Stability of Doubly Periodic Deformed Configurations of Plates and Shallow Shells

1970 ◽  
Vol 37 (3) ◽  
pp. 641-650 ◽  
Author(s):  
C. S. Hsu ◽  
S. S. Lee
Keyword(s):  
Stability Analysis ◽  
Nonlinear Analysis ◽  
Large Deflection ◽  
Multiple Equilibrium ◽  
Jump Phenomenon ◽  
Periodic Surface ◽  
Shallow Shells ◽  
Equilibrium Configurations

Presented here is a nonlinear analysis of infinite plates and shallow shells, subjected to doubly periodic surface loadings. The drastically different behaviors predicted by the linear and the nonlinear theories are analyzed and discussed. It turns out that the transition from the small to the large deflection behavior involves nonlinear bifurcation and the existence of multiple equilibrium configurations, and it entails the question of stability. Seen in this light, it is easy to explain various features special to problems in this class, including the jump phenomenon. From the viewpoint of stability analysis, this class of problems is distinct and interesting in that the perturbations which can lead to instability have actually a higher degree of symmetry than the unperturbed configurations.

The effects of drivers’ aggressive characteristics on traffic stability from a new car-following model

2016 ◽  
Vol 30 (18) ◽  
pp. 1650243 ◽  
Author(s):  
Guanghan Peng ◽  
Li Qing
Keyword(s):  
Stability Analysis ◽  
Nonlinear Analysis ◽  
Traffic Flow ◽  
Linear Stability Analysis ◽  
Stable Condition ◽  
Mkdv Equation ◽  
Stable Region ◽  
Car Following ◽  
Car Following Model ◽  
The Stability

In this paper, a new car-following model is proposed by considering the drivers’ aggressive characteristics. The stable condition and the modified Korteweg-de Vries (mKdV) equation are obtained by the linear stability analysis and nonlinear analysis, which show that the drivers’ aggressive characteristics can improve the stability of traffic flow. Furthermore, the numerical results show that the drivers’ aggressive characteristics increase the stable region of traffic flow and can reproduce the evolution and propagation of small perturbation.

A GALERKIN MESHFREE METHOD WITH STABILIZED CONFORMING NODAL INTEGRATION FOR GEOMETRICALLY NONLINEAR ANALYSIS OF SHEAR DEFORMABLE PLATES

2011 ◽  
Vol 08 (04) ◽  
pp. 685-703 ◽  
Author(s):  
DONGDONG WANG ◽  
YUE SUN
Keyword(s):  
Nonlinear Analysis ◽  
Large Deflection ◽  
Lagrangian Description ◽  
Geometrically Nonlinear ◽  
Geometrically Nonlinear Analysis ◽  
Nodal Integration ◽  
Galerkin Meshfree ◽  
Shear Deformable ◽  
Shear Deformable Plates ◽  
Stabilized Conforming Nodal Integration

A Galerkin meshfree approach formulated within the framework of stabilized conforming nodal integration (SCNI) is presented for geometrically nonlinear analysis of large deflection shear deformable plates. This method is based upon a Lagrangian curvature smoothing in which the smoothed curvature is constructed within a nodal representative domain on the initial configuration. It is shown that the Lagrangian smoothed nodal gradients of the meshfree shape function is capable of exactly representing arbitrary constant curvature fields in the discrete sense of nodal integration. The consistent linearization is performed on the weak form of large deflection plate in the context of the total Lagrangian description. Subsequently, the discrete incremental equations are obtained by the method of SCNI in which to relieve the locking as well as ensure the stability of the present scheme, the bending contribution is evaluated using the smoothed nodal gradients, while the membrane and shear contributions are computed with the direct nodal gradients. The effectiveness of the present method is thoroughly demonstrated through several numerical examples.

scholarly journals Effect of Material Nonlinearity on Large Deflection of Variable-Arc-Length Beams Subjected to Uniform Self-Weight

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Chainarong Athisakul ◽  
Boonchai Phungpaingam ◽  
Gissanachai Juntarakong ◽  
Somchai Chucheepsakul
Keyword(s):  
Differential Equations ◽  
Large Deflection ◽  
Numerical Solutions ◽  
Nonlinear Differential Equations ◽  
Optimization Technique ◽  
Material Constant ◽  
Constitutive Law ◽  
Arc Length ◽  
Stress Strain Relation ◽  
Equilibrium Configurations

This paper presents a large deflection of variable-arc-length beams, which are made from nonlinear elastic materials, subjected to its uniform self-weight. The stress-strain relation of materials obeys the Ludwick constitutive law. The governing equations of this problem, which are the nonlinear differential equations, are derived by considering the equilibrium of a differential beam element and geometric relations of a beam segment. The model formulation presented herein can be applied to several types of nonlinear elastica problems. With presence of geometric and material nonlinearities, the system of nonlinear differential equations becomes complicated. Consequently, the numerical method plays an important role in finding solutions of the presented problem. In this study, the shooting optimization technique is employed to compute the numerical solutions. From the results, it is found that there is a critical self-weight of the beam for each value of a material constantn. Two possible equilibrium configurations (i.e., stable and unstable configurations) can be found when the uniform self-weight is less than its critical value. The relationship between the material constantnand the critical self-weight of the beam is also presented.

Nonlinear Analysis of a Thin Circular Functionally Graded Plate and Large Deflection Effects on the Forces and Moments

2008 ◽  
Vol 130 (1) ◽  
Author(s):  
A. Allahverdizadeh ◽  
A. Rastgo ◽  
M. H. Naei
Keyword(s):  
Nonlinear Analysis ◽  
Large Deflection ◽  
Volume Fraction ◽  
Plate Thickness ◽  
Functionally Grade ◽  
Functionally Graded ◽  
Governing Equations ◽  
Temperature Dependent ◽  
Harmonic Vibrations ◽  
Graded Material

Nonlinear analysis of a thin circular functionally grade plate is formulated in terms of von Karman’s dynamic equations. The plate thickness is constant and temperature-dependent functionally graded material (FGM) properties vary through the thickness of the plate. Forces and moments of the plate, due to large vibration amplitudes, are developed in this paper by solving the governing equations for harmonic vibrations. Corresponding results are illustrated in the case of steady-state free vibration. The results show that the variation of volume fraction index is influential in forces, moments, and FGM properties.

Nonlinear analysis of lattice model with the consideration of multiple optimal current differences for two-lane freeway

2015 ◽  
Vol 29 (04) ◽  
pp. 1550006 ◽  
Author(s):  
Guanghan Peng
Keyword(s):  
Numerical Simulation ◽  
Stability Analysis ◽  
Nonlinear Analysis ◽  
Traffic Flow ◽  
Linear Stability ◽  
Lattice Model ◽  
Mkdv Equation ◽  
Traffic System ◽  
Optimal Current ◽  
The Stability

In this paper, a new lattice model is proposed with the consideration of the multiple optimal current differences for two-lane traffic system. The linear stability condition and the mKdV equation are obtained with the considered multiple optimal current differences effect by making use of linear stability analysis and nonlinear analysis, respectively. Numerical simulation shows that the multiple optimal current differences effect can efficiently improve the stability of two-lane traffic flow. Furthermore, the three front sites considered, is the optimal state of two-lane freeway.

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