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All sourcesNASA NTRSDOE OSTI
NASA NTRS2015

Multi-Axis Independent Electromechanical Load Control for Docking System Actuation Development and Verification Using dSPACE

The development of highly complex and advanced actuation systems to meet customer demands has accelerated as the use of real-time testing technology expands into multiple markets at Moog. Systems developed for the autonomous docking of human rated spacecraft to the International Space Station (ISS), envelope multi-operational characteristics which place unique constraints on an actuation system. Real-time testing hardware has been used as a platform for incremental testing and development for the linear actuation system which controls initial capture and docking for vehicles visiting the ISS. This presentation will outline the role of dSPACE hardware as a platform for rapid control-algorithm prototyping as well as an Electromechanical Actuator (EMA) system dynamic loading simulator, both conducted at Moog to develop the safety critical Linear Actuator System (LAS) of the NASA Docking System (NDS).

Oesch, Christopher↗
NASA NTRSDate not supplied

Enhancements, Verification, and VMS Integration of VTOL Concept Vehicle Simulation Models

Advanced Rotorcraft Technology (ART) and the NASA Ames Aeromechanics branch have jointly developed FLIGHTLAB simulation models for Advanced Air Mobility (AAM) VTOL concept vehicles. The overarching purpose of the simulation model development is to establish a set of well defined reference vehicles for FLIGHTLAB users and the rotorcraft community. The ongoing research effort and enhancement of these AAM simulation models to fulfill the role of quality reference vehicles is this paper’s focus. The content of this paper expands on the established characteristics of these AAM models in three primary areas. First, enhancement of the lift+cruise and tiltwing models with elastic airframe properties is discussed. The process of setting up the elastic airframe model in FLIGHTLAB, as well as the impacts on flight characteristics are explained. The introduction of the elastic airframe modeling allows these models to be used in flight dynamics, loads, and vibration analysis of the configuration designs. Next, linear model generation from the enhanced simulation model is covered. Confirming the validity of the linearized models is of importance, as these linear models are utilized for flight control design and tuning for these experimental configurations. For the final focus, the progress towards implementation of these models into the NASA Ames Vertical Motion Simulator (VMS) is described. This task seeks to demonstrate the procedures of integrating a FLIGHTLAB flight simulation in the VMS environment, test fully integrated simulation with communication between flight dynamics, control, and propulsion models, and explore the essential aspects of simulation model integration in a full flight simulator environment. This includes I/O definition, initialization, trim, flying, etc. By expanding the capabilities of the AAM simulation models, they continue to develop as valuable and approachable modeling references.

VMS↗
NASA NTRS2015

2015 Occupant Protection Standing Review Panel

The 2015 Occupant Protection (OP) Risk Standing Review Panel (from here on referred to as the SRP) participated in a WebEx/teleconference with members of the Space Human Factors and Habitability (SHFH) Element, representatives from the Human Research Program (HRP), NASA Headquarters, and NASA Research and Education Support Services on November 3, 2015 (list of participants is in Section VII of this report). The SRP reviewed the updated research plans for the Risk of Injury from Dynamic Loads (OP Risk). The SRP agrees that the Gaps are relevant and appropriate to mitigate the injury risk. All the appropriate and relevant Tasks have been identified to fill the Gaps. Depending upon the findings, additional tasks may need to be identified or modified. Excellent progress has been made since the 2014 SRP meeting. Publications in peer-reviewed journals validate the scientific merit of the research findings. As detailed in this report, the SRP has specific comments, guidance, and information in the following areas: human finite element modeling, human vs. surrogate dynamic responses, chest injury risk curves, matched pair testing of Test device for Human Occupant Restraint (THOR) and Hybrid III, and disc herniation risk analysis.

Steinberg, Susan↗
NASA NTRS1978

Continuum models for beam-like and plate-like lattice structures

A simple, rational approach is presented for developing continuum models for large repetitive beam-like and plate-like lattices with arbitrary configurations subjected to static, thermal and dynamic loadings. The continuum models for these structures are shear flexible beams and plates. They account for local effects in the repeating element of the actual structure and are characterized by their thermoelastic strain and kinetic energies from which the equations of motion and constitutive relations can be derived. The procedure for developing the expressions for thermoelastic strain and kinetic energies of the continuum involves introducing basic assumptions regarding the variation of the temperature, displacement and strain components in one or two directions (for plate-like and beam-like lattices) and obtaining effective thermoelastic and dynamic coefficients of the continuum in terms of material properties and geometry of the original lattice structure. The high accuracy of the continuum models developed is demonstrated by means of numerical examples.

