Some quantitative evaluations on finite difference local and global results

Refined Schwarz-Christoffel (SC) conformal transformations allow us to perform reliable quantitative evaluation of the accuracy of local computation of electric and magnetic fields with limited effort, which can be useful to complement well known comparisons of global results. In this paper some examples are presented for mesh point potentials obtained by means of finite difference (FD) methods, but it is possible that similar considerations will be useful in the case of finite element methods (FEM) or meshless computations too.

Time Varying Meshing Stiffness of Cracked Sun and Ring Gears of Planetary Gear Train

The time varying meshing stiffness of normal and cracked spur gears of planetary gear train is studied by applying the unit normal forces at mesh point on the face width along the line of action of the single gear tooth in FE based software Ansys Workbench 14.5. The tooth deflections due to the applied forces at one mesh point are noted and a deflection matrix is established which is solved using Matlab to get net deflection and finally the meshing stiffness of gear tooth at particular mesh point. The process is repeated for other mesh points of gear tooth by rotating it to get meshing stiffness for whole gear tooth.

VISUAL DESIGN TOOL FOR ELECTROSTATIC LELSES

Current research presents a visual-computational tool to design and investigate round electrostatic lenses in sense of analysis procedure. The finite elements methods is adopted to find the electrostatic potential in the lens region. Laplace’s equation is first replaced by a certain functional which physically represent the electric energy stored in the electric field. This functional is then minimized at each mesh point with respect to the nearest eight ones. This minimization process is proved to be entirely equivalent to solving Laplace’s equation. The requirement that the functional being minimized is then yields a set of nine point equations which inter relate the potentials at adjacent mesh points. Finally this set of equations is solved to find the electrostatic potential at each mesh point in the region of the lens under consideration. The procedure steps mention above are coded to program written in visual basic. Hence an interface tool for analyzing and designing electrostatic lenses has been built up. Designing results proved that the introduced tools has an excellent outputs in comparison with the others written in not visual programming languages. Furthermore it easier for researchers and designer to use such a tool over their counterpart ones.

Mechanical Performance Calculation of Single-Layer Cable Mesh Point-Supported Glass Curtain Wall under Fire Conditions

High-strength prestressed cables were main bearing parts in single-layer cable mesh point-supported glass curtain wall structures, and it was always unable to take effective fire prevention measures on steel cables due to small sections. That the elastic modulus and yield strength of prestressed cables decreased sharply under fire conditions would threaten safety performance of the whole structure seriously. When glass breakage is considered and not considered, nonlinear finite element complete-process analysis for the single-layer cable mesh point-supported glass curtain wall structure was conducted. Influences of various factors on structure mechanical performance were studied under fire conditions. Through the calculation analysis of different joint constraint models, the ultimate temperature table suitable for different sizes and cable spacing of glass curtain walls was obtained under uniform heating conditions, and proposals for fire-resisting design were given.

Construct 2D Stable and Unstable Manifolds of Nonlinear Maps

The procedure resolves the insertion of new mesh point, the searching of the image (or pre-image) and computation of the 1D sub-manifolds following the new mesh point tactfully, it does not require the 1D sub-manifolds to be computed from the initial circle and avoids the assembling of mesh points. The performance of the algorithm is demonstrated with hyper chaotic 3D Hénon map and Lorenz system.

Analysis of Geometric Characteristics of Scroll Compression Chamber for Scroll Fluid Machine

Based on the general geometrical model of scroll compression chamber for scroll fluid machine, the geometric characteristics of scroll compression chamber, such as width, length, volume, and comprehensive curvature radius at the mesh point, and their variation as well are comprehensively analyzed. It is shown by the analysis that among all of the geometric characteristics, the width variation is the most complicated one; the comprehensive variation of the width together with the length can be used to determine the deformation processes of the chamber. The variability of its length, volume, and comprehensive curvature radius at meshing points should be taken as its basic deformation characteristics. For a scroll compression chamber with involute of circle, its deformation efficiency is higher and dynamic stability is excellent. At the same time, the scroll wrap with involute of circle is easy to fabricate and the profile with involute of circle is used widely for the major part of the scroll profile.