New Mathematical Modelling of Stabilizing Pile with Prestressed Tieback Anchors

This paper presents a novel mathematical modelling for analyzing stabilizing piles with prestressed tieback anchors. The new differential equations governing the mechanical response of the stabilizing pile are formulated and the boundary conditions considering the tie-back anchors are mathematically specified. Then, the system of differential equations is numerically solved by the high-accuracy Runge-Kutta finite difference method. A simple computer program has been written on the platform of MATLAB to run the procedure of the proposed algorithm. This approach is entirely different from the traditional finite element method used to design the anchored piles. The FEM is employed to verify the feasibility of the developed method. The comparative case study indicates that the proposed method has more higher modeling and computing efficiency than the FEM and can be an alternative method for designing the anchored pile used for slope stabilization.

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Boundary Value Problem for Analysis of Portal Double-Row Stabilizing Piles

Journal of Applied Mathematics ◽

10.1155/2013/485632 ◽

2013 ◽

Vol 2013 ◽

pp. 1-10

Author(s):

Cheng Huang

Keyword(s):

Finite Difference ◽

Finite Difference Method ◽

Boundary Value Problem ◽

Mechanical Behaviour ◽

Numerical Approach ◽

Internal Force ◽

High Accuracy ◽

Double Row ◽

Stabilizing Piles ◽

Stabilizing Pile

This paper presents a new numerical approach for computing the internal force and displacement of portal double-row piles used to stabilize potential landslide. First, the new differential equations governing the mechanical behaviour of the stabilizing pile are formulated and the boundary conditions are mathematically specified. Then, the problem is numerically solved by the high-accuracy Runge-Kutta finite difference method. A program package has been developed in MATLAB depending on the proposed algorithm. Illustrative examples are presented to demonstrate the validity of the developed program. In short, the proposed approach is a practical new idea for analyzing the portal double-row stabilizing pile as a useful supplement to traditional methods such as FEM.

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The mechanics of hearing: a comparative case study in bio-mathematical modelling

ANZIAM Journal ◽

10.21914/anziamj.v52i0.4556 ◽

2012 ◽

Vol 52 ◽

pp. 225

Author(s):

A. R. Champneys ◽

D. Avitabile ◽

M. Homer ◽

R. Szalai

Keyword(s):

Mathematical Modelling ◽

Comparative Case Study

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Construction of plastic contact deformation maps on ceramics: a case study on aluminum nitride

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100165641 ◽

1996 ◽

Vol 54 ◽

pp. 636-637

Author(s):

D. L. Callahan

Keyword(s):

Plastic Deformation ◽

Aluminum Nitride ◽

Mechanical Response ◽

Three Dimensional ◽

Bright Field Image ◽

Perfectly Plastic ◽

Contrast Analysis ◽

Deformation Patterns

Modern polishing, precision machining and microindentation techniques allow the processing and mechanical characterization of ceramics at nanometric scales and within entirely plastic deformation regimes. The mechanical response of most ceramics to such highly constrained contact is not predictable from macroscopic properties and the microstructural deformation patterns have proven difficult to characterize by the application of any individual technique. In this study, TEM techniques of contrast analysis and CBED are combined with stereographic analysis to construct a three-dimensional microstructure deformation map of the surface of a perfectly plastic microindentation on macroscopically brittle aluminum nitride.The bright field image in Figure 1 shows a lg Vickers microindentation contained within a single AlN grain far from any boundaries. High densities of dislocations are evident, particularly near facet edges but are not individually resolvable. The prominent bend contours also indicate the severity of plastic deformation. Figure 2 is a selected area diffraction pattern covering the entire indentation area.

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