Noor, A. K.↗
NASA NTRS1995

Algorithms for parallel flow solvers on message passing architectures

The purpose of this project has been to identify and test suitable technologies for implementation of fluid flow solvers -- possibly coupled with structures and heat equation solvers -- on MIMD parallel computers. In the course of this investigation much attention has been paid to efficient domain decomposition strategies for ADI-type algorithms. Multi-partitioning derives its efficiency from the assignment of several blocks of grid points to each processor in the parallel computer. A coarse-grain parallelism is obtained, and a near-perfect load balance results. In uni-partitioning every processor receives responsibility for exactly one block of grid points instead of several. This necessitates fine-grain pipelined program execution in order to obtain a reasonable load balance. Although fine-grain parallelism is less desirable on many systems, especially high-latency networks of workstations, uni-partition methods are still in wide use in production codes for flow problems. Consequently, it remains important to achieve good efficiency with this technique that has essentially been superseded by multi-partitioning for parallel ADI-type algorithms. Another reason for the concentration on improving the performance of pipeline methods is their applicability in other types of flow solver kernels with stronger implied data dependence. Analytical expressions can be derived for the size of the dynamic load imbalance incurred in traditional pipelines. From these it can be determined what is the optimal first-processor retardation that leads to the shortest total completion time for the pipeline process. Theoretical predictions of pipeline performance with and without optimization match experimental observations on the iPSC/860 very well. Analysis of pipeline performance also highlights the effect of uncareful grid partitioning in flow solvers that employ pipeline algorithms. If grid blocks at boundaries are not at least as large in the wall-normal direction as those immediately adjacent to them, then the first processor in the pipeline will receive a computational load that is less than that of subsequent processors, magnifying the pipeline slowdown effect. Extra compensation is needed for grid boundary effects, even if all grid blocks are equally sized.

Vanderwijngaart, Rob F.↗
DOE OSTI2023

In situ measurement of damage evolution in shocked magnesium as a function of microstructure

Accurate modeling and prediction of damage induced by dynamic loading in materials have long proved to be a difficult task. Examination of postmortem recovered samples cannot capture the time-dependent evolution of void nucleation and growth, and attempts at analytical models are hindered by the necessity to make simplifying assumptions, because of the lack of high-resolution, in situ, time-resolved experimental data. We use absorption contrast imaging to directly image the time evolution of spall damage in metals at ~1.6-μm spatial resolution. We observe a dependence of void distribution and size on time and microstructure. The insights gained from these data can be used to validate and improve dynamic damage prediction models, which have the potential to lead to the design of superior damage-resistant materials.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Understanding Microstructural Effects on Dynamic Performance Towards the Development of Shock Metamaterials

With the recent advances in additive manufacturing (AM), long-range periodic lattice assemblies are being developed for vibration and shock mitigation components in aerospace and military applications with unique geometric and topological structures. There has been extensive work in understanding the static properties associated with varying topology of these lattice architectures, but there is almost no understanding of microstructural affects in such structures under high-strain rate dynamic loading conditions. Here we report the shock behavior of lattices with varying intrinsic grain structures achieved by post process annealing. High resolution 316L stainless steel lattices were 3D printed by a laser-powder bed fusion machine and characterized by computed tomography. Subsequent annealing resulted in stress-relieved and recrystallized lattices. Overall the lattices had strong cubic texture aligning with the x-, y- and z-directions of the build with a preference outside the build direction (z). The recrystallized sample had more equiaxed polygonal grains and a layer of BCC ferrite at the surface of the structure approximately 1 grain thick. Upon dynamic compression the as-deposited lattice showed steady compaction behavior while the heat-treated lattices exhibit negative velocity behavior indicative of failure. We attribute this to the stiffer BCC ferrite in the annealed lattices becoming damaged and fragmenting during compression.

