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At least 343 records · Page 19

Free Vibration of Uncertain Unsymmetrically Laminated Beams

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.

Kapania, Rakesh K.↗

A geometric nonlinear degenerated shell element using a mixed formulation with independently assumed strain fields

A mixed formulation is chosen to overcome deficiencies of the standard displacement-based shell model. Element development is traced from the incremental variational principle on through to the final set of equilibrium equations. Particular attention is paid to developing specific guidelines for selecting the optimal set of strain parameters. A discussion of constraint index concepts and their predictive capability related to locking is included. Performance characteristics of the elements are assessed in a wide variety of linear and nonlinear plate/shell problems. Despite limiting the study to geometric nonlinear analysis, a substantial amount of additional insight concerning the finite element modeling of thin plate/shell structures is provided. For example, in nonlinear analysis, given the same mesh and load step size, mixed elements converge in fewer iterations than equivalent displacement-based models. It is also demonstrated that, in mixed formulations, lower order elements are preferred. Additionally, meshes used to obtain accurate linear solutions do not necessarily converge to the correct nonlinear solution. Finally, a new form of locking was identified associated with employing elements designed for biaxial bending in uniaxial bending applications.

Graf, Wiley E.↗

Open-source Numerical Modeling of Solidification Cracking Susceptibility: Application to Refractory Alloy Systems

Introduction. Alloys such as aluminum, nickel-base, and austenitic stainless steels are susceptible to solidification cracking during welding and 3D printing. Compositional optimization is one method used to effectively mitigate solidification cracking of those alloy systems. With the surge in hypersonic and in-space propulsion activities, refractory metals (Nb, Mo, Ta, W, and Re) and their alloy derivatives are increasing in importance due to their extreme high melting point and retention of high-temperature strength; however, their chemistry was most typically optimized to promote ductility during mechanical operations such as drawing and forming. Welding of such alloys has been a challenge due to a number of issues including solidification cracking, atmospheric contamination (O, C, and N), as well as a shift in ductile-to-brittle transition to higher temperature following grain growth induced by welding. Compositional optimization of refractory alloys for solidification cracking resistance in particular is desirable as their usage increases with the advent of advanced manufacturing methods such as 3D printing. This work evaluates the effect of compositional variation in refractory metal systems on the solidification cracking susceptibility with the goals of optimizing existing alloys and joining process techniques, and formulating new alloys with increased solidification cracking resistance. Experimental Procedures. A python code was developed in a Jupyter notebook environment (Michael and Sowards, 2023) to facilitate the calculation of crack susceptibility index proposed by Kou (2015). Composition is entered as a single point, or as a 1-D or 2-D array. The notebook calls pycalphad (Otis and Liu, 2017 and Bocklund et al, 2020) to calculate the evolution of fraction solid as a function of temperature (under either Scheil or equilibrium assumptions) and then evaluates steepness of the fraction solid curve near the terminal stage of solidification to predict solidification cracking resistance. Open source thermodynamic databases available at online repositories are used (van de Walle). The process is setup in an automated fashion to generate plots that show variation in solidification cracking susceptibility according to composition on 1-D line plots or 2-D contour plots. The Jupyter notebook and crack susceptibility algorithm was also integrated with a widely used commercial CALPHAD code for validation and alloy exploration. Results and Discussion. The crack susceptibility model was first validated against a series of refractory alloy compositions evaluated in past work which utilized a specialized Varestraint test built inside a vacuum chamber environment (Lessman and Gold, 1971). The alloys tested in the Varestraint apparatus included T-111 (Ta-8W-2Hf), ASTAR-811C (Ta-8W-1Re-0.7Hf-0.025C), FS-85 (Nb-27Ta-10W-1Zr), T-222 (Ta-9.6W-2.4Hf-0.01C), Ta-10W, B-66 (Nb-5Mo-5V-1Zr), and SCb-291 (Nb-10W-10Ta). The initial test of the model showed a strong correlation with empirical Varestraint data, i.e., a Spearman rank correlation between model predictions and hot cracking measurements was observed to be greater than 0.8. Following the validation, a set of refractory metal binary mixtures was investigated to evaluate sensitivity of Nb, Mo, W, and Ta to C, N, and O content. A series of plots were produced that suggest ppmw ranges of C, N, and O where solidification cracking increases significantly and reaches a maximum. Also comparative ranking of each primary refractory metal to each interstitial was produced. For example C produces greater cracking response in Mo whereas O produces greater cracking response in Ta and Nb. Such compositional values have utility in setting limits on pickup of these interstitial elements during welding and printing rather than using a one-size-fits-all approach. Furthermore, the results have use in determining additive powder recycling requirements, which is especially pertinent for refractory metal powders due to their high cost compared to conventional alloys. Another application created thousands of hypothetical alloys within the nominal specified composition range of two widely used refractory alloys C103 (Nb-10Hf-1Ti) and TZM (Mo-0.5Ti-0.1Zr). The cracking index was calculated for the alloys and results were fed into machine learning regression techniques including Multiple Linear Regression, Ridge Regression, and Lasso Regression to determine relative potency each alloying element had on computed solidification cracking index. A series of linear equations were produced that relate composition of C103 and TZM to solidification cracking index. The crack susceptibility of C103 for example is described by an equation of the form: cracking index ~ O + 0.667*C + 0.635*N + 0.00037*Ta – 0.0008*Hf (in wt.%) From that equation, it is clear that O has strong propensity to induce solidification cracking. Interestingly, Hf is shown to reduce calculated cracking response. Finally, realizing the potential of this method to discover new refractory alloy formulations across the period table that have low solidification cracking sensitivity, the code was applied to new untested alloy systems including W-Zr-C, W-Ta-C, and others. Conclusions. In summary, an open source numerical method has been developed using Python code to calculate Kou’s crack susceptibility index. The method was applied to refractory metals which are inherently difficult to study from a weldability testing standpoint since inert shielding gas is not sufficient and welding is typically done in vacuum, especially in light of findings presented here where oxygen has profound influence on solidification cracking. This work revealed the effect of compositional variations on a series of refractory metals and showed the framework defined here will be useful in 1) the development of new alloys that have improved weldability and 3D printability, 2) placing compositional limits on existing alloys, and 3) ensuring adequate controls of manufacturing processes such as 3D printing where powder reuse is critical. Keywords. pycalphad; Python; refractory metals; solidification cracking. References. B. Bocklund et. al. (2020) http://doi.org/10.5281/zenodo.3630657. S. Kou. (2015) https://doi.org/10.1016/j.actamat.2015.01.034. G.G. Lessmann and R.E. Gold. Welding Journal, issue 1, pp. 1-s – 8-s (1971). F.N. Michael and J.W. Sowards. NASA/TM-20230002218 (2023). R. Otis and Z.-K. Liu. (2017) http://doi.org/10.5334/jors.140. A. Van de Wallle et. al. (2018) https://doi.org/10.1016/j.calphad.2018.04.003.

