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NASA NTRS1984

Multiobjective optimization techniques for structural design

The multiobjective programming techniques are important in the design of complex structural systems whose quality depends generally on a number of different and often conflicting objective functions which cannot be combined into a single design objective. The applicability of multiobjective optimization techniques is studied with reference to simple design problems. Specifically, the parameter optimization of a cantilever beam with a tip mass and a three-degree-of-freedom vabration isolation system and the trajectory optimization of a cantilever beam are considered. The solutions of these multicriteria design problems are attempted by using global criterion, utility function, game theory, goal programming, goal attainment, bounded objective function, and lexicographic methods. It has been observed that the game theory approach required the maximum computational effort, but it yielded better optimum solutions with proper balance of the various objective functions in all the cases.

Rao, S. S.↗

NASA NTRS1990

Modelling of piezoelectric actuator dynamics for active structural control

The paper models the effects of dynamic coupling between a structure and an electrical network through the piezoelectric effect. The coupled equations of motion of an arbitrary elastic structure with piezoelectric elements and passive electronics are derived. State space models are developed for three important cases: direct voltage driven electrodes, direct charge driven electrodes, and an indirect drive case where the piezoelectric electrodes are connected to an arbitrary electrical circuit with embedded voltage and current sources. The equations are applied to the case of a cantilevered beam with surface mounted piezoceramics and indirect voltage and current drive. The theoretical derivations are validated experimentally on an actively controlled cantilevered beam test article with indirect voltage drive.

Hagood, Nesbitt W.↗

NASA NTRS2007

Displacement Theories for In-Flight Deformed Shape Predictions of Aerospace Structures

Displacement theories are developed for a variety of structures with the goal of providing real-time shape predictions for aerospace vehicles during flight. These theories are initially developed for a cantilever beam to predict the deformed shapes of the Helios flying wing. The main structural configuration of the Helios wing is a cantilever wing tubular spar subjected to bending, torsion, and combined bending and torsion loading. The displacement equations that are formulated are expressed in terms of strains measured at multiple sensing stations equally spaced on the surface of the wing spar. Displacement theories for other structures, such as tapered cantilever beams, two-point supported beams, wing boxes, and plates also are developed. The accuracy of the displacement theories is successfully validated by finite-element analysis and classical beam theory using input-strains generated by finite-element analysis. The displacement equations and associated strain-sensing system (such as fiber optic sensors) create a powerful means for in-flight deformation monitoring of aerospace structures. This method serves multiple purposes for structural shape sensing, loads monitoring, and structural health monitoring. Ultimately, the calculated displacement data can be visually displayed to the ground-based pilot or used as input to the control system to actively control the shape of structures during flight.

Ko, William L.↗

NASA NTRS1992

Vibration transmission through rolling element bearings. IV - Statistical energy analysis

A theoretical broadband coupling-loss factor is developed analytically for use in the statistical energy analysis (SEA) of a shaft-bearing-plate system. The procedure is based on the solution of the boundary-value problem at the plate-bearing interface and incorporates a bearing-stiffness matrix developed by the authors. Three examples are utilized to illustrate the SEA incorporating the coupling-loss factor including: (1) a shaft-bearing-plate system; (2) a plate-cantilevered beam; and (3) a circular-shaft-bearing plate. The coupling-loss factor in the case of the thin plate-cantilevered beam is found to be more accurate than that developed by Lyon and Eichler (1964). The coupling-loss factor is described for the bearing system and extended to describe the mean-square vibratory response of a rectangular plate. The proposed techniques are of interest to the study of vibration and noise in rotating machinery such as gearboxes.

Lim, T. C.↗

NASA NTRS1984

Extensions of the Ritz-Galerkin method for the forced, damped vibrations of structural elements

The Ritz-Galerkin methods were used to obtain approximate solutions for free undamped, vibration problems. It is demonstrated that these same methods may be used straightforwardly to analyze forced vibrations with damping without requiring the free vibration eigenfunctions. It was shown that the Galerkin method is an effective technique for these types of problems. The Ritz method has the advantage that it does not need to satisfy the force-type boundary conditions, which is particularly important for plates and shells. Proper functionals representing the forcing and damping terms were developed. Two types of damping--viscous and material (hysteretic) are discussed. Distributed and concentrated exciting forces are treated. Numerical results are obtained for cantilevered beams and rectangular plates. The rates of convergence of the solutions are shown. Approximate solutions from the present methods are compared with the exact solutions for the cantilever beam.

