Non-linear Free Vibration of Single-layer Reticulated Shallow Spherical Shells

This paper presents an asymptotic analysis on non-linear free vibrations of single-layer reticulated shallow spherical shells composed of beam members placed in two orthogonal directions with the aid of a continuum model proposed by the author. By introducing a parameter variable which is determined by solving a cubic single-variable equation for the case of axisymmetry, the fundamental governing equations can be exactly satisfied. The asymptotic iteration method has been adopted to obtain an analytical solution for a non-linear characteristic relation between the amplitude and frequency of the structure. Numerical examples are given, and the phenomena indicating softening and hardening of such structures have been presented for various values of radius of curvature (or apex rise) of hinged or clamped spherical shells.

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A Non-Linear Model for Stability Analysis of Reticulated Shallow Shells with Imperfections

International Journal of Space Structures ◽

10.1177/026635119501000404 ◽

1995 ◽

Vol 10 (4) ◽

pp. 215-230 ◽

Cited By ~ 11

Author(s):

G.H. Nie ◽

Y.K. Cheung

Keyword(s):

Virtual Work ◽

Equivalent Model ◽

Radius Of Curvature ◽

Governing Equations ◽

Shallow Shells ◽

Coupled Equations ◽

Linear Characteristic ◽

Non Linear ◽

Linear Stability Problem ◽

Imperfection Factor

A non-linear stability problem of imperfect reticulated shallow shells with distorted rectangular meshes is investigated in this paper. The fundamental governing equations are deduced by adopting an equivalent model and the principle of the virtual work. For the reticulated shallow spherical shell under uniform vertical load, an axisymmetrical case is considered and the analytical solution of the coupled equations is given with the help of the asymptotical iteration method. Meanwhile, non-linear characteristic relations concerning load, deflection and imperfection factor are numerically analyzed. In particular, the corresponding solution degenerates to that of a reticulated circular plate when the radius of curvature of the structure R → ∞.

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Non-linear buckling analysis of functionally graded shallow spherical shells

Vietnam Journal of Mechanics ◽

10.15625/0866-7136/31/1/5491 ◽

2009 ◽

Vol 31 (1) ◽

pp. 17-30 ◽

Cited By ~ 4

Author(s):

Dao Huy Bich

Keyword(s):

External Pressure ◽

Buckling Analysis ◽

Functionally Graded ◽

Power Law Distribution ◽

Governing Equations ◽

Spherical Shells ◽

Buckling Loads ◽

Linear Buckling ◽

Non Linear ◽

Linear Buckling Analysis

In the present paper the non-linear buckling analysis of functionally graded spherical shells subjected to external pressure is investigated. The material properties are graded in the thickness direction according to the power-law distribution in terms of volume fractions of the constituents of the material. In the formulation of governing equations geometric non-linearity in all strain-displacement relations of the shell is considered. Using Bubnov-Galerkin's method to solve the problem an approximated analytical expression of non-linear buckling loads of functionally graded spherical shells is obtained, that allows easily to investigate stability behaviors of the shell.

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EFFECT OF THE THROUGH-THE-THICKNESS TEMPERATURE DISTRIBUTION ON THE RESPONSE OF LAYERED AND COMPOSITE SHELLS

International Journal of Applied Mechanics ◽

10.1142/s1758825109000393 ◽

2009 ◽

Vol 01 (04) ◽

pp. 581-605 ◽

Cited By ~ 18

Author(s):

S. BRISCHETTO

Keyword(s):

Temperature Distribution ◽

Heat Conduction Equation ◽

Single Layer ◽

Stress Fields ◽

Thickness Direction ◽

Governing Equations ◽

Spherical Shells ◽

Correct Evaluation ◽

Linear Temperature ◽

Principle Of Virtual Displacements

This paper considers the thermal stress problem of thick and thin multilayered cylindrical and spherical shells including carbon fiber reinforced layers and/or a central soft core. The following two cases are considered: (i) the temperature distribution in thickness direction is assumed linear; (ii) the temperature distribution in thickness direction is calculated via Fourier's heat conduction equation. Carrera's Unified Formulation and the Principle of Virtual Displacements are used to obtain the governing equations in the case of shells with constant radii of curvature subjected to established temperature conditions on their upper and lower surfaces. Both Equivalent Single Layer and Layer Wise models with an order of expansion in the thickness direction from linear to fourth order are considered. The importance of refined models for a correct evaluation of displacement and stress fields in multilayered shells can be noted. Furthermore, it has been shown that results obtained assuming a linear temperature profile in the thickness direction can be meaningless.

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Analysis of non-linear behaviour of imperfect shallow spherical shells on pasternak foundation by the asymptotic iteration method

International Journal of Pressure Vessels and Piping ◽

10.1016/s0308-0161(03)00043-7 ◽

2003 ◽

Vol 80 (4) ◽

pp. 229-235 ◽

Cited By ~ 13

Author(s):

G.H. Nie

Keyword(s):

Iteration Method ◽

Asymptotic Iteration Method ◽

Pasternak Foundation ◽

Spherical Shells ◽

Non Linear ◽

Linear Behaviour

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Investigation on Non-linear Characteristic of Yawing Moment of Twin-tailed Configuration

32nd AIAA Applied Aerodynamics Conference ◽

10.2514/6.2014-2992 ◽

2014 ◽

Author(s):

Ye Qin ◽

Yankui Wang ◽

Qian Li

Keyword(s):

Linear Characteristic ◽

Non Linear

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Vibration of rotating circular cylindrical shells with distributed springs

Journal of Mechanics ◽

10.1093/jom/ufab008 ◽

2021 ◽

Vol 37 ◽

pp. 346-358

Author(s):

Fuchun Yang ◽

Xiaofeng Jiang ◽

Fuxin Du

Keyword(s):

Boundary Conditions ◽

Galerkin Method ◽

Shell Theory ◽

Rotation Speed ◽

Cylindrical Shells ◽

Free Vibrations ◽

Governing Equations ◽

Natural Response ◽

Circular Cylindrical Shells ◽

The Galerkin Method

Abstract Free vibrations of rotating cylindrical shells with distributed springs were studied. Based on the Flügge shell theory, the governing equations of rotating cylindrical shells with distributed springs were derived under typical boundary conditions. Multicomponent modal functions were used to satisfy the distributed springs around the circumference. The natural responses were analyzed using the Galerkin method. The effects of parameters, rotation speed, stiffness, and ratios of thickness/radius and length/radius, on natural response were also examined.

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On the Motion of Granular Materials Due to Shear

10.1115/imece2000-1991 ◽

2000 ◽

Author(s):

Mehrdad Massoudi ◽

Tran X. Phuoc

Keyword(s):

Finite Difference ◽

Granular Materials ◽

Continuum Model ◽

Theory Model ◽

Governing Equations ◽

Flat Plates ◽

Material Parameters ◽

Finite Difference Technique ◽

Linear Differential ◽

The Continuum

Abstract In this paper we study the flow of granular materials between two horisontal flat plates where the top plate is moving with a constant speed. The constitutive relation used for the stress is based on the continuum model proposed by Rajagopal and Massoudi (1990), where the material parameters are derived using the kinetic theory model proposed by Boyle and Massoudi (1990). The governing equations are non-dimensionalized and the resulting system of non-linear differential equations is solved numerically using finite difference technique.

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