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DOE OSTI2021

On the Symmetry of Blast Waves

This paper presents a brief historical review of G. I. Taylor’s solution of the point blast wave problem which was applied to the Trinity test of the first atomic bomb. Lie group symmetry techniques (also referred to throughout this paper as geometric techniques) are used to derive Taylor’s famous two-fifths law that relates the position of a blast wave to the time after the explosion and the total energy released. The theory of exterior differential systems is combined with the method of characteristics to demonstrate that the solution of the blast wave problem is directly related to the basic relationships that exist between the symmetry (or geometry) and the physics of wave propagation through the equations of motion. The point blast wave model is cast in terms of two exterior differential systems, and both systems are shown to be integrable with local solutions for the velocity, pressure, and density along curves in space and time behind the blast wave. This work is dedicated to the memory of Professor Roy Axford, who introduced many of his students to the topic of symmetry analysis of differential equations.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

DOE OSTI2016

SU-F-T-127: Charged Particle Transport in Condensed Media

Purpose: Provide quality interaction cross sections for charged particle Monte Carlo (MC) track structure codes and evaluate low energy electron transport in condensed media. Methods: MC methods and codes are often used to model or simulate charged particle radiation transport in matter. Detailed (or event-by-event) track structure simulations are of special interest for the modeling of the physical and chemical stages of radiation action with matter and the initial radiation damage to biological systems. They require reliable interaction cross sections of all radiation qualities considered (e.g., electrons, protons, alpha particles, light and heavy ions) with the target material under consideration, mainly in the condensed phase, including liquids and solids. Interaction cross sections are calculated using the dielectric formalism, a mixture of first principles, theoretical modeling and experimental information for bulk and surface transport and implemented into MC track structure codes. Secondary electron emission yields from amorphous solid water (ASW) and thin metal foils (copper and gold) after fast proton impact are simulated and measured experimentally. Results: After considering different transport models for bulk and surface transport and a careful modeling of the experimental geometry, simulated secondary electron emission yields follow the trends of experimental data well. Furthermore, yields for electron emissions below 50 eV are sensitive to differential elastic scattering cross sections. Conclusion: Low-energy electron transport in condensed media is still a challenge for detailed track structure simulation codes. Interaction cross-sections, transport models, and target geometry need to be considered adequately. The research was funded in part by NSF Major Research Instrumentation Program 2009, Award Number: 0923270 and by NIH/NCI R01 CA93351.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2018

Scattering forms and the positive geometry of kinematics, color and the worldsheet

The search for a theory of the S-Matrix over the past five decades has revealed surprising geometric structures underlying scattering amplitudes ranging from the string worldsheet to the amplituhedron, but these are all geometries in auxiliary spaces as opposed to the kinematical space where amplitudes actually live. Motivated by recent advances providing a reformulation of the amplituhedron and planar N = 4 SYM amplitudes directly in kinematic space, we propose a novel geometric understanding of amplitudes in more general theories. The key idea is to think of amplitudes not as functions, but rather as differential forms on kinematic space. We explore the resulting picture for a wide range of massless theories in general spacetime dimensions. For the bi-adjoint Φ3 scalar theory, we establish a direct connection between its “scattering form” and a classic polytope — the associahedron — known to mathematicians since the 1960’s. We find an associahedron living naturally in kinematic space, and the tree level amplitude is simply the “canonical form” associated with this “positive geometry”. Fundamental physical properties such as locality and unitarity, as well as novel “soft” limits, are fully determined by the combinatorial geometry of this polytope. Furthermore, the moduli space for the open string worldsheet has also long been recognized as an associahedron. We show that the scattering equations act as a diffeomorphism between the interior of this old “worldsheet associahedron” and the new “kinematic associahedron”, providing a geometric interpretation and simple conceptual derivation of the bi-adjoint CHY formula. We also find “scattering forms” on kinematic space for Yang-Mills theory and the Non-linear Sigma Model, which are dual to the fully color-dressed amplitudes despite having no explicit color factors. This is possible due to a remarkable fact—“Color is Kinematics”— whereby kinematic wedge products in the scattering forms satisfy the same Jacobi relations as color factors. Finally, all our scattering forms are well-defined on the projectivized kinematic space, a property which can be seen to provide a geometric origin for color-kinematics duality.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS1972

