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At least 163 records · Page 9

Automated Finite Element Modeling of Wing Structures for Shape Optimization

The displacement formulation of the finite element method is the most general and most widely used technique for structural analysis of airplane configurations. Modem structural synthesis techniques based on the finite element method have reached a certain maturity in recent years, and large airplane structures can now be optimized with respect to sizing type design variables for many load cases subject to a rich variety of constraints including stress, buckling, frequency, stiffness and aeroelastic constraints (Refs. 1-3). These structural synthesis capabilities use gradient based nonlinear programming techniques to search for improved designs. For these techniques to be practical a major improvement was required in computational cost of finite element analyses (needed repeatedly in the optimization process). Thus, associated with the progress in structural optimization, a new perspective of structural analysis has emerged, namely, structural analysis specialized for design optimization application, or.what is known as "design oriented structural analysis" (Ref. 4). This discipline includes approximation concepts and methods for obtaining behavior sensitivity information (Ref. 1), all needed to make the optimization of large structural systems (modeled by thousands of degrees of freedom and thousands of design variables) practical and cost effective.

Harvey, Michael Stephen↗

Deflections of anisotropic sandwich beams with variable face sheets and core thicknesses

A sandwich construction consists of a low-density core material with high strength face sheets bounded to the top and bottom surfaces. The construction has been widely used in the aerospace and marine industries due to its outstanding characteristics such as noise absorption, weight minimization, heat insulation, and better bending stiffness. In sandwich structures used in high-performance aircraft, the face sheets are often made of fiber-reinforced composite materials and the core is made of honeycomb. The structures may also have variable thickness so as to satisfy aerodynamic requirements. In the stress analysis, the constant-thickness face sheets are usually considered as membrane and the core is assumed to be inextensible but deformable in the thickness direction. The static behavior of variable-thickness, isotropic and homogeneous sandwich beams was successfully studied by employing a constant-thickness theory but allowing stiffnesses to vary in accordance with local thickness variations. It has been recently found in a refined theory that the analyses based on the constant thickness theory locally can lead to significant errors in structural responses if the sandwich beam is thickness-tapered and the cores are deformable in transverse shear. The errors arise mainly from two factors: (1) the transverse shear components of the membrane forces in the face sheets alter the transverse shears carried by the core; and (2) the face-sheet membrane strains arise from transverse shear deformation of the core. In practice the variable thickness may not only exist in core but also in face sheets. The thickness-variations may even be a type of step function. In this case the transverse shear stress in the face sheets and bending stress in the core should be taken into account in the refined theory mentioned. In the present study, energy principles are employed in deriving governing equations for general bending of anisotropic sandwich beams with variable thickness in both face sheets and cores. Solutions to these equations are based on a finite difference scheme. As an example in application, a simply supported thickness-tapered sandwich beam subject to a concentrated load at its center is considered. Let W' be the maximum deflection of the beam in which face sheets are considered as membrane, while W'' is that based on using the modified refined theory. It is found that W' is always larger than W'', however, the magnitude of (W'- W'') appears to be insensitive to the change of the taper of the beam.

Lu, Chu-Ho↗

Kinetically Tunable, Active Auxetic, and Variable Recruitment Active Textiles from Hierarchical Assemblies

Multifunctional textiles with programmable, multi-axial, distributed, and scalable actuation are highly desirable and presently unrealized. 1D torque-unbalanced active yarns within 2D textile structures are exploited to produce soft and scalable active textiles that exhibit tunable displacements, forces, stiffnesses, and kinematic deformations. Through a textile hierarchy spanning active material composition, yarn construction, textile geometry, and system architecture, these active textiles accomplish kinetic tunability, variable recruitment behaviors, and auxetic effects without mechanical contact, called active auxetic effects. New modes of pre-programmed multi-axial performance are enabled by geometrically manipulating—specifically pre-stressing and constraining—active filaments in torsion and leveraging their structural elastic instability within a textile geometry. The new kinematic motion afforded by torque-unbalanced active yarns enhances the performance of active textiles, which accomplish tensile strokes over 40%, generated blocked forces up to 308 N m−1, and specific work over 0.4. kJ kg−1. Advances in active textiles are demonstrated through multifunctional 3D applications, including a variable constriction pump that exhibits sequential actuation, a wearable that conforms multi-axially around the body, and a soft exoskeleton that performs assistive motions and on-body anchoring simultaneously. By harnessing the capabilities of active materials within a textile hierarchy, advances in the potentiality of multifunctional textiles are presented.

