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NASA NTRS2010

Frequencies and Flutter Speed Estimation for Damaged Aircraft Wing Using Scaled Equivalent Plate Analysis

Equivalent plate analysis is often used to replace the computationally expensive finite element analysis in initial design stages or in conceptual design of aircraft wing structures. The equivalent plate model can also be used to design a wind tunnel model to match the stiffness characteristics of the wing box of a full-scale aircraft wing model while satisfying strength-based requirements An equivalent plate analysis technique is presented to predict the static and dynamic response of an aircraft wing with or without damage. First, a geometric scale factor and a dynamic pressure scale factor are defined to relate the stiffness, load and deformation of the equivalent plate to the aircraft wing. A procedure using an optimization technique is presented to create scaled equivalent plate models from the full scale aircraft wing using geometric and dynamic pressure scale factors. The scaled models are constructed by matching the stiffness of the scaled equivalent plate with the scaled aircraft wing stiffness. It is demonstrated that the scaled equivalent plate model can be used to predict the deformation of the aircraft wing accurately. Once the full equivalent plate geometry is obtained, any other scaled equivalent plate geometry can be obtained using the geometric scale factor. Next, an average frequency scale factor is defined as the average ratio of the frequencies of the aircraft wing to the frequencies of the full-scaled equivalent plate. The average frequency scale factor combined with the geometric scale factor is used to predict the frequency response of the aircraft wing from the scaled equivalent plate analysis. A procedure is outlined to estimate the frequency response and the flutter speed of an aircraft wing from the equivalent plate analysis using the frequency scale factor and geometric scale factor. The equivalent plate analysis is demonstrated using an aircraft wing without damage and another with damage. Both of the problems show that the scaled equivalent plate analysis can be successfully used to predict the frequencies and flutter speed of a typical aircraft wing.

Krishnamurthy, Thiagarajan↗

NASA NTRS2013

Hybrid Wing-Body Pressurized Fuselage and Bulkhead, Design and Optimization

The structural weight reduction of a pressurized Hybrid Wing-Body (HWB) fuselage is a serious challenge. Hence, research and development are presently being continued at NASA under the Environmentally Responsible Aviation (ERA) and Subsonic Fixed Wing (SFW) projects in collaboration with the Boeing Company, Huntington Beach and Air Force Research Laboratory (AFRL). In this paper, a structural analysis of the HWB fuselage and bulkhead panels is presented, with the objectives of design improvement and structural weight reduction. First, orthotropic plate theories for sizing, and equivalent plate analysis with appropriate simplification are considered. Then parametric finite-element analysis of a fuselage section and bulkhead are conducted using advanced stitched composite structural concepts, which are presently being developed at Boeing for pressurized HWB flight vehicles. With this advanced stiffened-shell design, structural weights are computed and compared to the thick sandwich, vaulted-ribbed-shell, and multi-bubble stiffened-shell structural concepts that had been studied previously. The analytical and numerical results are discussed to assess the overall weight/strength advantages.

Mukhopadhyay, Vivek↗

NASA NTRS2014

NASA Engineering and Safety Center Technical Bulletin No. 14-03: COPV Mechanical Model Validation

Global and local deformation measurements should be incorporated into the composite overwrapped pressure vessel (COPV) design and analysis process to allow correlation of these measurements with finite element analysis (FEA) models. This correlation improves understanding of liner, liner/overwrap interface, and composite deformation response in COPVs. The improved accuracy reduces error in subsequent analyses, such as fracture, fatigue, and stress rupture that are critical for COPV qualification.

