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The paper presents a first-principles study of the shear modulus tensor for perfect and imperfect Coulomb solids. Allowance is made for the effects of thermal fluctuations for temperatures up to the melting conditions. The present theory treats the cases of the long-range Coulomb interaction, where volume fluctuations should be avoided in the Ewald sums.
NiTi is a promising material for smart and active technologies due to its exhibition of the shape memory effect, superelasticity, and biocompatibility. The shape memory effect is tied to the reversible transition between the austenite and martensite phases. A major research direction is to alloy NiTi with Zr, Hf, Pd, Pt, etc., in order to tune the martensitic transition temperature (MTT). Modeling the MTT from first principles is challenging because the lattice dynamics is complicated by anharmonicity and various low-energy structures. Using density functional theory, the energy difference between the austenite and martensite phases of NiTi varies by up to 100 meV/atom depending on the choice of density functional, which is of the same order of the energy difference itself. Consequently, free energy calculations with different functionals can result in estimates of the MTT that vary by several hundred K. Using diffusion quantum Monte Carlo, we calculated the energy difference between the B2 and B19' structures of NiTi to be 70.9 +- 2.5 meV/atom.
We report Ca isotope fractionation among a co-genetic suite of samples from the Mauritanian Guelb el Azib ultramafic-mafic-anorthosite complex (GAC), which represents the fractional crystallization sequence of an igneous magma chamber. We investigate how the composition of an evolving crystallizing liquid and the resultant mineralogy of co-crystallizing assemblages affects inter-phase Ca isotope fractionation. Because the GAC is an Archean metamorphosed complex, we first investigate the resistance of the Ca isotope signature to secondary hydrothermal alteration and to metamorphism. While we cannot conclude here that Ca isotopes are undisturbed at the mineral scale, we show that they are preserved at the bulk rock scale. This is adequate for our study where several samples are almost monomineralic at the bulk scale level. The δ(exp 44/40)Ca (relative to NIST standard SRM 915a) of GAC layers range from −1.53 to 1.61‰, with the earliest-formed ultramafic cumulate layer being isotopically heaviest and the later, more felsic layers being isotopically lighter. For the first time, we show that plagioclase is much more enriched in light Ca isotopes compared to olivine and (Ca-) pyroxene. Monte Carlo simulations suggest that Ca isotopes are fractionated among co-existing silicate minerals during fractional crystallization, possibly in relation with the residual liquid composition. In qualitative agreement with computational models based on first principles lattice dynamics, we observe that Ca isotope fractionation is mineralogically controlled and importantly, that the degree of fractionation can vary according to the CaO composition of the residual liquid. While previous studies have aimed to understand partial melting as a source of Ca isotope fractionation, our results suggest that fractional crystallization is also a source of Ca isotope variability among co-genetic samples.
Monte Carlo Simulation and Stochastic FEA are used to predict randomness in the free vibration response of thin unsymmetrically laminated beams. For the present study, it is assumed that randomness in the response is only caused by uncertainties in the ply orientations. The ply orientations may become random or uncertain during the manufacturing process. A new 16-dof beam element, based on the first-order shear deformation beam theory, is used to study the stochastic nature of the natural frequencies. Using variational principles, the element stiffness matrix and mass matrix are obtained through analytical integration. Using a random sequence a large data set is generated, containing possible random ply-orientations. This data is assumed to be symmetric. The stochastic-based finite element model for free vibrations predicts the relation between the randomness in fundamental natural frequencies and the randomness in ply-orientation. The sensitivity derivatives are calculated numerically through an exact formulation. The squared fundamental natural frequencies are expressed in terms of deterministic and probabilistic quantities, allowing to determine how sensitive they are to variations in ply angles. The predicted mean-valued fundamental natural frequency squared and the variance of the present model are in good agreement with Monte Carlo Simulation. Results, also, show that variations between plus or minus 5 degrees in ply-angles can affect free vibration response of unsymmetrically and symmetrically laminated beams.
