State-vector equation with damping and vibration analysis of laminates

2007 ◽  
Vol 28 (2) ◽  
pp. 253-259 ◽  
Author(s):  
Guang-hui Qing ◽  
Jian-xin Xu ◽  
Jia-jun Qiu
Keyword(s):  
State Vector ◽  
Vibration Analysis ◽  
Vector Equation

Stability Analysis of Stiffened Plates Based on State-Vector Equation

2013 ◽  
Vol 671-674 ◽  
pp. 1561-1569
Author(s):  
Yan Li Wang ◽  
Guang Hui Qing
Keyword(s):  
Finite Element ◽  
State Vector ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Stiffened Plates ◽  
Variation Principle ◽  
Element Formulation ◽  
Vector Equation ◽  
Finite Element Software ◽  
The Stability

Firstly, based on the theory of state-vector equation, the semi-analysis finite element formulation for the stability of the plates under various boundary conditions was derived by modified Hellinger-Reissner (H-R) variation principle for the elastic material. Secondly, the three-dimensional models for the stability of stiffened plates were established. The semi-analytical solution of state equation for the stability of stiffened plates are proved to be efficient and accurate by comparing with the exact solutions of references and the numerical solutions of the finite element software through several examples.

A theory for the finite displacement of a thin-walled Bernoulli–Euler beam and lateral post-buckling analysis

2008 ◽  
Vol 464 (2094) ◽  
pp. 1543-1570 ◽  
Author(s):  
Tsuneo Usuki
Keyword(s):  
State Vector ◽  
Coefficient Matrix ◽  
The State ◽  
Vector Equation ◽  
Initial Value ◽  
Euler Beam ◽  
Lateral Buckling ◽  
Finite Displacement ◽  
Post Buckling ◽  
Runge Kutta

The state vector equation for lateral buckling in finite displacement theory is formulated using only the hypothesis of the Bernoulli–Euler beam. By using an appropriate orthogonalization of the warping functions, the normally complicated calculation has been processed systematically using only matrix notation. As a numerical analysis, the lateral buckling load on the cantilever receiving a concentrated end load on the upper flange was calculated using the coefficient matrix of the first-order increment; the post-buckling behaviour was investigated with increasing load. Since the state vector equation is a higher order nonlinear equation, the original coefficient matrix was fixed with an arbitrary initial value and the solution was provided by the Runge–Kutta transfer matrix method. Subsequent calculations were pursued in the same way with the solution obtained via Runge–Kutta methods as a new initial value and then shifted to the next load condition. This theory and analysis method does not employ an assumed displacement function, such as the Ritz's method; it is therefore useful for the finite displacement analysis of a beam with arbitrary boundary conditions and intermediate support conditions.

Monte Carlo Algorithms for Moments of Transition Arrays

1988 ◽  
Vol 102 ◽  
pp. 79-81
Author(s):  
A. Goldberg ◽  
S.D. Bloom
Keyword(s):  
Monte Carlo ◽  
State Vector ◽  
Basis Vector ◽  
Collective State ◽  
Dispersion Characteristics ◽  
Dipole Strength ◽  
The Third ◽  
Monte Carlo Algorithms ◽  
Third Moment ◽  
Very High

AbstractClosed expressions for the first, second, and (in some cases) the third moment of atomic transition arrays now exist. Recently a method has been developed for getting to very high moments (up to the 12th and beyond) in cases where a “collective” state-vector (i.e. a state-vector containing the entire electric dipole strength) can be created from each eigenstate in the parent configuration. Both of these approaches give exact results. Herein we describe astatistical(or Monte Carlo) approach which requires onlyonerepresentative state-vector |RV> for the entire parent manifold to get estimates of transition moments of high order. The representation is achieved through the random amplitudes associated with each basis vector making up |RV>. This also gives rise to the dispersion characterizing the method, which has been applied to a system (in the M shell) with≈250,000 lines where we have calculated up to the 5th moment. It turns out that the dispersion in the moments decreases with the size of the manifold, making its application to very big systems statistically advantageous. A discussion of the method and these dispersion characteristics will be presented.

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