Composite Overwrap Pressure Vehicle↗

NASA NTRS2019

Benchmarking Mixed Mode Failure in Progressive Damage and Failure Analysis Methods

The verification and validation of progressive-damage-analysis finite element methods are difficult but critical tasks to undertake during their development. Verification exercises assess whether a predictive analysis tool produces results that are consistent with the fundamental concepts and assumptions of the tool under evaluation. Ideally, closed-form analytical solutions can be derived for which method verification results can be compared. Problems selected for computational tool verification are often simple and isolate individual features of the tool. In the case of progressive damage finite element methods, verifications should be performed to evaluate the ability of the model to predict the initiation of damage and its growth through the finite element mesh under a variety of conditions. Mabson et al. proposed a test case of a unidirectional, fiber-reinforced plate with a center crack subjected to tensile loads to evaluate matrix crack propagation predictions. The problem was modeled using the Abaqus Hashin continuum damage mechanics (CDM) model for fiber-reinforced composites. Different combinations of matrix strengths and element sizes were used in the simulations, and the results were compared to a closed-form solution based on linear elastic fracture mechanics (LEFM). It was determined that the Abaqus CDM model could predict the LEFM solution of Mode I cracks only when the finite element mesh density met specific requirements based on the material properties. This paper presents closed-form LEFM solutions for a center notch mixed mode (CNMM) verification problem. Parametric finite element analyses were developed using progressive damage analysis methods of both the Discrete Damage Mechanics (DDM) and CDM classes. The progressive damage analysis methods applied in the analyses of the CNMM problem include CompDam and the Floating Node Method. Analyses were conducted with various mode mixities and element sizes to verify that the damage models were working as intended and to identify any limits of applicability.

Leone, Frank↗

NASA NTRS1991

Stability analysis of bridged cracks in brittle matrix composites

The bridging of matrix cracks by fibers is an important toughening mechanism in fiber reinforced brittle matrix composites. This paper presents the results of a nonlinear finite element analysis of the Mode-I propagation of a bridged matrix crack in a finite size specimen. The composite is modeled as an orthotropic continuum and the bridging due to the fibers is modeled as a distribution of tractions which resist crack opening. A critical stress intensity factor criterion is employed for matrix crack propagation while a critical crack opening condition is used for fiber failure. The structural response of the specimen (load-deflection curves) as well as the stress intensity factor of the propagating crack are calculated for various constituent properties and specimen configurations for both tensile and bending loading. By controlling the length of the bridged crack results are obtained which highlight the transition from stable to unstable behavior of the propagating crack.

Ballarini, Roberto↗

NASA NTRS1993

Geometrically nonlinear design sensitivity analysis on parallel-vector high-performance computers

Parallel-vector solution strategies for generation and assembly of element matrices, solution of the resulted system of linear equations, calculations of the unbalanced loads, displacements, stresses, and design sensitivity analysis (DSA) are all incorporated into the Newton Raphson (NR) procedure for nonlinear finite element analysis and DSA. Numerical results are included to show the performance of the proposed method for structural analysis and DSA in a parallel-vector computer environment.

Baddourah, Majdi A.↗

NASA NTRS2008

Modeling and Optimization for Morphing Wing Concept Generation II: Morphing Wing Modeling and Structural Sizing Techniques - Part 1

This report documents a series of investigations to develop an approach for structural sizing of various morphing wing concepts. For the purposes of this report, a morphing wing is one whose planform can make significant shape changes in flight - increasing wing area by 50% or more from the lowest possible area, changing sweep 30 or more, and / or increasing aspect ratio by as much as 200% from the lowest possible value. These significant changes in geometry mean that the underlying load-bearing structure changes geometry. While most finite element analysis packages provide some sort of structural optimization capability, these codes are not amenable to making significant changes in the stiffness matrix to reflect the large morphing wing planform changes. The investigations presented here use a finite element code capable of aeroelastic analysis in three different optimization approaches -a "simultaneous analysis" approach, a "sequential" approach, and an "aggregate" approach.