Low-frequency macroscopic instabilities of fully ionized magnetoplasma

Studies are described of low-frequency quasi-static instabilities in a fully ionized plasma. The plasma is assumed to be immersed in a uniform magnetic field, and is either uniform or has a number density gradient perpendicular to the magnetic field. A moment equation description of the ion and electron dynamics is used; collisions are assumed to have a strong effect on electron motion along the magnetic field. Before considering specific modes, a stability analysis is developed which allows a classification of wave growth characteristics to be made for a bounded system from solutions to the dispersion relation for an infinite system. Also, a method is given for calculating the normal mode frequencies and wave profiles by using the reflection coefficients at the boundaries. For wave propagation perpendicular to the magnetic field, the flute wave is studied in cylindrical geometry. The destabilizing effect of a radial electric field is considered by solving a differential equation.

Rognlien, T. D.↗

NASA NTRS1985

Mega-geomorphology and neotectonics

For several decades, subtle neotectonic effects involving several square kilometers have been studied in detail using remote sensing, primarily various types of stereo-aerial photographs at scales of 1:10,000 to 1:80,000. These subtle effects, especially local uplifts associated with growing structures of differential compaction, have been detected by the effect on drainage patterns, changes in hydraulic geometry of individuals channels or groups of channels, tonal halos (soil) and fracture patterns. The studies were extended with the advent of thermal IR imagery particularly in tonal analysis, and SLAR primarily in fracture pattern studies. Lately, quantitative efforts have begun attempting to link measured uplift over known structures with measured changes in hydraulic geometry and alluvial deposition. Thus, efforts are now underway attempting to quantify the relationship between neo- (micro-) tectonic changes and geomorphic parameters of drainage systems.

Lattman, L. H.↗

NASA NTRS1988

Novel tether-connected two-dimensional structures for low earth orbits

This paper proposes novel tether-connected two-dimensional structures with a size of several hundred square kilometers for low earth orbits. The attitude of these structures is gravitationally stabilized with respect to an earth-oriented reference frame. A stable shape is obtained by utilizing environmental forces such as differential air drag or electrodynamic forces which stiffen the system. Configurations which differ in geometry and in the number of connecting tethers are presented in the paper. The static stability of each configuration is analyzed as a function of design and orbital parameters. A brief discussion of the applications of such tethered systems is provided at the end of the paper.

Lorenzini, Enrico C.↗

NASA NTRS2005

In Vitro Experimental Model to Investigate the Biological Effects across the Bragg Curve of High-LET Radiation

The space environment consists of a varying field of radiation particles including high energy ions, with a spacecrafts shielding material providing the only major protection to astronauts from harmful exposure. Unlike lowLET gamma or Xrays, the presence of shielding does not always reduce the radiation risks for energetic charged particle exposure since the dose delivered by the charged particle increases sharply as the particle approaches the end of its range, a position known as the Bragg peak and the correlating spatial dose distribution identified as the Bragg curve. The Bragg curve does not necessarily represent the biological damage along the particle traversal since biological effects are influenced by the track structure of both primary and secondary particles. Therefore, the biological Bragg curve is dependent of the energy and the type of the primary particle, and may vary for different biological endpoints. Here we describe a unique irradiation geometry and experimental system to measure the biological response across the Bragg curve in one consistent biological sample. Polyethylene shielding was used to achieve a Bragg curve distribution with the beam geometry parallel to a monolayer of fibroblast cells. We present data that highlights the differential formation of DNA double strand breaks (DSBs) and chromosomal deletions across the Bragg curve in human fibroblasts irradiated with 600 MeV/nucleon iron ion beams. Qualitative analyses of gammaH2AX fluorescence, a known marker of DSBs, indicated potentially increased clustering of DNA damage before the Bragg peak, enhanced homogenous distribution at the peak, and provided visual evidence of high linear energy transfer (LET) particle traversal of cells beyond the Bragg peak in agreement with one-dimensional transport approximations. A biological response curve generated for micronuclei induction across the Bragg curve for 600 MeV/n Fe ions did not reveal an increase in the yield of micronuclei at the Bragg peak location. Assessment of such biological parameters employing the described in vitro experimental system may provide improved platforms to measure a number of biological consequences of shielding materials across the Bragg curve for high charge and energy (HZE) ions.