This paper deals with the development of a reliability methodology to assess the consequences of using hardware, without failure analysis or corrective action, that has previously demonstrated that it did not perform per specification. The subject of this paper arose from the need to provide a detailed probabilistic analysis to calculate the change in probability of failures with respect to the base or non-failed hardware. The methodology used for the analysis is primarily based on principles of Monte Carlo simulation. The random variables in the analysis are: Maximum Time of Operation (MTO) and operation Time of each Unit (OTU) The failure of a unit is considered to happen if (OTU) is less than MTO for the Normal Operational Period (NOP) in which this unit is used. NOP as a whole uses a total of 4 units. Two cases are considered. in the first specialized scenario, the failure of any operation or system failure is considered to happen if any of the units used during the NOP fail. in the second specialized scenario, the failure of any operation or system failure is considered to happen only if any two of the units used during the MOP fail together. The probability of failure of the units and the system as a whole is determined for 3 kinds of systems - Perfect System, Imperfect System 1 and Imperfect System 2. in a Perfect System, the operation time of the failed unit is the same as that of the MTO. In an Imperfect System 1, the operation time of the failed unit is assumed as 1 percent of the MTO. In an Imperfect System 2, the operation time of the failed unit is assumed as zero. in addition, simulated operation time of failed units is assumed as 10 percent of the corresponding units before zero value. Monte Carlo simulation analysis is used for this study. Necessary software has been developed as part of this study to perform the reliability calculations. The results of the analysis showed that the predicted change in failure probability (P(sub F)) for the previously failed units is as high as 49 percent above the baseline (perfect system) for the worst case. The predicted change in system P(sub F) for the previously failed units is as high as 36% for single unit failure without any redundancy. For redundant systems, with dual unit failure, the predicted change in P(sub F) for the previously failed units is as high as 16%. These results will help management to make decisions regarding the consequences of using previously failed units without adequate failure analysis or corrective action.
The current effort addresses two issues important to the research conducted by the Thermal Radiation Group at Virginia Tech. The first research topic involves the development of a method which can properly model the diffraction of radiation as it enters an instrument aperture. The second topic involves the study of a potential next-generation space-borne radiometric instrument concept. Presented are multiple modeling efforts to describe the diffraction of monochromatic radiant energy passing through an aperture for use in the Monte-Carlo ray-trace environment. Described in detail is a deterministic model based upon Heisenberg's uncertainty principle and the particle theory of light. This method is applicable to either Fraunhofer or Fresnel diffraction situations, but is incapable of predicting the secondary fringes in a diffraction pattern. Also presented is a second diffraction model, based on the Huygens-Fresnel principle with a correcting obliquity factor. This model is useful for predicting Fraunhofer diffraction, and can predict the secondary fringes because it keeps track of phase. NASA is planning for the next-generation of instruments to follow CERES (Clouds and the Earth's Radiant Energy System), an instrument which measures components of the Earth's radiant energy budget in three spectral bands. A potential next-generation concept involves modification of the current CERES instrument to measure in a larger number of wavelength bands. This increased spectral partitioning would be achieved by the addition of filters and detectors to the current CERES geometry. The capacity of the CERES telescope to serve for this purpose is addressed in this thesis.
Because of the inherent complexity of fiber-reinforced laminated composites, it can be challenging to manufacture composite structures according to their exact design specifications, resulting in unwanted material and geometric uncertainties. In this research, we focus on the deterministic and probabilistic stability analysis of laminated structures subject to subtangential loading, a combination of conservative and nonconservative tangential loads, using the dynamic criterion. Thus a shear-deformable laminated beam element, including warping effects, is derived to study the deterministic and probabilistic response of laminated beams. This twenty-one degrees of freedom element can be used for solving both static and dynamic problems. In the first-order shear deformable model used here we have employed a more accurate method to obtain the transverse shear correction factor. The dynamic version of the principle of virtual work for laminated composites is expressed in its nondimensional form and the element tangent stiffness and mass matrices are obtained using analytical integration The stability is studied by giving the structure a small disturbance about an equilibrium configuration, and observing if the resulting response remains small. In order to study the dynamic behavior by including uncertainties into the problem, three models were developed: Exact Monte Carlo Simulation, Sensitivity Based Monte Carlo Simulation, and Probabilistic FEA. These methods were integrated into the developed finite element analysis. Also, perturbation and sensitivity analysis have been used to study nonconservative problems, as well as to study the stability analysis, using the dynamic criterion.
