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

1995 ◽  
Vol 10 (4) ◽  
pp. 215-230 ◽  
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 → ∞.

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

2000 ◽  
Vol 15 (1) ◽  
pp. 53-58 ◽  
Author(s):  
G. H. Nie
Keyword(s):  
Continuum Model ◽  
Single Layer ◽  
Free Vibrations ◽  
Asymptotic Iteration Method ◽  
Radius Of Curvature ◽  
Governing Equations ◽  
Spherical Shells ◽  
Linear Characteristic ◽  
Non Linear ◽  
Variable Equation

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.

scholarly journals Non-linear analysis of laminated composite doubly curved shallow shells

2006 ◽  
Vol 28 (1) ◽  
pp. 43-55
Author(s):  
Dao Huy Bich
Keyword(s):  
Laminated Composite ◽  
Governing Equations ◽  
Shallow Shells ◽  
Approximate Analytical Solutions ◽  
Linear Buckling ◽  
Non Linear ◽  
Vibration Problems ◽  
Doubly Curved ◽  
Analytical Expressions ◽  
Load Deflection Curve

This paper deals with governing equations and approximate analytical solutions based on some wellknown assumptions to the non-linear buckling and vibration problems of laminated composite doubly curved shallow shells. Obtained results will be presented by analytical expressions of the lower critical load, the postbuckling load-deflection curve and the fundamental frequency of non-linear free vibration of the shell.

Influence of magneto-electric environments on size-dependent bending results of three-layer piezomagnetic curved nanobeam based on sinusoidal shear deformation theory

2017 ◽  
Vol 21 (8) ◽  
pp. 2751-2778 ◽  
Author(s):  
Mohammad Arefi ◽  
Ashraf M Zenkour
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Virtual Work ◽  
Nonlocal Parameter ◽  
Shear Deformation Theory ◽  
Radius Of Curvature ◽  
Governing Equations ◽  
Size Dependent ◽  
Magnetic Potentials ◽  
Sinusoidal Shear Deformation Theory

In this work, an analytical solution for bending analysis of the three-layer curved nanobeams is presented. The nanobeams are including a nanocore and two piezomagnetic face-sheets. The structure is subjected to applied electric and magnetic potentials while is resting on Pasternak's foundation. To reach more accurate results, sinusoidal shear deformation theory is employed to derive displacement field of the curved nanobeams. In addition, nonlocal electro-magneto-elasticity relations are employed to derive governing equations of bending based on the principle of virtual work. The analytical results are presented for simply supported curved nanobeam to discuss the influence of important parameters on the vibration and bending results. The important parameters are included spring and shear parameters of the foundation, applied electric and magnetic potentials, nonlocal parameter, and radius of curvature of curved nanobeam.

Thermal Post-Buckling Analysis of Functionally Graded Composite Plates with Nonlinear Aerodynamic Forces

2010 ◽  
Vol 123-125 ◽  
pp. 280-283
Author(s):  
Chang Yull Lee ◽  
Ji Hwan Kim
Keyword(s):  
Material Properties ◽  
Numerical Solutions ◽  
Virtual Work ◽  
Shear Deformation Theory ◽  
Composite Plates ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Governing Equations ◽  
Functionally Graded Composite ◽  
Post Buckling

The post-buckling of the functionally graded composite plate under thermal environment with aerodynamic loading is studied. The structural model has three layers with ceramic, FGM and metal, respectively. The outer layers of the sandwich plate are different homogeneous and isotropic material properties for ceramic and metal. Whereas the core is FGM layer, material properties vary continuously from one interface to the other in the thickness direction according to a simple power law distribution in terms of the volume fractions. Governing equations are derived by using the principle of virtual work and numerical solutions are solved through a finite element method. The first-order shear deformation theory and von-Karman strain-displacement relations are based to derive governing equations of the plate. Aerodynamic effects are dealt by adopting nonlinear third-order piston theory for structural and aerodynamic nonlinearity. The Newton-Raphson iterative method applied for solving the nonlinear equations of the thermal post-buckling analysis

scholarly journals Vibration and Instability of Rotating Composite Thin-Walled Shafts with Internal Damping

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Ren Yongsheng ◽  
Zhang Xingqi ◽  
Liu Yanghang ◽  
Chen Xiulong
Keyword(s):  
Virtual Work ◽  
Numerical Study ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Dynamical Analysis ◽  
Design Parameters ◽  
Internal Damping ◽  
Analysis Method ◽  
Governing Equations ◽  
Thin Walled

The dynamical analysis of a rotating thin-walled composite shaft with internal damping is carried out analytically. The equations of motion are derived using the thin-walled composite beam theory and the principle of virtual work. The internal damping of shafts is introduced by adopting the multiscale damping analysis method. Galerkin’s method is used to discretize and solve the governing equations. Numerical study shows the effect of design parameters on the natural frequencies, critical rotating speeds, and instability thresholds of shafts.

scholarly journals Non-linear buckling analysis of functionally graded shallow spherical shells

2009 ◽  
Vol 31 (1) ◽  
pp. 17-30 ◽  
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.

