Wall boundary conditions for high-order finite-difference schemes in computational aeroacoustics

High-order finite-difference schemes are less dispersive and dissipative but, at the same time, more isotropic than low-order schemes. They are well suited for solving computational acoustics problems. High-order finite-difference equations, however, support extraneous wave solutions which bear no resemblance to the exact solution of the original partial differential equations. These extraneous wave solutions, which invariably degrade the quality of the numerical solutions, are usually generated when solid-wall boundary conditions are imposed. A set of numerical boundary conditions simulating the presence of a solid wall for high-order finite-difference schemes using a minimum number of ghost values is proposed. The effectiveness of the numerical boundary conditions in producing quality solutions is analyzed and demonstrated by comparing the results of direct numerical simulations and exact solutions.This work was supported by the NASA Lewis Research Center Grant NAG 3-1267 and in part by the NASA Langley Research Center Grant NAG 1-1479 and the Florida State University through time granted on its Cray-YMP Supercomputer.     

Multi-scale finite element analyses of sheet metals by using SEM-EBSD measured crystallographic RVE models

In this study, two multi-scale analyses codes are newly developed by combining a homogenization algorithm and an elastic/crystalline viscoplastic finite element (FE) method (Nakamachi, E., 1988. A finite element simulation of the sheet metal forming process. Int. J. Numer. Meth. Eng. 25, 283–292; Nakamachi, E., Dong, X., 1996. Elastic/crystalline viscoplastic finite element analysis of dynamic deformation of sheet metal. Int. J. Computer-Aided Eng. Software 13, 308–326; Nakamachi, E., Dong, X., 1997. Study of texture effect on sheet failure in a limit dome height test by using elastic/crystalline viscoplastic finite element analysis. J. Appl. Mech. Trans. ASME(E) 64, 519–524; Nakamachi, E., 1998. Elastic/crystalline viscoplastic finite element modeling based on hardening–softening evaluation equation. In: Proc. of the 6th NUMIFORM, pp. 315–321; Nakamachi, E., Hiraiwa, K., Morimoto, H., Harimoto, M., 2000a. Elastic/crystalline viscoplastic finite element analyses of single- and poly-crystal sheet deformations and their experimental verification. Int. J. Plasticity 16, 1419–1441; Nakamachi, E., Xie, C.L., Harimoto, M., 2000b. Drawability assessment of BCC steel sheet by using elastic/crystalline viscoplastic finite element analyses. Int. J. Mech. Sci. 43, 631–652); (1) a “semi-implicit” finite element (FE) code and (2) a “dynamic explicit” FE code. These were applied to predict the plastic strain induced yield loci and the formability of sheet metal in the macro scale, and simultaneously the crystal texture and hardening evolutions in the micro scale. The isotropic and kinematical hardening laws are employed in the crystalline plasticity constitutive equation. For the multi-scale structure, two-scales are considered. One is a microscopic polycrystal structure and the other a macroscopic elastic plastic continuum. We measure crystal morphologies by using the SEM-EBSD apparatus with a unit of about 3.8 μm voxel, and define a three dimensional (3D) representative volume element (RVE) for the micro polycrystal structure, which satisfy the periodicity condition of crystal orientation distribution. A “micro” finite element modeling technique is newly established to minimize the total number of finite elements in the micro scale. Next, the “semi-implicit” crystallographic homogenization FE code, which employs the SEM-EBSD measured RVE, is applied to the 99.9% pure-iron uni-axial tensile problem to predict the texture evolution and the subsequent yield loci in the various strain paths. These “semi implicit” results reveal that the plastic strain induced anisotropy in the micro and macro levels can be predicted by our FE analyses. The kinematical hardening law leads a distinct plastic strain induced anisotropy. Our “dynamic-explicit” FE code is applied to simulate the limit dome height (LDH) test problem of the mild steel DQSK, the high strength steel HSLA and the aluminum alloy AL6022 sheet metals, which were adopted as the NUMISHEET2005 Benchmark sheet metals (Smith, L.M., Pourboghrat, F., Yoon, J.-W., Stoughton, T.B., 2005. NUMISHEET2005. In: Proc. of 6th Int. Conf. Numerical Simulation of 3D Sheet Metal Forming Processes, PART A and B(Benchmark), pp. 409–451) to estimate formability. The “dynamic explicit” results reveal that the initial crystal orientation distribution has a large affects to a plastic strain induced texture and anisotropic hardening evolutions and sheet formability.     

Generalizations and error analysis of the iterative operator splitting method

The properties of iterative splitting with two bounded linear operators have been analyzed by Faragó et al. For more than two operators, iterative splitting can be defined in many different ways. A large class of the possible extensions to this case is presented in this paper and the order of accuracy of these methods are examined. A separate section is devoted to the discussion of two of these methods to illustrate how this class of possible methods can be classified with respect to the order of accuracy.     

Correlation between the sub-structure parameters and the manufacturing technologies of metal threads in historical textiles using X-ray line profile analysis

Micro-structure can talk when documentation is missing. In ancient Roman or medieval periods, kings, queens, or just rich people decorated their clothes or even their horse covers richly with miniature jewels or metal threads. The origin or the fabrication techniques of these ancient threads is often unknown. Thirteen thread samples made of gold or gilt silver manufactured during the last sixteen hundred years are investigated for the micro-structure in terms of dislocation density, crystallite size, and planar defects. In a few cases, these features are compared with sub-structure of similar metallic threads prepared in modern, twentieth century workshops. The sub-structure is determined by X-ray line profile analysis, using high resolution diffractograms with negligible instrumental broadening. On the basis of the sub-structure parameters, we attempt to assess the metal-threads manufacturing procedures on samples stemming from the fourth century A.D. until now.     

Dynamical similarity of multi-block catenary arches and rocking blocks subjected to horizontal base excitation

Nonlinear Dynamics - In this paper, the dynamical similarity of multi-block catenary arches and columns is discussed, which can be used for the simplified design of rocking arches. The basic...     

The novel application of Fourier thermal analysis in foundry technologies

The process of casting in sand moulds is used for a large volume of castings manufactured in the world. Internal channels and complex geometries of these products are formed by the placement of cores within the mould cavity. Resin-bound sand mixtures are essential ingredients in engine component manufacturing. In this study, a state-of-the-art application of Fourier thermal analysis in foundry technologies is presented. Investigation of decomposition phenomena of resin-bound moulding materials during casting production is a brand new area to use the potential of thermal sciences. Temperature measurements in test samples of standard types of moulding mixtures were performed. The registered cooling curves were processed by a numerical iteration algorithm to determine the amount of heat absorbed during degradation of the moulding material. Thermogravimetric analysis (TG) and differential thermal analysis (DTA) of sand mixtures were carried out to compare the results of the Fourier thermal analysis with TG and DTA curves.