first observation is that the initial n-I illl~li~V increase of its magnitude [4,5,6,11]. It is also found that plastic yielding has a significant effect of weakening spherical shells, the degree of this effect increased with increase of the thickness-to-radius ratio.…”

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confidence: 88%

A comparative study on the elastic‐plastic collapse strength of initially imperfect deep spherical shells

Kao

1981

Numerical Meth Engineering

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Unfortunately, earlier tests conducted in Ref.[2] provided only one-fourth of the collapse strength predicted by the classical buckling theory. The huge discrepancy existed between the theory and the test is traceable. The test specimens used in Ref. [2] were formed from flat plates, which inevitable introduced significant departures from sphericity as well as variations in thickness and residual stresses. Since the initial imperfection among these adverse factors introduced has been assumed to be the primary source that affects the collapse strength of shell structures [3][4][5][6], the discrepancy is consequential and their comparison is inappropriate.To eliminate or at least partially reduce the adverse effect from flat plates, a series of nearly perfect machined shells were made in Refs.[7-9].The test results showed their collapse -2-strength was nearly 90% of the classical buckling pressure.These tests not only provide a strong support to the classical small deflection buckling theory of initially perfect spherical shells, but indicate that the initial imperfection does play a significant role in reducing shell load-carrying capacity.In view of the practicality, it is very difficult, if not impossible, to manufacture or measure most spherical shells with sufficient accuracy to justify the use of classical shell buckling formulas in design. It thus becomes evident that we should consider the unevenness factors in the shell buckling analysis. Since most contributions to the unevenness factors, such as variation in thickness, residual stress, boundary conditions, etc. may be, at least on occasions, are fairly well controlable, the effect of initial departures from sphericity appears most worthy of investigation.In connection with this investigation, the large deflection elastic buckling analysis was performed in Ref.[5] for complete spherical shells with a dimple type of initial imperfections.Focused only on shallow spherical portions of these complete shells, numerical solutions of these modified shell structures[6] compare quite satisfactorily with those of [5].The comparison by itself prompts a basic assumption that the collapse of initially imperfect shell structures is primarily a local phenomenon and therefore critically dependent on local geometry.For the purpose of the same investigation with an extension -3- As mentioned in the previous Section, the large deformation elastic-plastic thin shallow spherical shell theory [4] is utilized in this paper to predict the collapse strength of initially imperfect deep spherical shells. A shell is called "thin" if the ratio of its thickness to the radius of curvature of its middle surface is much less than unity; and a spherical shell is called "shallow" if its rise at the center is less than, say, one-eight of its base diameter.The geometry of a clamped spherical cap is shown in Fig. l(a), in which H is the central height, R the shell radius to the midsurface of the shell, a the base radius, and h the shell thickness; W(r) and U(r) are displacement components al...

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confidence: 88%

A comparative study on the elastic‐plastic collapse strength of initially imperfect deep spherical shells

Kao

1981

Numerical Meth Engineering

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“…[ 46 , 47 ], where a Ritz-Galerking procedure was proposed to solve a dynamic buckling problem for clumped spherical members. A finite difference method was applied, instead, in [ 48 , 49 , 50 ], to check for the sensitivity of the dynamic buckling response of spherical caps to some initial manufacturing imperfections. Novel theoretical shear deformation theories were applied in Refs.…”

Section: Introductionmentioning

confidence: 99%

Numerical Study on the Buckling Behavior of FG Porous Spherical Caps Reinforced by Graphene Platelets

et al. 2023

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The buckling response of functionally graded (FG) porous spherical caps reinforced by graphene platelets (GPLs) is assessed here, including both symmetric and uniform porosity patterns in the metal matrix, together with five different GPL distributions. The Halpin–Tsai model is here applied, together with an extended rule of mixture to determine the elastic properties and mass density of the selected shells, respectively. The equilibrium equations of the pre-buckling state are here determined according to a linear three-dimensional (3D) elasticity basics and principle of virtual work, whose solution is determined from classical finite elements. The buckling load is, thus, obtained based on the nonlinear Green strain field and generalized geometric stiffness concept. A large parametric investigation studies the sensitivity of the natural frequencies of FG porous spherical caps reinforced by GPLs to different parameters, namely, the porosity coefficients and distributions, together with different polar angles and stiffness coefficients of the elastic foundation, but also different GPL patterns and weight fractions of graphene nanofillers. Results denote that the maximum and minimum buckling loads are reached for GPL-X and GPL-O distributions, respectively. Additionally, the difference between the maximum and minimum critical buckling loads for different porosity distributions is approximately equal to 90%, which belong to symmetric distributions. It is also found that a high weight fraction of GPLs and a high porosity coefficient yield the highest and lowest effects of the structure on the buckling loads of the structure for an amount of 100% and 12.5%, respectively.

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“…Further results concerning the dynamic buckling of imperfect caps can be found in Refs. [17][18][19], where the possibility of having plastic deformations was considered as well.…”

Section: Introductionmentioning

confidence: 99%

Asymmetric Vibrations and Chaos in Spherical Caps under Uniform Time-varying Pressure Fields

Iarriccio

Zippo

Pellicano

2021

Preprint

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This paper presents a study on nonlinear asymmetric vibrations in shallow spherical caps under pressure loading. The Novozhilov’s nonlinear shell theory is used for modelling the structural strains. A reduced-order model is developed through the Rayleigh-Ritz method and Lagrange equations. The equations of motion are numerically integrated using an implicit solver. The bifurcation scenario is addressed by varying the external excitation frequency. The occurrence of asymmetric vibrations related to quasi-periodic and chaotic motion is shown through the analysis of time histories, spectra, Poincaré maps, and phase planes.

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Nonlinear dynamic buckling of spherical caps with initial imperfections

Cited by 30 publications

References 12 publications

A comparative study on the elastic‐plastic collapse strength of initially imperfect deep spherical shells

A comparative study on the elastic‐plastic collapse strength of initially imperfect deep spherical shells

Numerical Study on the Buckling Behavior of FG Porous Spherical Caps Reinforced by Graphene Platelets

Asymmetric Vibrations and Chaos in Spherical Caps under Uniform Time-varying Pressure Fields

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