Non-Linear Control of a Neutralisation Process

1971 ◽  
Vol 4 (9) ◽  
pp. T151-T157 ◽  
Author(s):  
P D Roberts
Keyword(s):  
Simulation Study ◽  
Digital Simulation ◽  
Linear Control ◽  
Attractive Alternative ◽  
Error Signal ◽  
Linear Controller ◽  
Linear Characteristic ◽  
Non Linear ◽  
On Line ◽  
Extra Parameter

The paper describes a digital simulation study of the application of a non-linear controller to the regulation of a single stage neutralisation process. In the controller, the proportional gain increases with amplitude of controller error signal. The performance of the non-linear controller is compared with that of a conventional linear controller and with the performance obtained by employing a linear controller with a linearisation network designed to compensate for the non-linear characteristic of the neutralisation curve. Although the performance of the non-linear controller is inferior to that obtained by employing a perfect linearisation network, its performance is still considerably superior to that obtained by using a conventional linear controller when operating at a symmetrical point on the neutralisation curve. In contrast to the linearisation network technique, the non-linear controller contains only one extra parameter and can be readily tuned on-line without prior knowledge of the neutralisation curve. Hence, it can be considered as an attractive alternative for the control of neutralisation processes.

Symmetric Thermo-Electro-Elastic Response of Piezoelectric Hollow Cylinder Under Thermal Shock Using Lord–Shulman Theory

2020 ◽  
Vol 20 (05) ◽  
pp. 2050059
Author(s):  
S. M. H. Jani ◽  
Y. Kiani
Keyword(s):  
Thermal Shock ◽  
Differential Quadrature Method ◽  
Elastic Response ◽  
Governing Equations ◽  
Coupled Equations ◽  
Piezoelectric Hollow Cylinder ◽  
Time Marching ◽  
Generalized Differential ◽  
Lord And Shulman Theory ◽  
Marching Scheme

The response of a long hollow cylindrical vessel made from a piezoelectric material is considered in the present investigation. The piezoelectric vessel is subjected to a thermal shock on one surface. The generalized piezo-thermo-elasticity formulation of Lord and Shulman is adopted which contains a single relaxation time to consider the finite speed of temperature wave propagation. The response of the cylinder is assumed to be axi-symmetric. Three coupled equations are established as the governing equations, which are the equation of motion, the energy equation and the Maxwell equation. These equations are transformed into the dimensionless ones. With the aid of the generalized differential quadrature method, these equations are discretized in the radial direction. After that, with the aid of the Newmark time marching scheme, the temporal evolutions of the thermo-electro-elastic parameters are obtained. Novel numerical results are presented to obtain the response of the cylinder subjected to a thermal shock using the Lord and Shulman theory of thermoelasticity.

Investigation on Free Vibration of Buckled Beams

2012 ◽  
Vol 433-440 ◽  
pp. 41-44 ◽  
Author(s):  
Ming Hsu Tsai ◽  
Wen Yi Lin ◽  
Kuo Mo Hsiao ◽  
Fu Mio Fujii
Keyword(s):  
Free Vibration ◽  
Virtual Work ◽  
Beam Theory ◽  
Taylor Series Expansion ◽  
Element Formulation ◽  
Governing Equations ◽  
Nonlinear Beam ◽  
Buckled Beams ◽  
Buckled Beam ◽  
D’Alembert Principle

The objective of this study is to investigate the deformed configuration and free vibration around the deformed configuration of clamped buckled beams by co-rotational finite element formulation. The principle of virtual work, d'Alembert principle and the consistent second order linearization of the nonlinear beam theory are used to derive the element equations in current element coordinates. The governing equations for linear vibration are obtained by the first order Taylor series expansion of the equation of motion at the static equilibrium position of the buckled beam. Numerical examples are studied to investigate the natural frequencies of clamped buckled beams with different slenderness ratios under different axial compression.

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