Vibrations and stability of anisotropic and sandwich cylindrical shells of arbitrary cross section
Vibrations and stability of anisotropic and sandwich cylindrical shells of arbitrary cross section
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Vibrations and stability of anisotropic and sandwich cylindrical shells of arbitrary cross section
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A buckling formulation for anisotropic curved panels with variable curvature is presented in this paper. The variable curvature panel is assumed to consists of two or more panels of constant but different curvatures. Bezier functions are used as Ritz functions Displacement (C(sup 0)), and slope (C(sup 1)) continuities between segments are imposed by manipulation of the Bezier control points. A first-order shear-deformation theory is used in the buckling formulation. Results obtained from the present formulation are compared with those from finite element simulations and are found to be in good agreement.
Equations of theory of shells consisting of several anisotropic layers
Basic technical theories and engineering calculation equations for anisotropic plates and shells made of rigid reinforced plastics, mainly laminated fiberglass, are presented and discussed. Solutions are given for many problems of design of structural plates and shells, including curved sections and tanks, as well as two chapters on selection of the optimum materials, are given. Accounting for interlayer shearing and transverse separation, which are new engineering properties, are discussed. Application of the results obtained to thin three ply plates and shells wth a light elastic filler is presented and discussed.
Finite element papers published in the open literature on the static bending and free vibration of layered, anisotropic, and composite plates and shells are reviewed. A literature review of large-deflection bending and large-amplitude free oscillations of layered composite plates and shells is also presented. Non-finite element literature is cited for continuity of the discussion.
Nonlinear and bifurcation buckling equations for elastic, stiffened, geometrically perfect, right-circular cylindrical, anisotropic shells subjected to combined loads are presented that are based on Sanders' shell theory. Based on these equations, a three-parameter approximate Rayleigh-Ritz solution and a classical solution to the buckling problem are presented for cylinders with simply supported edges. Extensive comparisons of results obtained from these solutions with published results are also presented for a wide range of cylinder constructions. These comparisons include laminated-composite cylinders with a wide variety of shell-wall orthotropies and anisotropies. Numerous results are also given that show the discrepancies between the results obtained by using Donnell's equations and variants of Sanders' equations. For some cases, nondimensional parameters are identified and "master" curves are presented that facilitate the concise representation of results.
Structurally orthotropic shells analyzed by compliance method
This study is an extension of a previous investigation of the combined effect of axisymmetric thickness variation and axisymmetric initial geometric imperfection on buckling of isotropic shells under uniform axial compression. Here the anisotropic cylindrical shells are investigated by means of Koiter's energy criterion. An asymptotic formula is derived which can be used to determine the critical buckling load for composite shells with combined initial geometric imperfection and thickness variation. Results are compared with those obtained by the software packages BOSOR4 and PANDA2.
A special three-dimensional element based on the total Lagrangian description of the motion of a layered anisotropic composite medium is developed, validated and employed to analyze laminated anisotropic composite shells. The element contains the following features: geometric nonlinearity, dynamic (transient) behavior and arbitrary lamination scheme and lamina properties. Numerical results of nonlinear bending, natural vibration, and transient response are presented to illustrate the capabilities of the element.
Stress analysis of anisotropic viscoelastic cylindrical shell
Stability of cylindrical shell of anisotropic homogeneous layers in supersonic gas stream
An integrated computer program entitled Field Analysis of Shells of Revolution (FASOR) currently under development for NASA is described. When completed, this code will treat prebuckling, buckling, initial postbuckling and vibrations under axisymmetric static loads as well as linear response and bifurcation under asymmetric static loads. Although these modes of response are treated by existing programs, FASOR extends the class of problems treated to include general anisotropy and transverse shear deformations of stiffened laminated shells. At the same time, a primary goal is to develop a program which is free of the usual problems of modeling, numerical convergence and ill-conditioning, laborious problem setup, limitations on problem size and interpretation of output. The field method is briefly described, the shell differential equations are cast in a suitable form for solution by this method and essential aspects of the input format are presented. Numerical results are given for both unstiffened and stiffened anisotropic cylindrical shells and compared with previously published analytical solutions.
A review is made of the different approaches used for modeling multilayered composite shells. Discussion focuses on different approaches for developing two-dimensional shear deformation theories; classification of two-dimensional theories based on introducing plausible displacement, strain and/or stress assumptions in the thickness direction; first-order shear deformation theories based on linear displacement assumptions in the thickness coordinate; and efficient computational strategies for anisotropic composite shells. Extensive numerical results are presented showing the effects of variation in the lamination and geometric parameters of simply supported composite cylinders on the accuracy of the static and vibrational responses predicted by eight different modeling approaches (based on two-dimensional shear deformation theories).
Chemical design of multicomponent nanocrystals requires atomic-level understanding of reaction kinetics. Here, we apply single-particle imaging coupled with atomistic simulation to study reaction pathways and rates of Pd@Au and Cu@Au core-shell nanocubes undergoing oxidative dissolution. Quantitative analysis of etching kinetics using in situ transmission electron microscopy (TEM) imaging reveals that the dissolution mechanism changes from predominantly edge-selective to layer-by-layer removal of Au atoms as the reaction progresses. Dissolution of the Au shell slows down when both metals are exposed, which we attribute to galvanic corrosion protection. Morphological transformations are determined by intrinsic anisotropy due to coordination-number-dependent atom removal rates and extrinsic anisotropy induced by the graphene window. Our work demonstrates that bimetallic coreshell nanocrystals are excellent probes for the local physicochemical conditions inside TEM liquid cells. Furthermore, single-particle TEM imaging and atomistic simulation of reaction trajectories can inform future design strategies for compositionally and architecturally sophisticated nanocrystals.
An efficient computational method for the nonlinear dynamic analysis of quasi-symmetric anisotropic structures is proposed. The application of mixed models simplifies the analytical development and improves the accuracy of the response predictions, and operator splitting allows the reduction of the analysis model of the quasi-symmetric structure to that of the corresponding symmetric structure. The preconditoned conjugate gradient provides a stable and effective technique for generating the unsymmetric response of the structure as the sum of a symmetrized response plus correction modes. The effectiveness of the strategy is demonstrated with the example of a laminated anisotropic shallow shell of quadrilateral planform subjected to uniform normal loading.
Model for predicting solar shell effect on anisotropic solar cosmic ray propagation
To study the effect of cancellations within long-range interactions on local isotropy at the small scales, we calculate explicitly the degree of cancellation in distant interactions in the simulations of Yeung & Brasseur and Yeung, Brasseur & Wang using the single scale disparity parameter 's' developed by Zhou. In the simulations, initially isotropic simulated turbulence was subjected to coherent anisotropic forcing at the large scales and the smallest scales were found to become anisotropic as a consequence of direct large-small scale couplings. We find that the marginally distant interactions in the simulation do not cancel out under summation and that the development of small-scale anisotropy is indeed a direct consequence of the distant triadic group, as argued by Yeung, et. al. A reduction of anisotropy at later times occurs as a result of the isotropizing influences of more local energy-cascading triadic interactions. Nevertheless, the local-to-nonlocal triadic group persists as an isotropizing influence at later times. We find that, whereas long-range interactions, in general, contribute little to net energy transfer into or out of a high wavenumber shell k, the anisotropic transfer of component energy within the shell increases with increasing scale separations. These results are consistent with results by Zhou, and Brasseur & Wei, and suggest that the anisotropizing influences of long range interactions should persist to higher Reynolds numbers. The residual effect of the forced distant group in this low-Reynolds number simulation is found to be forward cascading, on average.