Desai, N.↗

DOE OSTI2018

Design Optimization Study on the Single Tank Packed-bed Thermal Energy Storage System

Idaho National Laboratory (INL) is establishing the Dynamic Energy Transport and Integration Lab (DETAIL) as part of its commitment to research on nuclear-renewable hybrid energy systems and associated advanced reactor technologies. DETAIL is designed to allow several different energy systems to work in unison. Current plans include a PWR simulator, high-temperature steam electrolysis (HSTE) unit, and a renewable energy system (e.g., photovoltaics). DETAIL will provide the real world basis for studies on the systems integration and system configurations to be completed. Encompassed in the DETAIL program is the Thermal Energy Storage (TES) system. The TES system is one of the key components in DETAIL because it allows for the delayed release of energy and can be used to simulate storage capabilities currently being considered by utility providers. Of the various TES concepts, this paper deals with the single-tank packed bed TES system. Particular attention is given to the transient thermal behavior of fluid and solid particles within the packed bed thermocline tank and heat storage efficiency influenced by various design parameters. The effects of tank geometry (height-to-diameter ratio), filler size, filler packing ratio and operating temperature differentials are investigated. Based on the parametric study and cost analysis, the optimal TES tank design for DETAIL is discussed.

25 ENERGY STORAGE↗

DOE OSTI2014

Computational evaluation of the flexoelectric effect in dielectric solids

Flexoelectricity is a size-dependent electromechanical mechanism coupling polarization and strain gradient. It exists in a wide variety of materials, and is most noticeable for nanoscale objects, where strain gradients are higher. Simulations are important to understand flexoelectricity because experiments at very small scales are difficult, and analytical solutions are scarce. Here, we computationally evaluate the role of flexoelectricity in the electromechanical response of linear dielectric solids in two-dimensions. We deal with the higher-order coupled partial differential equations using smooth meshfree basis functions in a Galerkin method, which allows us to consider general geometries and boundary conditions. We focus on the most common setups to quantify the flexoelectric response, namely, bending of cantilever beams and compression of truncated pyramids, which are generally interpreted through approximate solutions. While these approximations capture the size-dependent flexoelectric electromechanical coupling, we show that they only provide order-of-magnitude estimates as compared with a solution fully accounting for the multidimensional nature of the problem. We discuss the flexoelectric mechanism behind the enhanced size-dependent elasticity in beam configurations. We show that this mechanism is also responsible for the actuation of beams under purely electrical loading, supporting the idea that a mechanical flexoelectric sensor also behaves as an actuator. The predicted actuation-induced curvature is in a good agreement with experimental results. The truncated pyramid configuration highlights the critical role of geometry and boundary conditions on the effective electromechanical response. Our results suggest that computer simulations can help understanding and quantifying the physical properties of flexoelectric devices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

Implementation of Material and Geometry Criticality Search in RMC Code

RMC is a continuous-energy Reactor Monte Carlo neutron and photon transport code being developed by Department of Engineering Physics at Tsinghua University, Beijing. For the use of simulation of reactor control or design of reactor with unknown material and geometry parameters, an accurate and efficient method of eigenvalue search is implemented in RMC code. The eigenvalue search focuses on two types of parameters. One is nuclide atom density, called material search, which includes the fuel density, enrichment or boron concentration. Perturbation theory of Monte Carlo Code, like differential operator method and adjoint-weighted perturbation method has been widely researched in sensitivity and uncertainty study. For material search, the perturbation algorithm needs to coupled with flexible material control block and optimized strategy. The other type of parameter is surface position, called geometry search, which includes fuel rod diameter, pitch and control rod position. MC21 iterated on surface position based on bisection method or regula-falsi method, and directly recalculated k-eff until it converged to target error interval. In this paper, the differential operator method, improved Newton-Raphson method is introduced. Based on these methods, the global material search is implemented. Then based on material search and finite method, global geometry search is implement. Finally, fuel enrichment, boron concentration and control rod position in normal PWR assembly are searched. The results show that RMC can search material and geometry parameters accurately and efficiently. In this paper, global eigenvalue search of material and geometry parameters have been implemented in RMC code. They are based on the differential operator method in Monte Carlo perturbation theory. The differential operator method samples δk/δρ{sub r}, δ{sup 2}k/δρ{sub r}{sup 2} along with k-eff estimator. Therefore it won't take up too much additional computational resource. For homogeneous material search, fission source effect has little effect of accuracy and can be ignored. The results of fuel enrichment and boron concentration searches in assembly show that improved Newton-Raphson method can iterate efficiently until k-eff is in the error interval. Based on material search and finite difference formula, the geometry parameter, like control rod axial position, can iterate until k-eff is in the error interval. However, the tiny perturbed region may not contain enough tracks to simulate. Besides, the large number density's relative change up to -1 may cause underestimation of Δk-eff, and then slope of k-x curve. This will cause non-convergence for Newton- Raphson method. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS1995

