Hybrid Numerical-Analytical Scheme for Locally Inhomogeneous Elastic Waveguides

Numerical simulation of guided wave excitation, propagation, and diffraction in laminate structures with local inhomogeneities (obstacles) is associated with high computational cost due to the need for a mesh-based approximation of extended domains with a rigorous account for the radiation conditions at infinity. To obtain computationally efficient solutions, hybrid numerical-analytical approaches are currently being developed, based on linking a numerical solution in a local vicinity of the source and/or obstacles with an explicit analytical representation in the external semi-infinite domain. However, the developed methods are generally not widely spread because the possibility of such coupling with an external multimode wave field is generally not provided in standard finite-element (FE) software. We propose a scheme that allows the use of the FE software as a black box for the required correct matching of local numerical and global analytical solutions (FEM-An). The FEM is used to obtain a set of local numerical solutions that serve as a basis in the inner domain. These solutions satisfy the boundary conditions induced by guided wave modes so that they fit correctly with the modal expansion in the outer region. The expansion coefficients of both FE and modal decompositions are determined then from the condition of stress and displacement continuity at the interface between the inner and outer domains. This scheme was numerically validated against analytical solutions to test problems and FE solutions for long waveguide sections with perfect match layer absorbing conditions at the ends (FEM PML). Along the way, it turned out that the FEM-PML approach gives an incorrect result in the backward-wave bands and at high frequencies. The application of the FEM-An hybrid scheme is illustrated by examples of Lamb wave diffraction by elastic inclusions and delaminations

2 x 2 Polyethylene Reflected and Moderated Highly Enriched Uranium System with Rhenium

The 2 × 2 array HEU-Re experiment was performed on the Planet universal critical assembly machine on November 4th, 2003 at the Los Alamos Critical Experiments Facility (LACEF) at Los Alamos National Laboratory (LANL). For this experiment, there were 10 ½ units, each full unit containing four HEU foils and two rhenium foils. The top unit contained only two HEU foils and two rhenium foils. A total of 42 HEU foils were used for this experiment. Rhenium is a desirable cladding material for space nuclear power applications. This experiment consisted of HEU foils interleaved with rhenium foils and is moderated and reflected by polyethylene plates. A unit consisted of a polyethylene plate, which has a recess for rhenium foils, and four HEU foils in a single layer in the top recess of each polyethylene plate. The Planet universal criticality assembly machine has been previously used in experiments containing HEU foils interspersed with SiO2 (HEU-MET-THERM-001), Al (HEU-MET-THERM-008), MgO (HEU-MET-THERM-009), Gd foils (HEU-MET-THERM-010), 2 × 2 × 26 Al (HEU-MET-THERM-012), Fe (HEU-MET-THERM-013 and HEU-MET-THERM-015), 2 × 2 × 23 SiO2 (HEU-MET-THERM-014), 2 × 2 × 11 hastalloy plates (HEU-MET-THERM-016), and concrete (HEU-MET-THERM-018). The 2 × 2 array of HEU-Re is considered acceptable for use as a benchmark critical experiment

2 x 2 Polyethylene Reflected and Moderated Highly Enriched Uranium System with Rhenium

The 2 × 2 array HEU-Re experiment was performed on the Planet universal critical assembly machine on November 4th, 2003 at the Los Alamos Critical Experiments Facility (LACEF) at Los Alamos National Laboratory (LANL). For this experiment, there were 10 ½ units, each full unit containing four HEU foils and two rhenium foils. The top unit contained only two HEU foils and two rhenium foils. A total of 42 HEU foils were used for this experiment. Rhenium is a desirable cladding material for space nuclear power applications. This experiment consisted of HEU foils interleaved with rhenium foils and is moderated and reflected by polyethylene plates. A unit consisted of a polyethylene plate, which has a recess for rhenium foils, and four HEU foils in a single layer in the top recess of each polyethylene plate. The Planet universal criticality assembly machine has been previously used in experiments containing HEU foils interspersed with SiO2 (HEU-MET-THERM-001), Al (HEU-MET-THERM-008), MgO (HEU-MET-THERM-009), Gd foils (HEU-MET-THERM-010), 2 × 2 × 26 Al (HEU-MET-THERM-012), Fe (HEU-MET-THERM-013 and HEU-MET-THERM-015), 2 × 2 × 23 SiO2 (HEU-MET-THERM-014), 2 × 2 × 11 hastalloy plates (HEU-MET-THERM-016), and concrete (HEU-MET-THERM-018). The 2 × 2 array of HEU-Re is considered acceptable for use as a benchmark critical experiment

Computing and Information PETROV-GALERKIN METHOD WITH LOCAL GREEN’S FUNCTIONS IN SINGULARLY PERTURBED CONVECTION-DIFFUSION PROBLEMS

Abstract. Previous theoretical and computational investigations have shown high efficiency of the local Green’s function method for the numerical solution of singularly perturbed problems with sharp boundary layers. However, in several space variables those functions, used as projectors in the Petrov-Galerkin scheme, cannot be derived in a closed analytical form. This is an obstacle for the application of the method when applied to multi-dimensional problems. The present work proposes a semi-analytical approach to calculate the local Green’s function, which opens a way to effective practical application of the method. Besides very accurate approximation, the matrix stencils obtained with these functions allow the use of fast and stable iterative solution of the large sparse algebraic systems that arise from the grid-discretization. The advantages of the method are illustrated by numerical examples. Key Words. Convection-diffusion equation, Petrov-Galerkin discretization, Fourier transform, integral equations, iterative solution. 1

Evaluation of Effective Elastic Properties of Nitride NWs/Polymer Composite Materials Using Laser-Generated Surface Acoustic Waves

In this paper we demonstrate a high potential of transient grating method to study the behavior of surface acoustic waves in nanowires-based composite structures. The investigation of dispersion curves is done by adjusting the calculated dispersion curves to the experimental results. The wave propagation is simulated using the explicit integral and asymptotic representations for laser-generated surface acoustic waves in layered anisotropic waveguides. The analysis of the behavior permits to determine all elastic constants and effective elastic moduli of constituent materials, which is important both for technological applications of these materials and for basic scientific studies of their physical properties