• Structural Engineering and Mechanics
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• v.47 no.4
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• pp.559-573
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• 2013

Geometrically non-linear axisymmetric bending of a shallow spherical shell with a clamped or a simply supported edge under axisymmetric load was investigated numerically. The partial load was introduced by the Heaviside step function, and the solution was obtained by the finite difference and the Newton-Raphson methods. The thickness of the shell was considered to be uniform and the material was assumed to be homogeneous and isotropic. Sensitivity analysis was made for three geometrical parameters. The accuracy of the algorithm was checked by comparing the central deflection, the radial membrane stress at the edge, or the transverse shear force with the solutions of plates and shells in the literature and good agreement was obtained. The main findings of the study can be outlined as follows: (i) If the shell is fully loaded the central deflection of a clamped shell is larger than that of a simply supported shell provided that the shell is not very shallow, (ii) if the shell is partially loaded the central deflection of the shell is sensitive to the parameters of thickness, depth, and partial loading but the influence of the boundary conditions is negligible.

• Journal of the Korea Institute of Military Science and Technology
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• v.7 no.3 s.18
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• pp.157-164
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• 2004

This is a boundary integral formulation for elastic shallow shell structures subjected to both membrane and bending loads. Fundamental solutions for shell actions are determined from the plate solutions and, finally the corresponding kernel functions for shell BIEs can be constructed. It is illustrated by solving an example of uniform load of spherical cap.

• International Journal of Naval Architecture and Ocean Engineering
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• v.12 no.1
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• pp.680-690
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• 2020

In ocean environment, the sound speed gradient of seawater has an important influence on far field sound propagation. The FEM/BEM is used to decouple the vibroacoustic radiation of the spherical shell, and the Green function of the virtual source chain is adopted for decoupling. For far field radiated Sound Pressure Level (SPL), the Beam Displacement Ray normal Mode (BDRM) is employed. The vibration and near-/far-field radiated SPL of spherical shell is analyzed in shallow sea uniform layer, negative/positive gradient, negative thermocline environment, and deep-sea sound channel. Results show that the vibroacoustic radiation of spherical shell acted at 300Hz can be analogous to dipole. When the radiated field of the spherical shell is dominated by large-grazing-angle waves, it can be analogous to vertically distributed dipole, and the far field radiated SPL is lower; while similar to horizontally distributed dipole if dominated by small-grazing-angle waves, and the far field SPL is high.

• Advances in nano research
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• v.17 no.2
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• pp.95-107
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• 2024

In this article, the semi-analytical method was used to analyze the nonlinear dynamic stability and vibration analysis of sandwich shallow spherical shells (SSSS). The SSSS was considered as functionally graded carbon nanotube-reinforced composites (FG-CNTRC) with three new patterns of FG-CNTRC. The governing equation was obtained and discretized utilizing the Galerkin method by implementing the von Kármán-Donnell nonlinear strain-displacement relations. The nonlinear dynamic stability was analyzed by means of the fourth-order Runge-Kutta method. Then the Budiansky-Roth criterion was employed to obtain the critical load for the dynamic post-buckling. The approximate solution for the deflection was represented by suitable mode functions, which consisted of the three modes of transverse nonlinear oscillations, including one symmetrically and two asymmetrical mode shapes. The influences of various geometrical characteristics and material parameters were studied on the nonlinear dynamic stability and vibration response. The results showed that the order of layers had a significant influence on the amplitude of vibration and critical dynamic buckling load.

• Steel and Composite Structures
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• v.18 no.3
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• pp.693-709
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• 2015

In this article, nonlinear free vibration behaviour of functionally graded spherical panel is analysed. A nonlinear mathematical model is developed based on higher order shear deformation theory for shallow shell by taking Green-Lagrange type of nonlinear kinematics. The material properties of functionally graded material are assumed to be varying continuously in transverse direction and evaluated using Voigt micromechanical model in conjunction with power-law distribution. The governing equation of the shell panel is obtained using Hamilton's principle and discretised with the help of nonlinear finite element method. The desired responses are evaluated through a direct iterative method. The present model has been validated by comparing the frequency ratio (nonlinear frequency to linear frequency) with those available published literatures. Finally, the effect of geometrical parameters (curvature ratio, thickness ratio, aspect ratio and support condition), power law indices and amplitude of vibration on the frequency ratios of spherical panel have been discussed through numerical experimentations.

• Structural Engineering and Mechanics
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• v.53 no.4
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• pp.661-679
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• 2015

In this article, nonlinear finite element solutions of bending responses of functionally graded spherical panels are presented. The material properties of functionally graded material are graded in thickness direction according to a power-law distribution of volume fractions. A general nonlinear mathematical shallow shell model has been developed based on higher order shear deformation theory by taking the geometric nonlinearity in Green-Lagrange sense. The model is discretised using finite element steps and the governing equations are obtained through variational principle. The nonlinear responses are evaluated through a direct iterative method. The model is validated by comparing the responses with the available published literatures. The efficacy of present model has also been established by demonstrating a simulation based nonlinear model developed in ANSYS environment. The effects of power-law indices, support conditions and different geometrical parameters on bending behaviour of functionally graded shells are obtained and discussed in detail.