Active auxetic effects↗

Stability and bifurcation analysis of oscillators with piecewise-linear characteristics - A general approach

A general approach is developed for determining the periodic solutions and their stability of nonlinear oscillators with piecewise-smooth characteristics. A modified harmonic balance/Fourier transform procedure is devised for the analysis. The procedure avoids certain numerical differentiation employed previously in determining the periodic solutions, therefore enhancing the reliability and efficiency of the method. Stability of the solutions is determined via perturbations of their state variables. The method is applied to a forced oscillator interacting with a stop of finite stiffness. Flip and fold bifurcations are found to occur. This led to the identification of parameter ranges in which chaotic response occurred.

Noah, S. T.↗

Mechanics of Preloaded Bolt Tensile Loading With Focus on Load Introduction Factor

The bolt tensile and joint separation loads are directly influenced by the locations at which the external loads enter the clamped members of a preloaded bolted joint (PBJ) and the associated load-paths through the joint. This physical load introduction mechanism affecting the bolt tensile loading is typically represented in the bolt tensile load equation, in part, by a load introduction factor (LIF), which was shown by H.M. Lee of Marshall Spaceflight Center to be a natural product of the bolt tensile load equation using a linear spring stiffness model. This LIF, being a function of load-path stiffness, has subsequently been denoted as the stiffness-based LIF (SBLIF), providing a framework to calculate the LIF using whatever load-path stiffness approximations are appropriate. Expanding upon the work of Lee, it is shown that the SBLIF and the joint stiffness factor are functions of the stiffnesses of the same load-paths and regions within a PBJ, and thus they should not be treated as independent variables. Mathematical expressions for the SBLIF are presented. Comparisons are shown between the analytically calculated SBLIF, the analytically calculated geometric LIF (GLIF), which is a simple clamped-member thickness ratio, the experimentally derived LIF, and the LIF determined by finite element analysis (FEA). Using experiment and FEA as a benchmark, the SBLIF, using traditional load-path stiffness approximations, enables a more accurate prediction of bolt tensile loading than the GLIF, although it can be unconservative near joint separation. The GLIF generally attributes more of the externally applied tensile load to the bolt than does the SBLIF, potentially resulting in heavier and/or more costly bolted joints. Mathematical relationships between the SBLIF and the GLIF are developed. Supplemental material is provided in the appendixes where the historical practice of using the joint compressive stiffness in place of the joint tensile stiffness is evaluated. The appendixes include step-by-step examples demonstrating the calculation of the SBLIF using traditional stiffness approximations and conclude with the development of the joint diagram in terms of the SBLIF, culminating into formulas for the key features of a joint diagram, which is useful for programming.

Load Path↗

A space-time adaptive finite element method with exponential time integrator for the phase field model of pitting corrosion

In this paper we propose a space-time adaptive finite element method for the phase field model of pitting corrosion, which is a parabolic partial differential equation system consisting of a phase variable and a concentration variable. A major challenge in solving this phase field model is that the problem is very stiff, which makes the time step size extremely small for standard temporal discretizations. Another difficulty is that a high spatial resolution is required to capture the steep gradients within the diffused interface, which results in very large number of degrees of freedom for uniform meshes. To overcome the stiffness of this model, we combine the Rosenbrock–Euler exponential integrator with Crank–Nicolson scheme for the temporal discretization. Moreover, by exploiting the fact that the speed of the corroding interface decreases with time, we derive an adaptive time stepping formula. For the spatial approximation, we propose a simple and efficient strategy to generate adaptive meshes that reduces the computational cost significantly. Thus, the proposed method utilizes local adaptivity and mesh refinement for efficient simulation of the corrosive dissolution over long times in heterogeneous media with complex microstructures. We also present an extensive set of numerical experiments in both two and three dimensional spaces to demonstrate efficiency and robustness of the proposed method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Thermochemical nonequilibrium in atomic hydrogen at elevated temperatures