36 MATERIALS SCIENCE↗
NASA NTRS2002

Turbomachinery Course

In this viewgraph presentation, information and diagrams are provided on rocket engine turbopumps. These turbomachines are highly complex and have several unique features: (1) They are generally very high power density machines; (2) They experience high fluid dynamic loads; (3) They are exposed to severe thermal shocks in terms of rapid starts and stops and extremely high heat transfer coefficients; (4) They have stringent suction performance requirements to minimize tank weight; (5) Their working fluids significantly impact the design: oxidizers are generally explosive, they afford almost no lubrication for bearings and seals, some fuels can degrade material properties, cryogenics result in severe thermal gradients; (6) Their life requirements are short relative to other turbomachines in that there are hundreds of cycles and a few hours of operation for reusable systems. The design of rocket engine turbomachines is a systems engineering challenge because multiple engineering disciplines must be integrated to deal with issues pertaining to stress, structural dynamics, hydrodynamics, aerodynamics, thermodynamics, and materials and process selection.

Stinson, Henry↗
NASA NTRS2011

NASA Occupant Protection Standards Development

Current National Aeronautics and Space Administration (NASA) occupant protection standards and requirements are based on extrapolations of biodynamic models, which were based on human tests performed under pre-Space Shuttle human flight programs where the occupants were in different suit and seat configurations than is expected for the Multi Purpose Crew Vehicle (MPCV) and Commercial Crew programs. As a result, there is limited statistical validity to the occupant protection standards. Furthermore, the current standards and requirements have not been validated in relevant spaceflight suit, seat configurations or loading conditions. The objectives of this study were to develop new standards and requirements for occupant protection and rigorously validate these new standards with sub-injurious human testing. To accomplish these objectives we began by determining which critical injuries NASA would like to protect for. We then defined the anthropomorphic test device (ATD) and the associated injury metrics of interest. Finally, we conducted a literature review of available data for the Test Device for Human Occupant Restraint New Technology (THOR-NT) ATD to determine injury assessment reference values (IARV) to serve as a baseline for further development. To better understand NASA s environment, we propose conducting sub-injurious human testing in spaceflight seat and suit configurations with spaceflight dynamic loads, with a sufficiently high number of subjects to validate no injury during nominal landing loads. In addition to validate nominal loads, the THOR-NT ATD will be tested in the same conditions as the human volunteers, allowing correlation between human and ATD responses covering the Orion nominal landing environment and commercial vehicle expected nominal environments. All testing will be conducted without the suit and with the suit to ascertain the contribution of the suit to human and ATD responses. In addition to the testing campaign proposed, additional data analysis is proposed to mine existing human injury and response data from other sources, including military volunteer testing, automotive Crash Injury Research Engineering Network (CIREN), and IndyCar impact and injury data. These data sources can allow a better extrapolation of the ATD responses to off-nominal conditions above the nominal range that can safely be tested. These elements will be used to develop injury risk functions for each of the injury metrics measured from the ATD. These risk functions would serve as the basis for the NASA standards. Finally, we propose defining standard test methodology for evaluating future spacecraft designs against the IARVs, including developing a star-rating system to allow crew safety comparisons between vehicles.

Somers, Jeffrey T.↗
DOE OSTI2025

Multi-objective automatic discovery of optimized metamaterials for varying velocity impact protection

Mechanical metamaterials have demonstrated exceptional impact performance while remaining lightweight. Impact resistance has traditionally been investigated using quasi-static simulations, often with the assumption that performance will translate to high-velocity impact scenarios. However, critical crash protection parameters—such as peak stress and absorbed energy—are highly sensitive to impact velocity, leading to inconsistent performance under dynamic loading. To address this, we introduce a strain-rate-aware, active deep learning framework that enables multi-objective optimization of impact protection metrics across a wide range of impact velocities. Our framework captures the strain-rate sensitivity of architected lattices by learning to control spatial gradation in cellular metamaterials, resulting in over 200 % enhancement in impact protection relative to state-of-the-art designs such as Voronoi and re-entrant lattices. We demonstrate its practical utility by designing next-generation lattice structures for automotive bumper systems that satisfy multiple, velocity-specific safety criteria—capabilities beyond those of conventional designs. More than just a predictive tool, this framework marks the first step towards enabling adaptable impact-resistant structures across dynamic regimes.

