Boundary Connectivity Research Articles

Dynamic stiffness analysis of toroidal shells

The free vibration of a toroidal shell is studied using the dynamic stiffness method. The dynamic stiffness method eliminates both spatial discretization error and mesh generation. Moreover, with a finite number of degrees of freedom, the dynamic stiffness method can predict an infinite number of natural frequencies. The dynamic behavior of the toroidal shell is modeled by DMV (Donnell-Mushtari-Vlasov) linear thin shell theory in the present paper. However, the procedure can be adapted to be used with any other linear thin shell theory without difficulty. Since a close form solution of toroidal shell using DMV theory is not (yet) possible, in order to obtain the desired dynamic stiffness matrix, a finite number of Fourier's series terms are taken in the circumferential direction and the unknown longitudinal displacements are then solved from the reduced governing equations exactly. The solution obtained from the dynamic stiffness method can be regarded as semi-analytical due to the Fourier approximation. With the dynamic stiffness matrices in hands, a toroidal shell with different boundary conditions and connections (to other toroidal shells) can be analyzed. This paper presents the procedure and assumption made in order to obtain the dynamic stiffness matrix of a toroidal shell in harmonic oscillation. Also some numerical examples will be given and discussed.

The impact of grain boundary character distribution on fracture in polycrystals

The importance of structural effects on intergranular fracture is discussed in order to understand, predict and control fracture in polycrystals. The heterogeneity of fracture in a polycrystal has been found to be due to the difference in structure-dependent propensity to intergranular fracture among grain boundaries. The grain boundary character distribution (GBCD) which describes the type and frequency of grain boundaries is shown to be one of important microstructural factors affecting fracture processes and characteristics. A recent prediction of GBCD-controlled toughness and brittle-ductile transition is introduced. The importance of the connectivity of grain boundaries, the so-called grain boundary correlation number, is also discussed. Recent successful achievement of the control of intergranular brittleness is presented as an application of the result of basic research on fracture to the control of intergranular brittleness by grain boundary design and control in advanced materials.

Orientation Imaging of the Microstructure of Polycrystalline Materials

ABSTRACTRecent developments, coupling the scanning electron microscope with image processing and crystallographic analysis, now make it possible to automatically index many thousands of lattice orientations exposed on section planes in polycrystalline materials. Backscattered Kikuchi diffraction patterns obtained from high-gain SIT and CCD cameras are analyzed using the Hough transformation (Cartesian coordinates - polar coordinates) in order to identify diffraction band widths and interplanar angles. From this basic information local lattice orientation can be determined. Information from raw data sets (in excess of 100,000 single orientations in some examples) can be used to construct orientation imaging micrographs which emphasize certain aspects of the exposed field of lattice orientations. Thus, features of the spatial placement of lattice orientation (including grain boundary misorientation, microtexture, and connectivity of the microstructure) are readily studied. In this paper these techniques are reviewed, and recent explorations of the connectivity of grain boundary misorientation structure are presented for an interesting nickel-chromium-iron alloy.

On the Energy Decay of a Linear Thermoelastic Bar and Plate

It is shown that the energy of a thermoelastic bar and plate decays exponentially fast. The energy method, combined with a multiplier technique and compactness property, is used.

Identification of the boundary surfaces in 3D finite element codes

For a given 3D FEM net defined by a domain connectivity array a boundary connectivity array is generated. The latter contains boundary nodes over which subsequent boundary elements are spanned. An algorithm can be used to check the consistency of the input connectivity array. It can also be useful in pre and postprocessors in hidden lines removal. A list of appropriate routines is included.

Magnetic Field Dependence of Jc in A T1–1223 Wire; Presence of Pinning and Good Grain Boundary Connectivity.