A numerical study of the nonequilibrium flow of atomic hydrogen in a cascade arc was performed to obtain insight into the physics of the hydrogen cascade arc. A rigorous mathematical model of the flow problem was formulated, incorporating the important nonequilibrium transport phenomena and atomic processes which occur in atomic hydrogen. Realistic boundary conditions, including consideration of the wall electrostatic sheath phenomenon, were included in the model. The governing equations of the asymptotic region of the cascade arc were obtained by writing conservation of mass and energy equations for the electron subgas, an energy conservation equation for heavy particles and an equation of state. Finite-difference operators for variable grid spacing were applied to the governing equations and the resulting system of strongly coupled, stiff equations were solved numerically by the Newton-Raphson method.

Scott, R. K.↗

Stability theorems for multidimensional linear systems with variable parameters

A Liapunov-type approach is used to derive two equivalent theorems which govern the stability of coupled linear systems with varying multiple parameters. The theorems generalize some of the existing theorems applicable to systems with constant parameters and the Sonin-Polya theorem applicable to a single-degree-of-freedom system with variable coefficients. As an illustration, the proposed theorems are applied to mechanical systems with varying inertia, stiffness, gyroscopic, and damping terms, and velocity and position-dependent forces.

Shrivastava, S. K.↗

Composite Elastic Skins for Shape-Changing Structures

Composite elastic skins having tailorable mechanical properties have been invented for covering shape-changing ( morphable ) structures. These skins are intended especially for use on advanced aircraft that change shapes in order to assume different aerodynamic properties. Many of the proposals for aircraft that could perform large aerodynamic shape changes require flexible skins that could follow shape changes of internal structures driven by actuators. Examples of such shape changes can include growth or shrinkage of bumps, conformal changes in wing planforms, cambers, twists, and bending of integrated leading- and trailing-edge flaps. Prior to this invention, there was no way of providing smooth aerodynamic surfaces capable of large deflections while maintaining smoothness and sufficient rigidity. Although latex rubber, silicone rubber, and similar conventional materials can be made into smooth coverings, they are not suitable for this purpose because, in order to impart required stiffness against out-of-plane bending, it would be necessary to make the coverings excessively thick, thereby necessitating the use of impractically large actuation forces. The basic idea of the invention is that of smoothly wrapping an underlying variable structure with a smooth skin that can be stretched or otherwise warped with low actuation force in one or both in-plane direction(s) and is relatively stiff against out-of-plane bending. It is envisioned that a skin according to the invention could be stretched as much as 20 percent in a desired direction. Because this basic idea admits of numerous variations, the following description is necessarily oversimplified for the sake of brevity.

Cagle, Christopher M.↗

Charts for the Determination of Wing Torsional Stiffness Required for Specified Rolling Characteristics or Aileron Reversal Speed

A series of charts are presented by which the wing torsional stiffness required to meet a given standard of rolling effectiveness may be quickly determined. The charts may also be used to obtain quickly the aileron reversal speed and the variation of the loss in rolling effectiveness with airspeed. The charts apply to linearly tapered wings and elliptical wings of tubular-shell construction having various aspect ratios with aileron span and location of ailerons as variables. In the derivation of the charts, induced lift effects have been taken into account and the form of the wing-torsional-stiffness curve has been assumed.

