256 research outputs found
Mesoscale models and approximate solutions for solids containing clouds of voids
For highly perforated domains the paper addresses a novel approach to study mixed boundary value problems for the equations of linear elasticity in the framework of mesoscale approximations. There are no assumptions of periodicity involved in the description of the geometry of the domain. The size of the perforations is small compared to the minimal separation between neighboring defects and here we discuss a class of problems in perforated domains, which are not covered by the homogenization approximations. The mesoscale approximations presented here are uniform. Explicit asymptotic formulas are supplied with the remainder estimates. Numerical illustrations, demonstrating the efficiency of the asymptotic approach developed here, are also given
Eigenvalue problem in a solid with many inclusions: asymptotic analysis
We construct the asymptotic approximation to the first eigenvalue and
corresponding eigensolution of Laplace's operator inside a domain containing a
cloud of small rigid inclusions. The separation of the small inclusions is
characterised by a small parameter which is much larger compared with the
nominal size of inclusions. Remainder estimates for the approximations to the
first eigenvalue and associated eigenfield are presented. Numerical
illustrations are given to demonstrate the efficiency of the asymptotic
approach compared to conventional numerical techniques, such as the finite
element method, for three-dimensional solids containing clusters of small
inclusions.Comment: 55 pages, 5 figure
Asymptotic analysis of in-plane dynamic problems for elastic media with rigid clusters of small inclusions.
We present formal asymptotic approximations of fields representing the in-plane dynamic response of elastic solids containing clusters of closely interacting small rigid inclusions. For finite densely perforated bodies, the asymptotic scheme is developed to approximate the eigenfrequencies and the associated eigenmodes of the elastic medium with clamped boundaries. The asymptotic algorithm is also adapted to address the scattering of in-plane waves in infinite elastic media containing dense clusters. The results are accompanied by numerical simulations that illustrate the accuracy of the asymptotic approach. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 2)'
From 3D Models to 3D Prints: an Overview of the Processing Pipeline
Due to the wide diffusion of 3D printing technologies, geometric algorithms
for Additive Manufacturing are being invented at an impressive speed. Each
single step, in particular along the Process Planning pipeline, can now count
on dozens of methods that prepare the 3D model for fabrication, while analysing
and optimizing geometry and machine instructions for various objectives. This
report provides a classification of this huge state of the art, and elicits the
relation between each single algorithm and a list of desirable objectives
during Process Planning. The objectives themselves are listed and discussed,
along with possible needs for tradeoffs. Additive Manufacturing technologies
are broadly categorized to explicitly relate classes of devices and supported
features. Finally, this report offers an analysis of the state of the art while
discussing open and challenging problems from both an academic and an
industrial perspective.Comment: European Union (EU); Horizon 2020; H2020-FoF-2015; RIA - Research and
Innovation action; Grant agreement N. 68044
The 1982 NASA/ASEE Summer Faculty Fellowship Program
A NASA/ASEE Summer Faculty Fellowship Research Program was conducted to further the professional knowledge of qualified engineering and science faculty members, to stimulate an exchange of ideas between participants and NASA, to enrich and refresh the research and teaching activities of participants' institutions, and to contribute to the research objectives of the NASA Centers
Application of multi-scale computational techniques to complex materials systems
The applications of computational materials science are ever-increasing, connecting fields far beyond traditional subfields in materials science. This dissertation demonstrates the broad scope of multi-scale computational techniques by investigating multiple unrelated complex material systems, namely scandate thermionic cathodes and the metallic foam component of micrometeoroid and orbital debris (MMOD) shielding. Sc-containing scandate cathodes have been widely reported to exhibit superior properties compared to previous thermionic cathodes; however, knowledge of their precise operating mechanism remains elusive. Here, quantum mechanical calculations were utilized to map the phase space of stable, highly-faceted and chemically-complex W nanoparticles, accounting for both finite temperature and chemical environment. The precise processing conditions required to form the characteristic W nanoparticle observed experimentally were then distilled. Metallic foams, a central component of MMOD shielding, also represent a highly-complex materials system, albeit at a far higher length scale than W nanoparticles. The non-periodic, randomly-oriented constituent ligaments of metallic foams and similar materials create a significant variability in properties that is generally difficult to model. Rather than homogenizing the material such that its unique characteristic structural features are neglected, here, a stochastic modeling approach is applied that integrates complex geometric structure and utilizes continuum calculations to predict the resulting probabilistic distributions of elastic properties. Though different in many aspects, scandate cathodes and metallic foams are united by complexity that is impractical, even dangerous, to ignore and well-suited to exploration with multi-scale computational methods
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