Skillen, Michael D.↗

NASA NTRS2017

Non-Linear Analysis of the NASA Super Pressure Balloons: Whole Flight Simulations

Tensys have a long-established background in the shape generation and load analysis of architectural stressed membrane structures. Founded upon their inTENS finite element analysis suite, these activities have broadened to encompass 'lighter than air' structures such as aerostats, airships, hybrid air vehicles and stratospheric balloons. Tensys have acted as consultants to the NASA Super Pressure Balloon (SPB) Program since 2004. Previous papers have focussed upon the application of inTENS to the overall structural and stability analysis of pumpkin type balloons as used in the SPB Program. Particular emphasis has been placed upon the ability to study both stress and stability at all stages of a flight. As the program has developed, increasing modelling fidelity has been introduced as design refinement has moved emphasis from the overall shape to the performance of individual details. Examples include the introduction of a contact capability into inTENS to better represent the separate cap layer of film. Localised investigations have considered the consequence of local geometric anomalies introduced during fabrication and the effects of debonding of the PBO tendon within its sleeve. Analysis to date has used a material model for the polyethylene shell film developed by Dr Rand of Winzen Engineering, supported by a program of fine resolution material tests at the Balloon Research and Development Laboratory (BRDL) at the GSFC Wallops Island Facility. Based upon work first reported by Schapery, this model has been incorporated into so-called 'snapshot' analyses within inTENS. For a given elapsed time point and temperature distribution, non-linear material properties are iteratively updated for the current stress state in each individual element until changes in those material properties are insignificant. This process has to be iterative as the film stresses and material properties are interdependent. Attempts to derive a time-stepping incremental viscoelastic capability using the Schapery Rand model encountered problems when dealing with the varying temperatures associated with balloon deployment, pressurisation and diurnal behaviour. An alternative approach has been developed by Pellegrino et al at Caltech, again with support from the NASA Balloon Program Office. This is a large strain non-linear viscoelastic model that includes film out-of-plane mechanical and thermal effects. Working from a unified base, this model can be utilised for time-stepping analyses in both a modulus or compliance mode, or a combination of both. This new capability is intended to enhance the current NASA balloon design process. This paper presents the implementation of the Caltech model into a specialist finite element suite, inTENS and its application to whole flight simulations.

Wakefield, David↗

NASA NTRS1977

Analysis of shear test method for composite laminates

An elastic plane stress finite element analysis of the stress distributions in four flat test specimens for in-plane shear response of composite materials subjected to mechanical or thermal loads is presented. The shear test specimens investigated include: slotted coupon, cross beam, losipescu, and rail shear. Results are presented in the form of normalized shear contour plots for all three in-plane stess components. It is shown that the cross beam, losipescu, and rail shear specimens have stress distributions which are more than adequate for determining linear shear behavior of composite materials. Laminate properties, core effects, and fixture configurations are among the factors which were found to influence the stress distributions.

Bergner, H. W., Jr.↗

NASA NTRS1986

Thermal-capillary analysis of small-scale floating zones Steady-state calculations

Galerkin finite element analysis of a thermal-capillary model of the floating zone crystal growth process is used to predict the dependence of molten zone shape on operating conditions for the growth of small silicon boules. The model accounts for conduction-dominated heat transport in the melt, feed rod and growing crystal and for radiation between these phases, the ambient and a heater. Surface tension acting on the shape of the melt/gas meniscus counteracts gravity to set the shape of the molten zone. The maximum diameter of the growing crystal is set by the dewetting of the melt from the feed rod when the crystal radius is large. Calculations with small Bond number show the increased zone lengths possible for growth in a microgravity environment. The sensitivity of the method to the shape and intensity of the applied heating distribution is demonstrated. The calculations are compared with experimental observations.