Pearson, Henry A↗

Nonuniform thermal environmental effects on space truss structural reliability

A three-bay, space, cantilever truss is probabilistically evaluated to quantify the range of uncertainties of buckling loads and member forces due to nonuniform thermal loads, applied loads and moments (mechanical loads), and combination of both. The truss members are assumed to be made from (1) aluminum tubes or (2) high modulus graphite-fiber/intermediate modulus epoxy-matrix composite tubes. Cumulative distribution function results show that certain combinations of thermal loads with mechanical loads reduce the probabilistic buckling loads and increase the magnitude of the member axial forces for aluminum truss. However, the reverse is true for composite truss due to very low coefficient of thermal expansion and higher stiffness of the composite. Finally, the sensitivities associated with the uncertainties in the structural, material, and load variables (primitive variables) are investigated. They show that buckling loads and member axial forces are most sensitive to the uncertainties in spacial (geometry) variables.

Pai, Shantaram S.↗

LSENS, a general chemical kinetics and sensitivity analysis code for gas-phase reactions: User's guide

A general chemical kinetics and sensitivity analysis code for complex, homogeneous, gas-phase reactions is described. The main features of the code, LSENS, are its flexibility, efficiency and convenience in treating many different chemical reaction models. The models include static system, steady, one-dimensional, inviscid flow, shock initiated reaction, and a perfectly stirred reactor. In addition, equilibrium computations can be performed for several assigned states. An implicit numerical integration method, which works efficiently for the extremes of very fast and very slow reaction, is used for solving the 'stiff' differential equation systems that arise in chemical kinetics. For static reactions, sensitivity coefficients of all dependent variables and their temporal derivatives with respect to the initial values of dependent variables and/or the rate coefficient parameters can be computed. This paper presents descriptions of the code and its usage, and includes several illustrative example problems.

Radhakrishnan, Krishnan↗

Bistable Collapsible Tubular Mast Booms

A promising candidate for deployable composite structures is the two-shelled Collapsible Tubular Mast (CTM) boom, which is to be employed on future solar sail and interplanetary small satellite platforms by the National Aeronautics and Space Administration (NASA). This is due to its two omega-shaped shells forming a closed-section which yields large stiffnesses that allowed for high dimensional stability. An inextensional analytical model describing the bending deformation mechanics of CTM booms was used to determine how design variables induce bistability, or the existence of two strain energy wells. Bistable booms were favorable due to low strain energy requirements for the coiled state and had more controllable deployment when compared to monostable booms. The effects of varying lamina material, laminate layup, and shell arc geometries between different inner and outer shell segments on the second strain energy well and stiffness properties were determined for cross-sections formed by circular segments. The full design space for two-shelled composite CTM booms was explored to evaluate the validity of the simple analytical model developed. Optimal CTM boom designs were manufactured and experimentally characterized for comparisons against model results. The model under-predicted the second stable coiled diameter of the complete two-shelled booms by 27-33% and as low as 3-8% for the individual shells wrapped alone.

Fernandez, Juan M.↗

Full-Scale Prop-Rotor Stability Tests on the XV3 at High Advance Ratios

Tests in the 40-by-80 foot wind tunnel were made at airspeeds from 40 to 195 knots. The aircraft was mounted with and without roll freedom. Rotor pylon configuration variables included the following: swashplate stabilization by mechanically coupling the swashplate to the wing or fuselage; pylon restraint stiffness and damping; hub restraint; and delta-three combined with swashplate retardation. Time histories were recorded of pylon motions and rotor loads following pulse-type excitations of the pylon. It was found that damping of the low frequency whirl mode increased with swashplate stabilization, pylon stiffness, and hub restraint.

Prop-Rotor↗

Effects of Rotor Design Variations on Tiltrotor Whirl-Mode Stability

Further increases in tiltrotor speeds are limited by coupled wing/rotor whirl-mode aeroelastic instability. Increased power, thrust, and efficiency are not enough: the whirl-mode stability boundary must also be improved. With current technology, very stiff, thick wings of limited aspect ratio are essential to meet the stability requirements, which severely limits cruise efficiency and maximum speed. Larger and more efficient tiltrotors will need longer and lighter wings, for which whirl-mode flutter is a serious design issue. Numerous approaches to improving the whirl-mode airspeed boundary have been investigated, typically focusing on wing design, active stability augmentation, and variable geometry rotors. The research reported herein applies the much simpler approach of sweeping the outboard blade sections. The effects-of control-system stiffness were also studied. Reference covers the first phase of the current research and discusses the evolution of the concept.