Radiative Instabilities in Three-Dimensional Astrophysical Masers

Inherent instabilities in the radiative transfer for astrophysical masers have been recognized and calculated in the linear maser idealization in our previous investigations. The same instabilities are now shown to occur in the more realistic, three-dimensional geometries. Fluctuations in the emergent flux result and may be related to the observed fluctuations in the radiative flux from the 1665 MHz OH masers that have been reported to occur on timescales as short as 1000 s. The time-dependent differential equations of radiative transfer are solved numerically for three-dimensional astrophysical masers. Computations are performed for spherical and elongated (rectangular parallelepiped) geometries.

Scappaticci, Gerardo A.↗

DOE OSTI2017

Spontaneous imbibition of water and determination of effective contact angles in the Eagle Ford Shale Formation using neutron imaging

Understanding of fundamental processes and prediction of optimal parameters during the horizontal drilling and hydraulic fracturing process results in economically effective improvement of oil and natural gas extraction. Although, the modern analytical and computational models can capture fracture growth, there is a lack of experimental data on spontaneous imbibition and wettability in oil and gas reservoirs for the validation of further model development. In this work, we used neutron imaging to measure the spontaneous imbibition of water into fractures of Eagle Ford Shale with known geometries and fracture orientations. An analytical solution for a set of nonlinear second-order differential equations was applied to the measured imbibition data to determine effective contact angles. The analytical solution fit the measured imbibition data reasonably well and determined effective contact angles were slightly higher than static contact angles due to effects of in-situ changes in velocity, surface roughness, and heterogeneity of mineral surfaces on the fracture surface. Additionally, small fracture widths may have retarded imbibition and affected model fits, which suggests that average fracture widths are not satisfactory for modeling imbibition in natural systems.

DiStefano, Victoria H. (ORCID:0000000160239716)↗

DOE OSTI2026

Unveiling in-gap states and Majorana zero modes in superconductor-topological insulator bilayer model

Interfaces between topological insulators and superconductors (SCs) are promising platforms for realizing Majorana zero modes (MZMs) via the superconducting proximity effect. We introduce a bilayer model consisting of the surface states of a three-dimensional topological insulator (3DTI) coupled to an 𝑠-wave superconductor and systematically study the role of interlayer tunneling strength (𝑡⊥) motivated by the recent growth of the Fe⁡(Te,Se)/Bi 2 ⁢Te 3 heterostructure. We find that increasing 𝑡⊥ shifts the proximity-induced (PrI) gap minimum away from the Γ point, giving rise to momentum-selective interference patterns that manifest as spatial oscillations in the in-gap states. We introduce an antidot with a magnetic vortex in the model and investigate the resulting in-gap states, including MZMs and Caroli–de Gennes–Matricon (CdGM) modes. With increasing hybridization strength, the energy separation between MZMs and CdGM states increases, enhancing the isolation of MZMs. Importantly, in the strong hybridization limit, the leading CdGM separation remains large in spite of the decrease in the PrI gap. Spin- and spatially resolved wavefunction analysis reveals angular momentum asymmetries absent in conventional 𝑠-wave systems. A direct comparison with a standalone 𝑠-wave superconductor confirms the emergence of distinct 𝑝-wave-like features in the bilayer geometry. Our results provide experimentally relevant predictions for tuning the stability of MZMs and their differentiation from the CdGM modes in SC-3DTI heterostructures and offer a theoretical framework for probing unconventional superconductivity in engineered topological systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2016