Duranceau, J. L.↗

NASA NTRS1992

Application of analysis techniques for low frequency interior noise and vibration of commercial aircraft

Finite element analysis (FEA), statistical energy analysis (SEA), and a power flow method (computer program PAIN) were used to assess low frequency interior noise associated with advanced propeller installations. FEA and SEA models were used to predict cabin noise and vibration and evaluate suppression concepts for structure-borne noise associated with the shaft rotational frequency and harmonics (less than 100 Hz). SEA and PAIN models were used to predict cabin noise and vibration and evaluate suppression concepts for airborne noise associated with engine radiated propeller tones. Both aft-mounted and wing-mounted propeller configurations were evaluated. Ground vibration test data from a 727 airplane modified to accept a propeller engine were used to compare with predictions for the aft-mounted propeller. Similar data from the 767 airplane was used for the wing-mounted comparisons.

Landmann, A. E.↗

NASA NTRS1992

On some recent advances in multidisciplinary analysis of hypersonic vehicles

This paper presents pertinent details of the development and application of an integrated, multidisciplinary finite element analysis tool for the effective modeling and simulation of aerospace vehicles including hypersonic ones. Recent advances in this connection include more efficient CFD solution techniques and also aeroservoelastic stability analysis methods that employ unsteady aerodynamic forces for computation of flutter and divergence speeds. An accelerated Euler solution procedure based on the Aitken acceleration technique has recently been implemented that effects considerable improvement in solution efficiency for the same level of solution accuracy, as evidenced by example problems presented in the paper. A summary of finite element numerical formulations for the various individual disciplines as well as for the unified aeroservoelastic analysis and some relevant numerical examples are also presented in the paper.

Gupta, K. K.↗

NASA NTRS1977

A stand-alone interactive graphics finite element modeling system

The finite element modeling (FEM) system described here is an interactive graphics system designed for use with an intelligent terminal. It offers an economical alternative to the conventional methods (hand compilation and remote terminals) of 2 and 3-dimensional model generation. Using local computing and local storage, this FEM system allows the operator to create and display 3-dimensional models entirely off-line from the host computer. This eliminates costly on-line computer and host-processing time, and makes the user more effective by greatly reducing computer response time. The system allows model generation by down-loading node and element data from the host computer or by using the system's model generation operations for digitizing and automatic creation. The system then generates completed model information in the desired analysis package's bulk data format and transmits it to the host computer for finite element analysis.

Gingerich, J. Z.↗

NASA NTRS2001

Porosity Measurement in Laminated Composites by Thermography and FEA

This paper presents the correlation between the through-thickness thermal diffusivity and the porosity of composites. Finite element analysis (FEA) was used to determine the transient thermal response of composites that were subjected to laser heating. A series of finite element models were built and thermal responses for isotropic and orthographic materials with various thermal diffusivities subjected to different heating conditions were investigated. Experiments were conducted to verify the models and to estimate the unknown parameters such as the amount of heat flux. The analysis and experimental results show good correlation between thermal diffusivity and porosity in the composite materials. They also show that both laser and flash heating can be used effectively to obtain thermal diffusivity. The current infrared thermography system is developed for use with flash heating. The laser heating models and the FEA results can provide useful tools to develop practical thermal diffusivity measurement scheme using laser heat.

Chu, Tsuchin Philip↗

NASA NTRS1983

Two-dimensional Finite Element Modeling for Modeling Tectonic Stress and Strain

Techniques of finite element analysis in two dimensional plane strain were applied to problems of geophysics and tectonics. More specifically, the flexibility of the finite element method was employed to address problems involving geological complexity and fault interactions. The modeling of effective anisotropy in material elastic properties proved useful in describing the deformation of faulted crustal blocks. The applications of this modeling work to problems of actual tectonics in southern California was explored. Preliminary models show encouraging agreement with measured tectonic strain in this region, and modeling work was done to gain an understanding of the stress state in a locked fault region with future seismic potential.

Lyzenga, G. A.↗

NASA NTRS1985

Development of non-linear finite element computer code

Recent work has shown that the use of separable symmetric functions of the principal stretches can adequately describe the response of certain propellant materials and, further, that a data reduction scheme gives a convenient way of obtaining the values of the functions from experimental data. Based on representation of the energy, a computational scheme was developed that allows finite element analysis of boundary value problems of arbitrary shape and loading. The computational procedure was implemental in a three-dimensional finite element code, TEXLESP-S, which is documented herein.