Brief Presenter Biography (35 word limit): Bohdan Wesely is an Aerospace Engineer in the Entry Systems and Technology Division at Ames. He has worked on a variety of projects for NASA including integrated TPS (thermal protection system) flight hardware deliveries and testing services for commercial partners. Introduction: TEMPEST is a new trajectory analysis framework that is designed to fill the gap between dedicated flight mechanics tools and aerothermal and TPS sizing tools. The project started as an SJSU master’s thesis and has since evolved into a general conceptual design tool capable of studying a wide variety of entry problems. Development is ongoing in the Entry Systems and Technology Division at NASA ARC. Why TEMPEST: Space missions involving entry into a planetary atmosphere involve a series of unique requirements across multiple disciplines. Whether it is traditional entry descent and landing (EDL), or aerocapture, the vehicle must navigate to its target landing location or orbit state, and the TPS must protect the payload during entry. The design process typically involves iterative handoffs between various flight mechanics, flow solver, and material response level tools. During the early conceptual phase, a wide variety of feasible trajectories are simulated in a Monte Carlo scenario which broadly satisfy the mission or landing requirements. Next, computational fluid dynamics (CFD), direct simulation Monte Carlo (DSMC), and other flow solver analyses are performed at various key trajectory points to generate an aero-database, heating and TPS design requirements also emerge at this stage. At this point, with updated aerodynamics from the various flow solvers, trajectories can be re-run, this in turn can change the required freestream conditions for the CFD tools, and as a project progresses, these analyses converge, and uncertainty is reduced. However, there is always a “hand-off” occurring between two inherently coupled phenomena. Analysis Description: One of the goals with TEMPEST is to use a variety of first principles estimation methods coupled with an atmosphere model to predict vehicle aerothermodynamics across the entire flight regime while propagating a 3 or 6 degree of freedom (DoF) trajectory. Aerodynamics methods include modified Newtonian, Maxwell and Cercignani- Lampis-Lord (CLL) for continuum, transitional, and free molecular flow regimes. Aerothermodynamics include boundary layer and reference enthalpy methods, and Mutation++ for non-equilibrium chemistry modeling. TEMPEST is also capable of stitching multiple trajectory segments together to study mission scenarios like multi-pass aerocapture and aero-gravity assists. Most of the program is implemented in MATLAB using modern system objects, it relies on several C++ shared libraries for supporting tools like Gmsh, the Global Reference Atmospheric Model (GRAM), and Mutation++. The various first principles aerothermal estimation methods are discretized across either a structured axisymmetric panel mesh or an unstructured tri-mesh generated from an open-source tool such as Gmsh, this allows solutions on the same mesh to be compared across tools such as CB-Aero. CFD Coupling. A physics-aware, gaussian process CFD anchoring scheme is proposed to adjust the various first principles methods as a CFD database is populated. One goal for this anchoring module is to inform the project where CFD should be run. Full knowledge of the entire trajectory, atmosphere, and aerothermodynamics allows for easier identification of high sensitivity areas and uncertainty quantification. While the first principles effects are well known and proven accurate in existing tools such as CB- Aero and Cart3D, a physics aware CFD anchoring scheme increases tool credibility across a project lifecycle. Material Response Modeling. Correct TPS sizing is critical for optimizing mass for science payloads and ensuring mission success. The process typically involves a thermal analysis along the trajectory with surface heating environments as a boundary condition. Several design constraints are maximum bondline temperature and maximum recession with various margining techniques. The material response tool FIAT, developed out of NASA Ames, is currently being integrated into the TEMPEST environment. TPS recession, shape change, mass loss, and mass property alteration are all factors that can perturb an entry trajectory. For missions like Mars 2020, recession was minimal and was safely handled separately as a post process. For missions such as Jupiter Galileo with a high TPS mass fraction or asteroid entries, recession plays a major role. The proposed fully coupled scheme is to use an epoch-based approach where the trajectory integration is halted after a recession threshold, the energy balance and FIAT are solved at each panel, the mesh, aerodynamics, and mass properties are updated, and the trajectory continues. Several computational tradeoffs have been made during the development of TEMPEST to limit the cost of a single trajectory and preserve its utility as a conceptual, rapid iteration tool. Conclusion: Development of TEMPEST is ongoing and the project is still in its infancy. This talk aims to showcase its unique capabilities to support future NASA entry systems missions.