pycalphad↗

A Physics-Based Work-Energy Formulation for Real-Time Trajectory Guidance of A Lunar Lander

Throughout the years, many researchers have calculated and optimized trajectory solutions for lunar landing systems by employing sophisticated mathematical methods, that include: Hamilton’s Principle of Variation, Pontryagin’s maximum principle, and well known convex-optimization techniques among others. Many of these approaches typically require expensive computational resources to achieve convergence in the solution. In an effort to reduce complexity and the computational load required to obtain real-time guidance commands, a simple physics-based work-energy approach has been formulated. This approach is based on the dissipation of the mechanical energy of the vehicle to its final desired energy state required to achieve a safe landing. The rocket engine(s) employed during landing (among other maneuvers) dissipates mechanical energy by both doing work against the velocity vector of the vehicle (thus defining the trajectory path), and by jettisoning mass. Therefore, by solving the energy dissipation problem at every step of the maneuver, a much simpler formulation that naturally and quickly attains convergence is obtained. This formulation is not limited to approach, landing, and divert maneuvers, but in principle it can be employed during de-orbiting, braking burn, ascent, as well as orbit insertion.

Guidance↗

A Physics-Based Work-Energy Formulation for Real-Time Trajectory Guidance of a Lunar Lander

Throughout the years, many researchers have calculated and optimized trajectory solutions for lunar landing systems by employing sophisticated mathematical methods, that include: Hamilton’s Principle of Variation, Pontryagin’s maximum principle, and well known convex-optimization techniques among others. Many of these approaches typically require expensive computational resources to achieve convergence in the solution. In an effort to reduce complexity and the computational load required to obtain real-time guidance commands, a simple physics-based work-energy approach has been formulated. This approach is based on the dissipation of the mechanical energy of the vehicle to its final desired energy state required to achieve a safe landing. The rocket engine(s) employed during landing (among other maneuvers) dissipates mechanical energy by both doing work against the velocity vector of the vehicle (thus defining the trajectory path), and by jettisoning mass. Therefore, by solving the energy dissipation problem at every step of the maneuver, a much simpler formulation that naturally and quickly attains convergence is obtained. This formulation is not limited to approach, landing, and divert maneuvers, but in principle it can be employed during de-orbiting, braking burn, ascent, as well as orbit insertion.