Leissa, A. W.↗

NASA NTRS1978

Simplified modeling for wind turbine modal analysis using NASTRAN

A detailed finite element model of the MOD-0 wind turbine tower was reduced to six beam elements (stick model). The method used to calculate the properties of the beam elements in the stick model was explained and the accuracy of the stick model in predicting natural frequencies and mode shapes was examined. Computer times were compared and several applications where the stick model was used are described. From results obtained from the MOD-0 tower it is concluded that a tower of this type can be modeled as a simple cantilever beam for modal analysis. However, this model should be limited to tower torsional modes and tower bending modes where the mode shape resembles a cantilever beam first bending mode shape.

Sullivan, T. L.↗

NASA NTRS1997

Validation of a Deterministic Vibroacoustic Response Prediction Model

This report documents the recently completed effort involving validation of a deterministic theory for the random vibration problem of predicting the response of launch pad structures in the low-frequency range (0 to 50 hertz). Use of the Statistical Energy Analysis (SEA) methods is not suitable in this range. Measurements of launch-induced acoustic loads and subsequent structural response were made on a cantilever beam structure placed in close proximity (200 feet) to the launch pad. Innovative ways of characterizing random, nonstationary, non-Gaussian acoustics are used for the development of a structure's excitation model. Extremely good correlation was obtained between analytically computed responses and those measured on the cantilever beam. Additional tests are recommended to bound the problem to account for variations in launch trajectory and inclination.

Caimi, Raoul E.↗

DOE OSTI2021

Transforming a Simple Structure Model to Represent a Complex Dynamic System with Unknown Boundary Restraints

Imposing a boundary condition on a structure can significantly alter its dynamic properties. However, sometimes the specifics of the new boundary conditions are not known. When the effects of a boundary condition are uncertain or there is not enough information, engineers need to excite the complex structure to obtain these modified properties. In order to experimentally obtain the new properties, engineers need multiple experiments and many outputs for interpolation in order to sufficiently represent the entire structure. In this study, the researchers attached a stinger to a cantilever beam, acting as a new transverse restraint of unknown properties. This paper presents a conversion expression that predicts the dynamic behavior of any point in the system with the new boundary condition. This expression relies only on one impact hammer experiment with one output and the model of the stinger-free cantilever beam, referred to as the simple structure. Researchers estimated the Transfer Function (TRF) of the beam and compared it with an experimentally measured TRF to validate the method. The mean absolute error of the estimated TRF compared to the experimental TRF is 1.99 dB. This demonstrates the use of the proposed method for estimating unmeasured TRFs in a system with an uncertain boundary condition using a single input, single output (SISO) test and a model of the simple structure.

42 ENGINEERING↗

NASA NTRS1991

Comparison of advanced reduced-basis methods for transient structural analysis

Two advanced reduced-basis methods for linear, transient structural analysis, the force-derivative method and the Lanczos method, are compared to two widely-used modal methods, the mode-displacement method and the mode-acceleration method. Comparisons are made for two linear example problems: a proportionally-damped cantilevered beam subject to a discrete tip load which varies linearly with time, and a discretely-damped multispan beam subject to a uniformly distributed load which varies as a quintic function of time. Results from the methods are compared in terms of the number of basis vectors required to obtain a desired level of accuracy and the associated computational times. The results are problem dependent, and it is shown that for the cantilevered beam problem, the mode-acceleration and force-derivative methods are the most efficient in terms of the number of basis vectors and computational time. The force-derivative method is shown to be the most effective method for solving the multispan beam problem with closely-spaced frequencies. In general, the force-derivative method is shown to produce an accurate solution using very few basis vectors and to require less computational time as compared to the other methods studied.

Mcgowan, David M.↗

NASA NTRS1991

Interlaminar fracture characterization: A current review

Interlaminar fracture characterization has been investigated for several years. Only now is it well enough understood for standardization organizations to attempt to write standard test methods. A review of the current philosophies in characterizing interlaminar fracture is presented. First, the mode 1, double cantilever beam test (DCB) for measuring G(sub 1c) and the end notched flexure (ENF) test for measuring G(sub 2c) are discussed. These tests have undergone the most extensive research throughout the years and are furthest towards standardization. In addition, the mode 2, end loaded split (ELS) specimen is discussed. Mixed mode fracture is also discussed and the recently developed mixed mode bending (MMB) test is detailed. Then, tests for evaluating mode 3 fracture toughness, including the split cantilever beam (SCB), are reviewed. Finally, the work done on interlaminar fracture characterization in fatigue is reviewed.