Programmable shape transformation of elastic spherical domes

We investigate mismatch strain driven programmable shape transformation of spherical domes and report the effects of different geometric and structural characteristics on dome behavior in response to applied mismatch strain. We envision a bilayer dome design where the differential swelling of the inner layer with respect to the passive outer layer in response to changes in dome surroundings (such as the introduction of an organic solvent) introduces mismatch strain within the bilayer system and causes dome shape transformation. Finite element analysis reveals that, in addition to snap-through, spherical domes undergo bifurcation buckling and eventually gradual bending to morph into cylinders with increasing mismatch strain. Besides demonstrating how the snap-through energy barrier depends on the spherical dome shape, our analysis identifies three distinct groups of dome geometries based on their mismatch strain-transformed configuration relationships. Our experiments with polymer-based elastic bilayer domes that exhibit differential swelling in organic solvents qualitatively confirm the finite element predictions. We establish that, in addition to externally applied stimuli (mismatch strain), bilayer spherical dome morphing can be tuned and hence programmed through its geometry and structural characteristics. Incorporation of an elastic instability mechanism such as snap-through within the framework of stimuli-responsive functional devices can improve their response time which is otherwise controlled by diffusion. Furthermore, our proposed design guidelines can be used to realize deployable, multi-functional, reconfigurable, and therefore, adaptive structures responsive to a diverse set of stimuli across multiple length scales.

36 MATERIALS SCIENCE↗

DOE OSTI2016

Fast multipurpose Monte Carlo simulation for proton therapy using multi- and many-core CPU architectures

Purpose: Accuracy in proton therapy treatment planning can be improved using Monte Carlo (MC) simulations. However the long computation time of such methods hinders their use in clinical routine. This work aims to develop a fast multipurpose Monte Carlo simulation tool for proton therapy using massively parallel central processing unit (CPU) architectures. Methods: A new Monte Carlo, called MCsquare (many-core Monte Carlo), has been designed and optimized for the last generation of Intel Xeon processors and Intel Xeon Phi coprocessors. These massively parallel architectures offer the flexibility and the computational power suitable to MC methods. The class-II condensed history algorithm of MCsquare provides a fast and yet accurate method of simulating heavy charged particles such as protons, deuterons, and alphas inside voxelized geometries. Hard ionizations, with energy losses above a user-specified threshold, are simulated individually while soft events are regrouped in a multiple scattering theory. Elastic and inelastic nuclear interactions are sampled from ICRU 63 differential cross sections, thereby allowing for the computation of prompt gamma emission profiles. MCsquare has been benchmarked with the GATE/GEANT4 Monte Carlo application for homogeneous and heterogeneous geometries. Results: Comparisons with GATE/GEANT4 for various geometries show deviations within 2%–1 mm. In spite of the limited memory bandwidth of the coprocessor simulation time is below 25 s for 10{sup 7} primary 200 MeV protons in average soft tissues using all Xeon Phi and CPU resources embedded in a single desktop unit. Conclusions: MCsquare exploits the flexibility of CPU architectures to provide a multipurpose MC simulation tool. Optimized code enables the use of accurate MC calculation within a reasonable computation time, adequate for clinical practice. MCsquare also simulates prompt gamma emission and can thus be used also for in vivo range verification.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2016

A Study of Physics-Informed Deep Learning for System Fluid Dynamics Closures

The sub-grid-scale (SGS) physics models, or so-called closure relations (CR), are essential in thermal-fluid modeling and simulation codes, ranging from large-eddy simulation to system-level thermo-fluid dynamic problems. While details vary, all thermo-fluid codes solve coupled mass-momentum-energy conservation partial differential equations (PDE). Traditionally, the analytical form of closure models has to be known, and then we calibrate the model using data from a set of applicable experiments. Characteristically, it takes long effort to gain insights and mechanistic understanding needed for developing closure models. Such a model is a compact form of data. The long time required for new model development limits the pace of model application while dealing with new geometries, new coolants or system conditions, particularly in newly designed systems. Alternative to mechanistic and semi-analytical models, it is possible to discover the pattern of closure relations by applying the modern machine learning methods to the body of relevant experimental data. Deep learning (DL) is a relatively new branch in the machine learning family, and a major breakthrough has been achieved since Hinton introduces a fast algorithm to efficiently train a feed-forward neural network (NN) with multilayer perceptrons. Generally, any NN with more than two layers is considered as deep learning, and it contains a large number of hyper-parameters to achieve pattern recognition or regression for complex datasets. Hornik shows that multilayer NN is compatible with universal approximation theorem. There is no constraint for a multilayer NN to capture the properties of any measurable information. This capability makes DL attractive for closure models in a system thermal-hydraulic code. As system geometry and/or operating conditions change, new physical experiments (increasingly sophisticated) are conducted to support evaluation and revision of closure models. Such a so-called data-driven modeling relaxes the structural form of system codes to directly assimilate data instead of hard-wiring the model to pre-calibrated correlations. The objective of this research is to enable cost-effective development of a DL-based closure that reflects the data. The previous work on applying machine learning techniques to fluid dynamics focused on statistical learning with basic NN from direct numerical simulations (DNS) dataset. In the present work, we show that DL-based closure models can cause the fluid calculation to diverge if multilayer NN is used. To address the issue, we investigate conditions by which the DL-based closure models work compatibly, stably, and effectively with PDE-constrained forward prediction problems. Optimally meeting the compatibility conditions constitutes a physics-informed deep learning (PIDL) strategy. We refer to this process as PDE-constrained machine learning or PDE-ML. To develop the technical basis for PDE-ML using DL-based fluid dynamics closure, numerical experiments are performed for manufactured problems of increasing complexity. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRS1977