Deep learning↗
DOE OSTI2023

Non-linear Wire Rope Isolator Model to Enhance Transportation Simulation of Fragile Equipment

Abstract Introduction Wire rope isolators are often used as means of vibration isolation for the transportation of fragile machine equipment. When deployed as suspension systems in a transportation scenario, a simple spring–damper model is often used to predict the dynamic loads that act on the structure being transported. However, this simple model has proved to be too simplistic to be used in the development of an accurate numerical model that can predict the vibration levels experienced by the inner components of fragile equipment during its transportation. This paper describes the experimental tests conducted on a wire rope isolator used for the transportation of the prototype SSR1 cryomodule. Materials and methods A hysteretic Bouc–Wen model has been used to analytically describe the force–deformation relationship of the wire rope isolators. The developed model of the isolator has been implemented in a larger model to simulate the actual transportation of the prototype SSR1 cryomodule, a section of the new PIP-II linear accelerator under construction at Fermilab. A series of multibody dynamic simulations with rigid and flexible components was used to numerically determine the acceleration of some critical components. Results and conclusions An actual experimental transportation was simulated using two numerical models: the developed Bouc–Wen model and a conventional spring–damper model. It is shown how the Bouc–Wen formulation of the isolator characteristics drastically improves the correspondence between experimental and simulated results if compared to a spring–damper model, especially in the range of 0–30 Hz which is the most critical for transportation problems.

42 ENGINEERING↗
NASA NTRS1995

An active magnetic bearing with high T(sub c) superconducting coils and ferromagnetic cores

A proof-of-feasibility demonstration showed that high-T(sub c) superconductor (HTS) coils can be used in a high-load, active magnetic bearing in LN2. A homopolar radial bearing with commercially wound HTS (Bi 2223) bias and control coils produced over 890 N (200 lb) radial load capacity (measured non-rotatings) and supported a shaft to 14,000 rpm. The goal was to show that HTS coils can operate stably with ferromagnetic cores in a feedback controlled system at a current density similar to that for Cu in LN2. The bias coil, wound with non-twisted, multifilament HTS conductor, dissipated negligible power for its direct current. The control coils, wound with monofilament HTS sheathed in Ag, dissipated negligible power for direct current. AC losses increased rapidly with frequency and quadratically with AC amplitude. Above about 2 Hz, the effective resistance of the control coils exceeds that of the silver which is in electrical parallel with the oxide superconductor. These results show that twisted multifilament conductor is not needed for stable levitation but may be desired to reduce control power for sizable dynamic loads.

Brown, G. V.↗
NASA NTRS2014

How Well Does the Latest Anthropomorphic Test Device Mimic Human Impact Responses?

One of the goals of the NASA Occupant Protection Group is to understand the human tolerance to dynamic loading. This knowledge has to come through indirect approaches such as existing human response databases, anthropometric test devices (ATD), animal testing, post‐mortem human subjects, and models. This study investigated the biofidelity of the National Highway Traffic Safety Administration's ATD named the THOR (test device for human occupant restraint). If THOR responds comparably to humans, then it could potentially be used as a human surrogate to help validate space vehicle requirements for occupant protection. The THOR responses to frontal and spinal impacts (ranging from 8 to 12 G with rise times of 40, 70, and 100 ms) were measured and compared to human volunteer responses (95 trials in frontal and 58 in spinal) previously collected by the U. S. Air Force on the same horizontal impact accelerator. The impact acceleration profiles tested are within the expected range of multi‐purpose crew vehicle (MPCV) landing dynamics. A correlation score was calculated for each THOR to human comparison using CORA (CORrelation and Analysis) software. A two‐parameter beta distribution model fit was obtained for each dependent variable using maximum likelihood estimation. For frontal impacts, the THOR head x‐acceleration peak response correlated with the human response at 8 and 10‐G 100 ms but not 10‐G 70 ms. The phase lagged the human response. Head z‐acceleration was not correlated. Chest x‐acceleration was in phase, had a higher peak response, and was well correlated with lighter subjects (Cora = 0.8 for 46 kg vs. Cora = 0.4 for 126 kg). Head x‐displacement had a leading phase. Several subjects responded with the same peak displacement but the mean of the group was lower. The shoulder x‐displacement was in phase but had higher peaks than the human response. For spinal impacts, the THOR head x‐acceleration was not well correlated. Head and chest z‐acceleration was in phase but had a higher peak response. Chest z‐acceleration was highly correlated with heavier subjects at lower G pulses (Cora = 0.86 for 125 kg at 8 G). The human response was variable in shoulder z‐displacement but the THOR was in phase and was comparable to the mean peak response. Head xand z‐displacement was in phase but had higher peaks. Seat pan forces were well correlated, were in phase, but had a larger peak response than most subjects. The THOR does not respond to frontal and spinal impacts exactly the same way that a human does. Some responses are well matched and others are not. Understanding the strengths and weaknesses of this ATD is an important first step in determining its usefulness in occupant protection at NASA

Newby, N.↗
NASA NTRS2014

How Well Does the Latest Anthropomorphic Test Device Mimic Human Impact Responses?