Guidance↗

Performance Analysis and Design Synthesis (PADS) computer program. Volume 1: Formulation

The program formulation for PADS computer program is presented. It can size launch vehicles in conjunction with calculus-of-variations optimal trajectories and can also be used as a general-purpose branched trajectory optimization program. In the former use, it has the Space Shuttle Synthesis Program as well as a simplified stage weight module for optimally sizing manned recoverable launch vehicles. For trajectory optimization alone or with sizing, PADS has two trajectory modules. The first trajectory module uses the method of steepest descent; the second employs the method of quasilinearization, which requires a starting solution from the first trajectory module.

Source record↗

Solution of an optimal control lifting body entry problem by an improved method of perturbation functions

This paper presents a solution to a complex lifting reentry three-degree-of-freedom problem by using the calculus of variations to minimize the integral of the sum of the aerodynamics loads and heat rate input to the vehicle. The entry problem considered does not have state and/or control constraints along the trajectory. The calculus of variations method applied to this problem gives rise to a set of necessary conditions which are used to formulate a two point boundary value (TPBV) problem. This TPBV problem is then numerically solved by an improved method of perturbation functions (IMPF) using several starting co-state vectors. These vectors were chosen so that each one had a larger norm with respect to show how the envelope of convergence is significantly increased using this method and cases are presented to point this out.

Garcia, F., Jr.↗

An application of extremal field guidance in statistical low thrust guidance analysis

The subject of this paper is the application of extremal field guidance to the covariance analysis of low thrust retargeting guidance. The general procedure for low thrust navigation analysis is briefly reviewed. The basic equations of trajectory optimization and extremal field guidance are presented with emphasis on the low thrust problem. The adopted formulation includes thruster on-off times as control variables and accounts for the effects of model parameter variations. A method of solution of the guidance equations is outlined; and the application of the solution in a covariance analysis, including a procedure for the treatment of model parameter variations as either biases or first order Gauss-Markov stochastic processes, is discussed.

Jacobson, R. A.↗

Patched-grid computations of high-speed inlet flows

Two implicit algorithms for the compressible Navier-Stokes equations are applied to the computation of high-speed inlet flows typical of those which are encountered on propulsion systems of advanced hypersonic vehicles. A patched grid formulation is used to treat accurately the blunt cowl interaction with the forebody compression field and efficiently treat variations in inlet geometry downstream of the inlet entrance. Results from the two algorithms, each based on an upwind-biased spatial differencing approach for the convective and pressure terms within a flux-difference-splitting framework, are compared with experimental results for both inlets, and reasonable agreement is found.

Thomas, J. L.↗

An upwind-biased space marching algorithm for supersonic viscous flow

The modifications are documented which were made to the Langley Aerothermodynamic Upwind Relaxation Algorithm which allow it to compute solutions in a space marching manner. The space marching flux is formulated to be either first- or second-order accurate, using Roe's upwind differencing or Symmetric Total Variation Diminishing differencing, respectively. The algorithm solves the thin layer Navier-Stokes equations, and is subject to the same flow restrictions as a parabolized Navier-Stokes solver. Each cross flow plane is locally iterated in time until converged, then marched in space to the next station. The algorithm is tested on a sphere-cone geometry and a geometry which models the windward side of the Space Shuttle Orbiter. Computational results for surface heating are compared to ground based experimental data. In addition, space marching predictions for surface pressure are compared against values from the original algorithm.

Greene, Francis A.↗

Modeling of resistive sheets in finite element solutions

A formulation is presented for modeling a resistive card in the context of the finite element method. The appropriate variational function is derived and for validation purposes, results are presented for the scattering by a metal-backed cavity loaded with a resistive card.

Jin, J. M.↗

Modeling of resistive sheets in finite element solutions

A formulation is presented for modeling a resistive card in the context of the finite element method. The appropriate variational function is derived and for variational purposes results are presented for the scattering by a metal-backed cavity loaded with a resistive card.

Jin, J. M.↗

Modeling of resistive sheets in finite element solutions

A formulation is presented for modeling a resistive card in the context of the finite element method. The appropriate variational function is derived and for variational purposes results are presented for the scattering by metal-backed cavity loaded with a resistive card.

