Representative volume element-based three-dimensional models with various nanofiller geometries and process parameters are presented for the design and analysis of composite materials. Analytical, computer-aided design, and computer-aided engineering tools are integrated to develop user interface tools with automated three-dimensional models for mechanical and electrical analyses. Various process parameters in the manufacture of nanocomposites are quantified using image analysis techniques. A filler-to-filler distance algorithm is incorporated in developing a three-dimensional network of fillers within matrix representative volume element to account for filler–filler interactions and compatibility. The stress–strain behavior of metal matrix nanocomposites, the effective modulus, and the electrical conductivity of polymer nanocomposite fibers are presented as case studies to demonstrate the capabilities of the developed representative volume element-based design and analysis tools. The unique automated design and analysis framework presented in this study integrates various software tools, quantifies the effect of process parameters of experimental composites with nanofillers, and provides quick what-if analysis for manufacturing application-specific composites.
Admissible region methods for initial orbit determination are generally implemented without considering uncertainty in observations or observer state. In this paper a generalization of the admissible region approach is introduced that more accurately accounts for uncertainty in the constraint hypothesis parameters used to generate the admissible region. Considering the uncertainty to have Gaussian distributions, the proposed relationship between provided information uncertainty and admissible region uncertainty results directly in an analytical approximate probability density function. The methodology is extended to account for admissible regions with multiple overlapping constraint hypothesis. The proposed approach is applied to an example optical detection to demonstrate the quality of the approximation and the sensitivity of the resulting distribution to typical errors.
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