• Steel and Composite Structures
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• v.44 no.2
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• pp.155-169
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• 2022

In the present paper an analytical model was developed to study the non-linear vibrations of Functionally Graded Carbon Nanotube (FG-CNT) reinforced doubly-curved shallow shells using the Multiple Scales Method (MSM). The nonlinear partial differential equations of motion are based on the FGM shallow shell hypothesis, the non-linear geometric Von-Karman relationships, and the Galerkin method to reduce the partial differential equations associated with simply supported boundary conditions. The novelty of the present model is the simultaneous prediction of the natural frequencies and their mode shapes versus different curvatures (cylindrical, spherical, conical, and plate) and the different types of FG-CNTs. In addition to combining the vibration analysis with optimization algorithms based on the genetic algorithm, a design optimization methode was developed to maximize the natural frequencies. By considering the expression of the non-dimensional frequency as an objective optimization function, a genetic algorithm program was developed by valuing the mechanical properties, the geometric properties and the FG-CNT configuration of shallow double curvature shells. The results obtained show that the curvature, the volume fraction and the types of NTC distribution have considerable effects on the variation of the Dimensionless Fundamental Linear Frequency (DFLF). The frequency response of the shallow shells of the FG-CNTRC showed two types of nonlinear hardening and softening which are strongly influenced by the change in the fundamental vibration mode. In GA optimization, the mechanical properties and geometric properties in the transverse direction, the volume fraction, and types of distribution of CNTs have a considerable effect on the fundamental frequencies of shallow double-curvature shells. Where the difference between optimized and not optimized DFLF can reach 13.26%.

• The Bulletin of The Korean Astronomical Society
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• v.40 no.1
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• pp.65.3-66
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• 2015

The determination of three dimensional parameters (e.g., radial speed, angular width, source location) of Coronal Mass Ejections (CMEs) is very important for space weather forecast. To estimate these parameters, several cone models based on a flat cone or a shallow ice-cream cone with spherical front have been suggested. In this study, we investigate which cone model is proper for halo CME morphology using 33 CMEs which are identified as halo CMEs by one spacecraft (SOHO or STEREO-A or B) and as limb CMEs by the other ones. From geometrical parameters of these CMEs such as their front curvature, we find that near full ice-cream cone CMEs (28 events) are dominant over shallow ice-cream cone CMEs (5 events). So we develop a new full ice-cream cone model by assuming that a full ice-cream cone consists of many flat cones with different heights and angular widths. This model is carried out by the following steps: (1) construct a cone for given height and angular width, (2) project the cone onto the sky plane, (3) select points comprising the outer boundary, (4) minimize the difference between the estimated projection points with the observed ones. We apply this model to several halo CMEs and compare the results with those from other methods such as a Graduated Cylindrical Shell model and a geometrical triangulation method.

• The Bulletin of The Korean Astronomical Society
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• v.41 no.1
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• pp.47.1-47.1
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• 2016

The determination of three dimensional parameters (e.g., radial speed, angular width, source location) of Coronal Mass Ejections (CMEs) is very important for space weather forecast. To estimate these parameters, several cone models based on a flat cone or a shallow ice-cream cone with spherical front have been suggested. In this study, we investigate which cone model is proper for halo CME morphology using 26 CMEs which are identified as halo CMEs by one spacecraft (SOHO or STEREO-A or B) and as limb CMEs by the other ones. From geometrical parameters of these CMEs such as their front curvature, we find that near full ice-cream cone CMEs are dominant over shallow ice-cream cone CMEs. Thus we develop a new full ice-cream cone model by assuming that a full ice-cream cone consists of many flat cones with different heights and angular widths. This model is carried out by the following steps: (1) construct a cone for given height and angular width, (2) project the cone onto the sky plane, (3) select points comprising the outer boundary, (4) minimize the difference between the estimated projection speeds with the observed ones. We apply this model to 12 SOHO halo CMEs and compare the results with those from other stereoscopic methods (a geometrical triangulation method and a Graduated Cylindrical Shell model) based on multi-spacecraft data.

• Structural Engineering and Mechanics
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• v.68 no.5
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• pp.527-536
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• 2018

The free vibration frequency responses of the graded flat and curved (cylindrical, spherical, hyperbolic and elliptical) panel structures investigated in this research considering the rectangular and tilted planforms under unlike temperature loading. For the numerical implementation purpose, a micromechanical model is prepared with the help of Voigt's methodology via the power-law type of material model. Additionally, to incur the exact material strength, the temperature-dependent properties of each constituent of the graded structure included due to unlike thermal environment. The deformation kinematics of the rectangular/tilted graded shallow curved panel structural is modeled via higher-order type of polynomial functions. The final form of the eigenvalue equation of the heated structure obtained via Hamilton's principle and simultaneously solved numerically using finite element steps. To show the solution accuracy, a series of comparison the results are compared with the published data. Some new results are exemplified to exhibit the significance of power-law index, shallowness ratio, aspect ratio and thickness ratio on the combined thermal eigen characteristics of the regular and tilted graded panel structure.