Becker, E. B.↗

NASA NTRS1992

Thermostructural applications of heat pipes for cooling leading edges of high-speed aerospace vehicles

Heat pipes have been considered for use on wing leading edge for over 20 years. Early concepts envisioned metal heat pipes cooling a metallic leading edge. Several superalloy/sodium heat pipes were fabricated and successfully tested for wing leading edge cooling. Results of radiant heat and aerothermal testing indicate the feasibility of using heat pipes to cool the stagnation region of shuttle-type space transportation systems. The test model withstood a total seven radiant heating tests, eight aerothermal tests, and twenty-seven supplemental radiant heating tests. Cold-wall heating rates ranged from 21 to 57 Btu/sq ft-s and maximum operating temperatures ranged from 1090 to 1520 F. Follow-on studies investigated the application of heat pipes to cool the stagnation regions of single-stage-to-orbit and advanced shuttle vehicles. Results of those studies indicate that a 'D-shaped' structural design can reduce the mass of the heat-pipe concept by over 44 percent compared to a circular heat-pipe geometry. Simple analytical models for heat-pipe startup from the frozen state (working fluid initially frozen) were adequate to approximate transient, startup, and steady-state heat-pipe performance. Improvement in analysis methods has resulted in the development of a finite-element analysis technique to predict heat-pipe startup from the frozen state. However, current requirements of light-weight design and reliability suggest that metallic heat pipes embedded in a refractory composite material should be used. This concept is the concept presently being evaluated for NASP. A refractory-composite/heat-pipe-cooled wing leading edge is currently being considered for the National Aero-Space Plane (NASP). This concept uses high-temperature refractory-metal/lithium heat pipes embedded within a refractory-composite structure and is significantly lighter than an actively cooled wing leading edge because it eliminates the need for active cooling during ascent and descent. Since the NASP vehicle uses cryogenic hydrogen to cool structural components and then burns this fuel in the combustor, hydrogen necessary for descent cooling only, when the vehicle is unpowered, is considered to be a weight penalty. Details of the design of the refractory-composite/heat-pipe-cooled wing leading edge are currently being investigated. Issues such as thermal contact resistance and thermal stress are also being investigated.

Camarda, Charles J.↗

NASA NTRS1993

Buckling analysis of curved composite sandwich panels subjected to inplane loadings

Composite sandwich structures are being considered for primary structure in aircraft such as subsonic and high speed civil transports. The response of sandwich structures must be understood and predictable to use such structures effectively. Buckling is one of the most important response mechanisms of sandwich structures. A simple buckling analysis is derived for sandwich structures. This analysis is limited to flat, rectangular sandwich panels loaded by uniaxial compression (N(sub x)) and having simply supported edges. In most aerospace applications, however, the structure's geometry, boundary conditions, and loading are usually very complex. Thus, a general capability for analyzing the buckling behavior of sandwich structures is needed. The present paper describes and evaluates an improved buckling analysis for cylindrically curved composite sandwich panels. This analysis includes orthotropic facesheets and first-order transverse shearing effects. Both simple support and clamped boundary conditions are also included in the analysis. The panels can be subjected to linearly varying normal loads N(sub x) and N(sub y) in addition to a constant shear load N(sub xy). The analysis is based on the modified Donnell's equations for shallow shells. The governing equations are solved by direct application of Galerkin's method. The accuracy of the present analysis is verified by comparing results with those obtained from finite element analysis for a variety of geometries, loads, and boundary conditions. The limitations of the present analysis are investigated, in particular those related to the shallow shell assumptions in the governing equations. Finally, the computational efficiency of the present analysis is considered.

Cruz, Juan R.↗