Martin, Roderick H.↗

DOE OSTI2023

An finite element analysis surrogate model with boundary oriented graph embedding approach for rapid design

Abstract In this work, we present a boundary oriented graph embedding (BOGE) approach for the graph neural network to assist in rapid design and digital prototyping. The cantilever beam problem has been solved as an example to validate its potential of providing physical field results and optimized designs using only 10 ms. Providing shortcuts for both boundary elements and local neighbor elements, the BOGE approach can embed unstructured mesh elements into the graph and performs an efficient regression on large-scale triangular-mesh-based finite element analysis (FEA) results, which cannot be realized by other machine-learning-based surrogate methods. It has the potential to serve as a surrogate model for other boundary value problems. Focusing on the cantilever beam problem, the BOGE approach with 3-layer DeepGCN model achieves the regression with mean square error (MSE) of 0.011 706 (2.41% mean absolute percentage error) for stress field prediction and 0.002 735 MSE (with 1.58% elements having error larger than 0.01) for topological optimization. The overall concept of the BOGE approach paves the way for a general and efficient deep-learning-based FEA simulator that will benefit both industry and Computer Aided Design (CAD) design-related areas.

42 ENGINEERING↗

NASA NTRS2006

Mode I Toughness Measurements of Core/Facesheet Bonds in Honeycomb Sandwich Structures

Composite sandwich structures will be used in many future applications in aerospace, marine and offshore industries due to the fact that the strength and stiffness to mass ratios surpass any other structural type. Sandwich structure also offers advantages over traditional stiffened panels such as ease of manufacturing and repair. During the last three decades, sandwich structure has been used extensively for secondary structure in aircraft (fuselage floors, rudders and radome structure). Sandwich structure is also used as primary structure in rotorcraft, the most common example being the trailing edge of rotor blades. As with other types of composite construction, sandwich structure exhibits several types of failure mode such as facesheet wrinkling, core crushing and sandwich buckling. Facesheet/core debonding has also been observed in the marine and aerospace industry. During this failure mode, peel stresses applied to an existing facesheet/core debond or an interface low in toughness, results in the facesheet being peeled from the core material, possibly leading to a significant loss in structural integrity of the sandwich panel. In an incident during a test on a liquid hydrogen fuel tank of the X-33 prototype vehicle, the outer graphite/epoxy facesheet and honeycomb core became debonded from the inner facesheet along significant areas, leading to failure of the tank. As a consequence of the accident; significant efforts were made to characterize the toughness of the facesheet/core bond. Currently, the only standardized method available for assessing the quality of the facesheet/core interface is the climbing drum peel test (ASTM D1781). During this test a sandwich beam is removed from a panel and the lip of one of the facesheets is attached to a drum, as shown in Fig. 1. The drum is then rotated along the sandwich beam, causing the facesheet to peel from the core. This method has two major drawbacks. First, it is not possible to obtain quantitative fracture data from the test and so the results can only be used in a qualitative manner. Second, only sandwich structure with thin facesheets can be tested (to facilitate wrapping of the facesheet around the climbing drum). In recognition of the need for a more quantitative facesheet/core fracture test, several workers have devised experimental techniques for characterizing the toughness of the facesheet/core interface. In all of these cases, the tests are designed to yield a mode I-dominated fracture toughness of the facesheet/core interface in a manner similar to that used to determine mode I fracture toughness of composite laminates. In the current work, a modified double cantilever beam is used to measure the mode I-dominated fracture toughness of the interface in a sandwich consisting of glass/phenolic honeycomb core reinforced with graphite epoxy facesheets. Two specimen configurations were tested as shown in Fig 2. The first configuration consisted of reinforcing the facesheets with aluminum blocks (Fig. 2a). In the second configuration unreinforced specimens were tested (Fig. 2b). Climbing drum peel tests were also conducted to compare the fracture behavior observed between this test and the modified double cantilever beam. This paper outlines the test procedures and data reduction strategies used to compute fracture toughness values from the tests. The effect of specimen reinforcement on fracture toughness of the facesheet/core interface is discussed.

Nettles, Alan T.↗

NASA NTRS1982

Structural fatigue test results for large wind turbine blade sections

In order to provide quantitative information on the operating life capabilities of wind turbine rotor blade concepts for root-end load transfer, a series of cantilever beam fatigue tests was conducted. Fatigue tests were conducted on a laminated wood blade with bonded steel studs, a low cost steel spar (utility pole) with a welded flange, a utility pole with additional root-end thickness provided by a swaged collar, fiberglass spars with both bonded and nonbonded fittings, and, finally, an aluminum blade with a bolted steel fitting (Lockheed Mod-0 blade). Photographs, data, and conclusions for each of these tests are presented. In addition, the aluminum blade test results are compared to field failure information; these results provide evidence that the cantilever beam type of fatigue test is a satisfactory method for obtaining qualitative data on blade life expectancy and for identifying structurally underdesigned areas (hot spots).