Coplanar tail-chase aerial combat as a differential game

A reduced-order version of the one-on-one aerial combat problem is studied as a pursuit-evasion differential game. The coplanar motion takes place at given speeds and given maximum available turn rates, and is described by three state equations which are equivalent to the range, bearing, and heading of one aircraft relative to the other. The purpose of the study is to determine those relative geometries from which either aircraft can be guaranteed a win, regardless of the maneuver strategies of the other. Termination is specified by the tail-chase geometry, at which time the roles of pursuer and evader are known. The roles are found in general, together with the associated optimal turn maneuvers, by solution of the differential game of kind. For the numerical parameters chosen, neither aircraft can win from the majority of possible initial conditions if the other turns optimally in certain critical geometries.

Merz, A. W.↗

NASA NTRS2000

Polar Plate Theory for Orthogonal Anisotropy

Laminated fiber-reinforced (or filamentary) composites are used today for their high strength-to-weight and stiffness-to-weight ratios. However, because of the anisotropic behavior of composites, determining the response on a macroscopic scale is challenging. This is particularly evident in the evaluation of the governing differential equations of a circular disk with the fibers of the lamina oriented with rectilinear orthogonality. This includes any situation involving a composite plate of circular geometry in which out-of-plane displacements due to load are desired, such as fastener pull through loading of a composite plate. Current analysis techniques use numerical methods with rectilinear coordinate systems to solve problems with circular geometry. These analyses over predict plate stiffness by 20% and underpredict failure by 70%. Consequently, there is a need to transform classical composite plate theory to a polar coordinate system. In order to better analyze structures with circular geometries the classical composite plate equations are transformed into the plate equations for a rectilinearly anisotropic composite in polar coordinates. A composite plate is typically a laminate of fibers in rectilinear directions. Subsequent to the lay-tip the necessary geometry is cut out of a rectangular plate. In a similar manner, the derivation of the plate equation starts with the fundamental definitions of strain, displacement and curvature and incorporates the material property angular dependence into the equilibrium equations for a differential polar element. In the transformed state, the stiffness coefficients are no longer constant, adding to the complexity of the governing differential equations. This paper discusses the new derivation and evaluation of the plate equations for a circular composite disk with orthogonal rectilinear anisotropy. The resultant new three partial differential equations, which describe the circular anisotropic plate, can be used to evaluate out-of-plane displacements for given load conditions in design of composite Structures. Without the formation of these unique plate equations, design of such structures is not a precise engineering accomplishment due to the lack of precise design tools. Such structures are over designed to compensate and costly tests need to be performed after production to validate safety. Though impossible to present the mathematical solution within the limits of this paper, the application of the newly derived plate equation in its orthotropic form for a balanced symmetric laminate compared favorably with test results and surpassed the results of standard numerical methods. Within the limitations of the problem foundation the predictive model provides a mechanism for establishing out-of-plane deflection levels for a circular composite plate. Future work in this area should include incorporating the circular composite plate equations in Finite Element Models. The new anisotropic polar plate equations call be utilized as a design tool so that the design more accurately meets the requirements, thus taking full advantage of the weight savings of composites. These accomplishments have not previously been presented to the engineering community nor ever proposed to the IAF. Should the proposed paper be accepted for presentation, attendance is assured.

Bailey, Michelle D.↗