Numerical Methods For Stability Analysis Research Articles

Graphical and Numerical Methods for Stability Analysis in Surrounding Rock of Underground Excavations, Example of Boukhadra Iron Mine N.E Algeria

Underground mining continues to progress to difficult, complex and deeper levels in order to tackle ascending demand of minerals. These deep mining occurs in a very hard conditions, in which right practice must be implemented in order to overcome the technical and safety challenges and reap economic gains. The redistributed stresses, large deformations and creeping behavior in such environments worried engineers and geoscientific researchers. The working technic in Boukhadra iron mine is based on the sublevels slaughtered, with room, pillar workings and roof behaviour. Based on rock mechanics and geotechnical engineering methods, our research adopted geo-mechanical and numerical approaches to predict the rock mass behaviour in Boukhadra underground mine and to deal its stability problem. The results show that plastic deformations and stress points increasingly in pillars. In zones with low cover, the tensile zones develop at the roof, leading to a progressive rupture giving rise to a droop. In some areas, fractures develop in a rather remarkable way; in this case the breaking of the pillars and collapse can occur generalized and brutal. The stability of room-and-pillar mines does not depend only pillars. It involves the determination of critical factors and limits of mining. Our study demonstrates that the use of scientific and technical achievements, have become a necessity in mining.

Numerical method for stability analysis of functionally graded beams on elastic foundation

This paper considers the problems of stability of non-uniform and axially functionally graded (FG) Euler–Bernoulli beams on elastic foundation. The boundary conditions of the beam are given in general form covering different classical supporting conditions. Furthermore, the boundary conditions are transformed into convenient form in order to avoid handling infinity values of the stiffness coefficients. The method of initial parameters in differential form is used for the numerical solution of the problem. The solution of the posed boundary value problem is reduced to the iterative solution of two initial value problems and homogeneous linear algebraic system of order two. The Richardson extrapolation method is employed to improve the accuracy of results. The performance of the method proposed has been validated by several numerical examples.

On stability of cylindrical shells of variable thickness with initial imperfections

The paper outlines a numerical method for stability analysis of cylindrical shells with initial imperfections. We solve a nonlinear buckling problem for a cylindrical shell with variable wall thickness under surface pressure. The imperfections of the shell are modeled as the first buckling mode. A probabilistic approach is used to determine the reliability against buckling of the cylindrical shell with the probability density of initial imperfections represented by uniform distribution, triangular distribution, or Gaussian distribution

Stability and Optimal Feedback Controls for Time-Delayed Linear Periodic Systems

An effective numerical method for stability analysis of feedback controls with time delay and for identifying optimal gains of the control is presented. The method develops a mapping of the system response in a finite dimensional state space. Minimization of the largest absolute value of eigenvalues of the mapping leads to optimal control gains. Numerical examples of both time-invariant and periodic linear systems are presented to demonstrate the method. We have found that the proposed method provides accurate stability boundaries and performance contours in the parametric space of control gains.

Mathematical models and numerical methods for stability analysis of materials subjected to radiation pulses

We consider problems in modeling the interaction between a solid body and radiation pulses having intensity of order 109−1015 W/m2. We construct one-dimensional mathematical models for radiative damage to materials on the basis of the theory of thermal erosion and the kinetic theory of stability.

The isothermal flash problem. Part I. Stability

Stability analysis is suggested as a preliminary step in isothermal flash calculations, and a number of numerical methods for stability analysis based on Gibbs' tangent plane criterion are described. These methods, which are applicable for both single phase and multiphase systems, are developed mainly for Equation of State calculations using a single model for all fluid phases. Special adaptions ensuring convergence in critical regions are discussed.