Jin, J. M.↗

Multiple scattering of electromagnetic waves by rain

As the operating frequencies of communications systems move higher into the millimeter wave region, the effects of multiple scattering in precipitation media become more significant. In this paper, general formulations are presented for single, first-order multiple, and complete multiple scattering. Included specifically are distributions of particle size, shape, and orientation angle, as well as variation in the medium density along the direction of wave propagation. Calculations are performed for rain. It is shown that the effects of higher-order scattering are not noticeable in either attenuation or channel isolation on a dual-polarized system until frequencies of about 30 GHz are reached. The complete multiple-scattering formulation presented gives accurate results at high millimeter wave frequencies as well as including realistic medium parameter distributions. Furthermore, it is numerically efficient.

Tsolakis, A.↗

Characterizing Porous and Nonporous Phenolic Resins from Molecular Dynamics Simulations

Phenolic resins are an important component of many ablative heat shield materials, which protect spacecrafts from the extreme temperatures reached during atmospheric entry. Examples include the high-density Heritage Carbon Phenolic (HCP) used in the Pioneer-Venus and Galileo missions, as well as the low-density Phenolic Impregnated Carbon Ablator (PICA) used in the Mars Science Laboratory and Mars 2020 missions. Additionally, recent developments within NASA have produced the mid-density Heatshield for Extreme Entry Environment Technology (HEEET) and its derivative 3D Woven Mid-Density Carbon Phenolic (3MDCP). Unlike the nonporous phenolic in HCP, PICA and HEEET/3MDCP are fabricated by infusing preforms with diluted phenolic formulations to obtain a lower density porous matrix. Despite the importance of the phenolic phase to the material response during entry, the variation in properties of porous and nonporous phenolic is not well understood. Here, we present an investigation of porous and nonporous phenolic resins using molecular dynamics (MD) simulations. Resin cure is mimicked in the simulations through the inclusion of representative reaction templates to generate accurate models of the complex crosslinked structures. To create porous models, explicit solvent molecules are included during the cure simulations. We observe nanoscale separation of the phenolic and solvent phases, which results in significant differences in the final structures of porous and nonporous models. In addition to a quantitative assessment of the network structure and porosity, we elucidate the effects of the phenolic formulation on the final material properties. These results are compared with experimental data as appropriate.

phenolic↗

Supersonic flow calculation using a Reynolds-stress and an eddy thermal diffusivity turbulence model

A second-order model for the velocity field and a two-equation model for the temperature field are used to calculate supersonic boundary layers assuming negligible real gas effects. The modeled equations are formulated on the basis of an incompressible assumption and then extended to supersonic flows by invoking Morkovin's hypothesis, which proposes that compressibility effects are completely accounted for by mean density variations alone. In order to calculate the near-wall flow accurately, correction functions are proposed to render the modeled equations asymptotically consistent with the behavior of the exact equations near a wall and, at the same time, display the proper dependence on the molecular Prandtl number. Thus formulated, the near-wall second order turbulence model for heat transfer is applicable to supersonic flows with different Prandtl numbers. The model is validated against flows with different Prandtl numbers and supersonic flows with free-stream Mach numbers as high as 10 and wall temperature ratios as low as 0.3. Among the flow cases considered, the momentum thickness Reynolds number varies from approximately 4,000 to approximately 21,000. Good correlation with measurements of mean velocity, temperature, and its variance is obtained. Discernible improvements in the law-of-the-wall are observed, especially in the range where the big-law applies.

Sommer, T. P.↗

Foundations of planetary quarantine.

Discussion of some of the problems in microbiology and engineering involved in the implementation of planetary quarantine. It is shown that the solutions require new knowledge in both disciplines for success at low cost in terms of both monetary outlay and man's further exploration of the planets. A related problem exists in that engineers are not accustomed to the wide variation of biological data and microbiologists must learn to work and think in more exact terms. Those responsible for formulating or influencing national and international policies must walk a tightrope with delicate balance between unnecessarily stringent requirements for planetary quarantine on the one hand and prevention of contamination on the other. The success of planetary quarantine measures can be assured only by rigorous measures, each checked, rechecked, and triple-checked to make sure that no errors have been made and that no factor has been overlooked.

Hall, L. B.↗

Quantum-mechanical transport equation for atomic systems.

A quantum-mechanical transport equation (QMTE) is derived which should be applicable to a wide range of problems involving the interaction of radiation with atoms or molecules which are also subject to collisions with perturber atoms. The equation follows the time evolution of the macroscopic atomic density matrix elements of atoms located at classical position R and moving with classical velocity v. It is quantum mechanical in the sense that all collision kernels or rates which appear have been obtained from a quantum-mechanical theory and, as such, properly take into account the energy-level variations and velocity changes of the active (emitting or absorbing) atom produced in collisions with perturber atoms. The present formulation is better suited to problems involving high-intensity external fields, such as those encountered in laser physics.

Berman, P. R.↗