One of the goals of the NASA Occupant Protection Group is to understand the human tolerance to dynamic loading. This knowledge has to come through indirect approaches such as existing human response databases, anthropometric test devices (ATD), animal testing, post-­‐mortem human subjects, and models. This study investigated the biofidelity of the National Highway Traffic Safety Administration's ATD named the THOR (test device for human occupant restraint). If THOR responds comparably to humans, then it could potentially be used as a human surrogate to help validate space vehicle requirements for occupant protection. The THOR responses to frontal and spinal impacts (ranging from 8 to 12 G with rise times of 40, 70, and 100 ms) were measured and compared to human volunteer responses (95 trials in frontal and 58 in spinal) previously collected by the U. S. Air Force on the same horizontal impact accelerator. The impact acceleration profiles tested are within the expected range of multi-­‐purpose crew vehicle (MPCV) landing dynamics. A correlation score was calculated for each THOR to human comparison using CORA (CORrelation and Analysis) software. A two-­‐parameter beta distribution model fit was obtained for each dependent variable using maximum likelihood estimation. For frontal impacts, the THOR head x-­‐acceleration peak response correlated with the human response at 8 and 10-­‐G 100 ms but not 10-­‐G 70 ms. The phase lagged the human response. Head z-­‐acceleration was not correlated. Chest x-­‐acceleration was in phase, had a higher peak response, and was well correlated with lighter subjects (Cora = 0.8 for 46 kg vs. Cora = 0.4 for 126 kg). Head x-­‐displacement had a leading phase. Several subjects responded with the same peak displacement but the mean of the group was lower. The shoulder x-­‐displacement was in phase but had higher peaks than the human response. For spinal impacts, the THOR head x-­‐acceleration was not well correlated. Head and chest z-­‐acceleration was in phase but had a higher peak response. Chest z-­‐acceleration was highly correlated with heavier subjects at lower G pulses (Cora = 0.86 for 125 kg at 8 G). The human response was variable in shoulder z-­‐displacement but the THOR was in phase and was comparable to the mean peak response. Head x-­‐ and z-­‐displacement was in phase but had higher peaks. Seat pan forces were well correlated, were in phase, but had a larger peak response than most subjects. The THOR does not respond to frontal and spinal impacts exactly the same way that a human does. Some responses are well matched and others are not. Understanding the strengths and weaknesses of this ATD is an important first step in determining its usefulness in occupant protection at NASA

Newby, Nate↗
NASA NTRS1987

Expansion of epicyclic gear dynamic analysis program

The multiple mesh/single stage dynamics program is a gear tooth analysis program which determines detailed geometry, dynamic loads, stresses, and surface damage factors. The program can analyze a variety of both epicyclic and single mesh systems with spur or helical gear teeth including internal, external, and buttress tooth forms. The modifications refine the options for the flexible carrier and flexible ring gear rim and adds three options: a floating Sun gear option; a natural frequency option; and a finite element compliance formulation for helical gear teeth. The option for a floating Sun incorporates two additional degrees of freedom at the Sun center. The natural frequency option evaluates the frequencies of planetary, star, or differential systems as well as the effect of additional springs at the Sun center and those due to a flexible carrier and/or ring gear rim. The helical tooth pair finite element calculated compliance is obtained from an automated element breakup of the helical teeth and then is used with the basic gear dynamic solution and stress postprocessing routines. The flexible carrier or ring gear rim option for planetary and star spur gear systems allows the output torque per carrier and ring gear rim segment to vary based on the dynamic response of the entire system, while the total output torque remains constant.