Acree, C. W., Jr.↗

Estimation of 3D Woven Design Sensitivities Using a Rapid Multiscale Analysis Technique

Highly-refined finite element models of three-dimension (3D) woven composite systems currently require excessive computational demands that limit their use in sensitivity analysis, uncertainty quantification, and optimization. An alternative analysis methodology was developed using the NASA Multiscale Analysis Tool (NASMAT) where multiscale models of a 3D woven composite (including inter-tow matrix voids and constituent failure) can be completed on a single central processing unit(CPU)on the order of ~30 s. To develop inputs and validation data for the NASMAT model, coupon and acid-digesting testing and x-ray computed tomography were performed. The NASMAT inputs were parameterized using a set of 25 input variables and distributions. These inputs were randomly sampled to generate a total of 100,000 NASMAT analyses that could be used to understand the influence of different material and geometric properties on the warp and weft-direction stiffness and strength. These analyses (including pre/post-processing) were performed in less than eight hours on a 120 CPU cluster. The computational efficiency of the NASMAT model enabled a sensitivity analysis to be performed, and dominant input variables were able to be identified. Key results were consistent with theoretical and experimental observations for the specific 3D woven system studied in this work.

NASMAT↗

Estimation of 3D Woven Design Sensitivities Using a Rapid Multiscale Analysis Technique

Highly-refined finite element models of three-dimension (3D) woven composite systems currently require excessive computational demands that limit their use in sensitivity analysis, uncertainty quantification, and optimization. An alternative analysis methodology was developed using the NASA Multiscale Analysis Tool (NASMAT) where multiscale models of a 3D woven composite (including inter-tow matrix voids and constituent failure) can be completed on a single central processing unit (CPU) on the order of ~30s. To develop inputs and validation data for the NASMAT model, coupon and acid-digesting testing and x-ray computed tomography were performed. The NASMAT inputs were parameterized using a set of 25 input variables and distributions. These inputs were randomly sampled to generate a total of 100,000 NASMAT analyses that could be used to understand the influence of different material and geometric properties on the warp and weft-direction stiffness and strength. These analyses (including pre/post-processing) were performed in less than eight hours on a 120 CPU cluster. The computational efficiency of the NASMAT model enabled a sensitivity analysis to be performed, and dominant input variables were able to be identified. Key results were consistent with theoretical and experimental observations for the specific 3D woven system studied in this work.

NASMAT↗

Coupled Vortex-Lattice Flight Dynamic Model with Aeroelastic Finite-Element Model of Flexible Wing Transport Aircraft with Variable Camber Continuous Trailing Edge Flap for Drag Reduction

This paper presents a coupled vortex-lattice flight dynamic model with an aeroelastic finite-element model to predict dynamic characteristics of a flexible wing transport aircraft. The aircraft model is based on NASA Generic Transport Model (GTM) with representative mass and stiffness properties to achieve a wing tip deflection about twice that of a conventional transport aircraft (10% versus 5%). This flexible wing transport aircraft is referred to as an Elastically Shaped Aircraft Concept (ESAC) which is equipped with a Variable Camber Continuous Trailing Edge Flap (VCCTEF) system for active wing shaping control for drag reduction. A vortex-lattice aerodynamic model of the ESAC is developed and is coupled with an aeroelastic finite-element model via an automated geometry modeler. This coupled model is used to compute static and dynamic aeroelastic solutions. The deflection information from the finite-element model and the vortex-lattice model is used to compute unsteady contributions to the aerodynamic force and moment coefficients. A coupled aeroelastic-longitudinal flight dynamic model is developed by coupling the finite-element model with the rigid-body flight dynamic model of the GTM.

Flexible Aicraft↗