Faddoul, J. R.↗

NASA NTRS1987

Positive position feedback control for large space structures

A new technique for vibration suppression in large space structures is investigated in laboratory experiments on a thin cantilever beam. This technique, called Positive Position Feedback, makes use of generalized displacement measurements to accomplish vibration suppression. Several features of Positive Position Feedback make it attractive for the large space structure control environment: The realization of the controller is simple and straightforward. Global stability conditions can be derived which are independent of the dynamical characteristics of the structure being controlled, i.e., all spillover is stabilizing. The method cannot be destabilized by finite actuator dynamics, and the technique is amenable to a strain-based sensing approach. The experiments control the first six bending modes of a cantilever beam, and make use of piezoelectric materials for actuators and sensors, simulating a piezoelectric active-member. The modal damping ratios are increased by factors ranging from 2 to 130.

Fanson, J. L.↗

DOE OSTI2020

Fracture Strength Determination Methods for Ceramic Materials Applied to Uranium Dioxide

The Advanced Fuels Campaign is currently focusing on development of accident-tolerant fuels that possess a range of property modifications intended to improve fuel performance during accident and transient conditions as well as extend license limits to burnups beyond 62 MWd/kgU. Both of these drivers have identified understanding and mitigating fuel cracking as a key performance criterion. Small-scale cantilever beam testing has been identified as a plausible method by which to collect fracture data for UO 2 as a function of chemical and structural evolutions introduced either during fabrication or irradiation. While this method has been found to be capable of providing data that are in reasonable agreement with literature for unirradiated UO 2 , the inherently small sample volumes that can be sampled limit its ability to capture the statistical nature of mechanisms that govern the fracture of brittle ceramics. A biaxial flexure strength test was developed to be used for unirradiated UO 2 . This method is standard in the community, but no systems presently in use at national laboratories, universities, or private companies are available to be used for nuclear fuel materials. This report describes the operation and benchmarking of this system, which has been validated for a number of common oxides. Future work will extend this system to characterization of both doped UO 2 and other relevant microstructural modifications that can also be measured using small-scale cantilever beam testing. Comparison of datasets collected using both methods will allow the overall applicability of small-scale techniques to be assessed and provide confidence or bounds on their use for irradiated fuels.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2022

Infusible thermoplastic resin based sandwich structures for wind blade applications and the influence of scrim on facesheet to core interface debonding

Infusible thermoplastic Elium® family of resins from Arkema have garnered much attention in recent years as a possible replacement for thermoset resins in laminate and sandwich composite manufacturing for wind blade applications due to its ease of recyclability and the ability to utilize existing manufacturing processes without imposing complicated variations. However, physical and mechanical properties of the proposed Elium® based thermoplastic composites must be comparable to existing epoxy (thermoset) based composites using manufacturing processes relevant for large wind turbine blades. A 13-meter-long demonstration blade was manufactured for that purpose and sandwich samples were obtained from that project for a detailed study. This paper details three-point flexural properties of unidirectional E-glass fiber reinforced acrylic and epoxy based sandwich panels with identical balsa wood core materials. In addition, to evaluate the relative merit considering debond failure mode, the interfacial critical strain energy release rate, predominantly in mode-1, was compared via single cantilever beam testing. In sandwich composites constructed with balsa wood core material, resin uptake by the balsa core is traditionally impeded via the insertion of a scrim material at the facesheet to core interface. Results revealed that inclusion of scrim mesh layer at the facesheet to core interface reduced flexural properties and strain energy release rates in panels infused with acrylic resin but did not significantly reduce these properties in epoxy infused facesheets.

Engineering↗

NASA NTRS1975

Effect of axial load on mode shapes and frequencies of beams

An investigation of the effect of axial load on the natural frequencies and mode shapes of uniform beams and of a cantilevered beam with a concentrated mass at the tip is presented. Characteristic equations which yield the frequencies and mode shape functions for the various cases are given. The solutions to these equations are presented by a series of graphs so that frequency as a function of axial load can readily be determined. The effect of axial load on the mode shapes are also depicted by another series of graphs.

Shaker, F. J.↗

NASA NTRS1992

Properties of powder-impregnated graphite/PEKK

Poly Ether Ketone Ketone (PEKK) powders were prepregged on AS4 (12K), IM7 (12K), and G30-500 (12K) carbon fibers and consolidated into unidirectional laminates. The preferred formulation of PEKK for the dry powder process was identified. Mechanical test data on panels prepared via the powder process agreed well with flex, short beam shear, and double cantilever beam values obtained previously on melt-impregnated material. IM7/PEKK composites showed superior mechanical properties to AS4/PEKK and G30-500/PEKK composites. Transverse flexural strength and fiber/resin contact angle correlated well as measures of the fiber/matrix interfacial strength.

Bucher, R. A.↗