Boyd, Linda Smith↗
NASA NTRSDate not supplied

Application of the MAT 213 Composite Impact Model to NASA Problems of Interest

A material model has been developed which incorporates several key capabilities which have been identified as lacking in currently available composite impact models. The material model utilizes experimentally based tabulated input to define the evolution of plasticity and damage as opposed to specifying discrete input parameters (such as modulus and strength). The material model has been implemented into LS-DYNA® as MAT 213. The model can simulate the nonlinear deformation, damage and failure that takes place in a composite under dynamic loading conditions. The deformation model utilizes an orthotropic plasticity formulation. For the damage model, the nonlinear unloading response that is observed prior to the point where the peak stress is reached can be simulated, as well as the stress degradation response that occurs after the peak stress is reached. A variety of failure models, including a generalized tabulated failure model which facilitates the utilization of general failure surfaces, have been implemented into MAT 213. Recent studies at NASA have concentrated on using MAT 213 to analyze both the impact and crush response of a variety of laminated and textile architectures. Several of these studies will be discussed in the presented paper. For example, a woven carbon/Kevlar composite is currently being examined for use in an energy absorber system for rotorcraft structures. MAT 213 analyses have been conducted to examine the ability of the model to accurately simulate the dynamic crush response of this material. Studies are also being conducted to examine the ability of MAT 213 to simulate the ballistic impact response of representative laminated and woven thermoplastic and thermoset matrix composites. NASA efforts are also concentrated on developing methods and processes for improving characterization methods and developing “best practices” for using MAT 213, a summary of which will be discussed in the paper.

Polymer Matrix Composites↗
NASA NTRS2009

Using Maximal Isometric Force to Determine the Optimal Load for Measuring Dynamic Muscle Power

Maximal power output occurs when subjects perform ballistic exercises using loads of ~30-50% of one-repetition maximum (1-RM). However, performing 1-RM testing prior to power measurement requires considerable time, especially when testing involves multiple exercises. Maximal isometric force (MIF), which requires substantially less time to measure than 1-RM, might be an acceptable alternative for determining the optimal load for power testing. PURPOSE: To determine the optimal load based on MIF for maximizing dynamic power output during leg press and bench press exercises. METHODS: Twenty healthy volunteers (12 men and 8 women; mean +/- SD age: 31+/-6 y; body mass: 72 +/- 15 kg) performed isometric leg press and bench press movements, during which MIF was measured using force plates. Subsequently, subjects performed ballistic leg press and bench press exercises using loads corresponding to 20%, 30%, 40%, 50%, and 60% of MIF presented in randomized order. Maximal instantaneous power was calculated during the ballistic exercise tests using force plates and position transducers. Repeated-measures ANOVA and Fisher LSD post hoc tests were used to determine the load(s) that elicited maximal power output. RESULTS: For the leg press power test, six subjects were unable to be tested at 20% and 30% MIF because these loads were less than the lightest possible load (i.e., the weight of the unloaded leg press sled assembly [31.4 kg]). For the bench press power test, five subjects were unable to be tested at 20% MIF because these loads were less than the weight of the unloaded aluminum bar (i.e., 11.4 kg). Therefore, these loads were excluded from analysis. A trend (p = 0.07) for a main effect of load existed for the leg press exercise, indicating that the 40% MIF load tended to elicit greater power output than the 60% MIF load (effect size = 0.38). A significant (p . 0.05) main effect of load existed for the bench press exercise; post hoc analysis indicated that the effect of load on power output was: 30% > 40% > 50% = 60%. CONCLUSION: Loads of 40% and 30% of MIF elicit maximal power output during dynamic leg presses and bench presses, respectively. These findings are similar to those obtained when loading is based on 1-RM.

Spiering, Barry A.↗
NASA NTRS1966

Matrix methods and automation in structural engineering

The partial differential equations of motion of shell structures subject to arbitrary loads may be extremely difficult or even impossible to solve. Since the digital computer is now an available tool for the structural engineer, current research has been directed toward methods which involve matrix formulation of large systems of algebraic equations and matrix solutions for discrete elements rather than the solution of the partial differential equations. These methods require rapid and accurate computer solutions. Recognizing the accuracy problems inherent in working with large matrices, a comprehensive survey of available computer programs was performed for large matrix inversion and for eigenvalue and eigenvector solutions under a Research Grant from the National Aeronautics and Space Administration and the techniques are developed in this paper for using these programs most efficiently for structural applications. The contents of the paper include: automation of matrix compilation, methods of very large matrix inversion and solution of simultaneous equation, and techniques for finding eigenvalues and vectors. In addition, a finite element stiffness matrix approach developed at the Denver Research Institute for both plates and shells subject to arbitrary dynamic loads is described as it was instrumented with complete automation on the digital computer.

Anita S West↗