ABSTRACTThe existence of effective pinning in single T1-layer 1223 superconductors has been reported [1–3], as opposed to lower values in T1- and Bi-double layer systems, which is intimately related to their crystal structures. In order to investigate the possibility of T1–1223 being applied as a practical superconductor, tape shaped wires of the chemical composition (T10.5Pb0.51 (Sr0.8Ba0.2Ca2Cu3O9were prepared. Transport Jc of T1–1223 was measured to be 1.8 × 104 A/cm2 at 77K in the absence of a magnetic field. These results seem to imply that T1–1223 has, not only effective pinning because of having a more 3-dimensional vortex line lattice like YBa2Cu3O7, but also better grain boundary weak-link performance than YBa2Cu3O7. PresenT1y it appears that T1–1223 may be a superior choice to make better superconducting wire, because of these considerations and of the higher Tc of 120K.(T10.5Pb0.5)1Sr2CaCu2O7 (T1–1212) also seems to have effective pinning, as well as T1–1223, supporting the idea that shorter Cu-O plane spacing, or absence of thicker insulating region such as T12O2 or Bi2O2 double layer, are beneficial for effective pinning through facilitating a better 3D-like vortex line lattice [4, 5]. Our “1212” and “1223” samples are good counter examples to the 2D pancake-like vortex theory [6, 7].

Limit states design considerations for gusset plates

Abstract In spite of the extensive use of gusset plates as connecting elements in a variety of structures over the years, current design criteria are essentially based on very limited research work, and primarily of elastic analytical background. For example, North American design practice uses the results of the elastic model studies of Whitmore, obtained through research that was completed in 1952. With these things in mind, the paper discusses the design considerations that must be made when designing for ultimate strength, specifically, utilizing the limit states design formulation. Thus, limit states design models are described for tension and compression applications of gusset plates, although it is noted that much more research is needed before the criteria for compression can be considered as complete. Of particular interest are the second-order deformation effects in gusset plates; these are recent findings in experimental studies. It is demonstrated how load application and direction as well as type and orientation of the boundary connections have a major influence on the strength and behavior of these plates. A final summary itemizes the design checks that should be made.

Semianalytic Numerical Studies of Turning Points Arising in Stiff Boundary Value Problems

A numerical algorithm for solving stiff boundary value problems with turning points is presented. The stiff systems are characterized as singularly perturbed differential equations. The numerical method is derived by appropriately discretizing the boundary layer and connection theory for such systems. Numerical results demonstrate the effectiveness of the method. In many cases the calculation proceeds with mesh increments which are orders of magnitude larger than those used by other known methods.

Semianalytic numerical studies of turning points arising in stiff boundary value problems

A numerical algorithm for solving stiff boundary value problems with turning points is presented. The stiff systems are characterized as singularly perturbed differential equations. The numerical method is derived by appropriately discretizing the boundary layer and connection theory for such systems. Numerical results demonstrate the effectiveness of the method. In many cases the calculation proceeds with mesh increments which are orders of magnitude larger than those used by other known methods.

Molecular Orbital Approach to Chemisorption. II. Atomic H, C, N, O, and F on Graphite

The calculation of the chemisorption behavior of atomic H, C, N, O, and F on a graphite basal (0001) surface is examined with the CNDO (complete neglect of differential overlap) molecular-orbital scheme. This approach is a semiempirical approximation to the Hartree-Fock self-consistent field procedure, in which the Hamiltonian explicitly depends upon both atomic and orbital charge distribution. The location of binding sites and changes in relative binding energies and net charges with the identity of the adsorbed species are explored with an extended carbon (0001) surface, simulated by an 18-carbon lattice with appropriate boundary connections. The strength of binding to the simulated graphite substrate increases in the order H, F, O, N, and C. The atoms C and N are most stable when positioned above the center of a hexagonal sixcarbon ring, whereas H, F, and O are most stable above the center of a bond connecting nearest-neighbor carbons. Calculated charge distributions are used to predict a work-function decrease with the adsorption of atomic H or N on graphite, but an increase with the adsorption of C, O, or F. The commonly used electronegativity reasoning is shown to be inadequate for the prediction of adsorbate-charge transfer.