Bending of flexible plates built-in eccentrically in an elastic contour
Equilibrium, compatibility, and contour equations for bending in rectangular flexible plate rigidly clamped to elastic ribs
FLEXIBLE BODY↗
SEARCH · Search NASA
Results for “ELASTIC BENDING”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Effect of Helicopter Blade Dynamics on Blade Aerodynamic and Structural Loads
The effect of rotor blade dynamics on aerodynamic and structural loads is examined for a conventional, main- rotor helicopter using both a comprehensive rotorcraft analysis (CAMRAD) and night test data. The impact of blade dynamics on blade section lift-coefficient time histories is studied by comparing predictions from both a rigid blade analysis and an elastic blade analysis with helicopter flight test data. The elastic blade analysis better predicts high-frequency behavior of section lift. In addition, components of the blade angle of attack, such as elastic blade twist, blade nap rate, blade slope velocity, and inflow, are examined as a function of blade mode. Elastic blade motion affects the blade angle of attack by a few tenths of a degree, and up to the sixth rotor harmonic. A similar study of the influence of blade dynamics on bending and torsion moments was also conducted. The modal analysis of the predicted blade structural loads suggested that five elastic bending deg of freedom (four flap and one lag) and three elastic torsion deg of freedom contributed to calculations of the blade structural loads. However, when structural bending load predictions from several elastic blade analyses were compared with flight test data, an elastic blade model consisting of only three elastic bending modes (first and second flap, and first lag), and two elastic torsion modes was found to be sufficient for maximum correlation.
Heffernan, Ruth M.↗
Flight Dynamics of Flexible Aircraft with Aeroelastic and Inertial Force Interactions
This paper presents an integrated flight dynamic modeling method for flexible aircraft that captures coupled physics effects due to inertial forces, aeroelasticity, and propulsive forces that are normally present in flight. The present approach formulates the coupled flight dynamics using a structural dynamic modeling method that describes the elasticity of a flexible, twisted, swept wing using an equivalent beam-rod model. The structural dynamic model allows for three types of wing elastic motion: flapwise bending, chordwise bending, and torsion. Inertial force coupling with the wing elasticity is formulated to account for aircraft acceleration. The structural deflections create an effective aeroelastic angle of attack that affects the rigid-body motion of flexible aircraft. The aeroelastic effect contributes to aerodynamic damping forces that can influence aerodynamic stability. For wing-mounted engines, wing flexibility can cause the propulsive forces and moments to couple with the wing elastic motion. The integrated flight dynamics for a flexible aircraft are formulated by including generalized coordinate variables associated with the aeroelastic-propulsive forces and moments in the standard state-space form for six degree-of-freedom flight dynamics. A computational structural model for a generic transport aircraft has been created. The eigenvalue analysis is performed to compute aeroelastic frequencies and aerodynamic damping. The results will be used to construct an integrated flight dynamic model of a flexible generic transport aircraft.
Nguyen, Nhan T.↗
A theory for the fracture of thin plates subjected to bending and twisting moments
Stress fields near the tip of a through crack in an elastic plate under bending and twisting moments are reviewed assuming both Kirchhoff and Reissner plate theories. The crack tip displacement and rotation fields based on the Reissner theory are calculated. These results are used to calculate the J-integral (energy release rate) for both Kirchhoff and Reissner plate theories. Invoking Simmonds and Duva's (1981) result that the value of the J-integral based on either theory is the same for thin plates, a universal relationship between the Kirchhoff theory stress intensity factors and the Reissner theory stress intensity factors is obtained for thin plates. Calculation of Kirchhoff theory stress intensity factors from finite elements based on energy release rate is illustrated. It is proposed that, for thin plates, fracture toughness and crack growth rates be correlated with the Kirchhoff theory stress intensity factors.
Hui, C. Y.↗
Experimental study of thin-walled composite beams
Thin-walled rectangular section composite beams are built out of graphite-epoxy prepreg tape using an autoclave molding technique. Cantilevered beams are tested under static loads using a specially-built apparatus and bending slope and elastic twist at a station are measured using a laser system. Measured bending slope and bending-induced twist distributions are correlated with predicted results obtained using a simple beam analysis as well as a refined finite element analysis. Natural vibration characteristics at different rotational speeds are determined experimentally by testing beams in a specially built 10 ft diameter vacuum chamber. The rotor is excited by piezo-electric crystals and response is determined from strain gages mounted on the surface. For composite beams with bending-twisting couplings (symmetric layup), effects of section warping and transverse shear on structural response are found to be substantial. These results were substantiated by the analyses.
Chandra, Ramesh↗
The surface crack problem in an orthotropic plate under bending and tension
The elasticity problem for an infinite orthotropic flat plate containing a series of through and part through cracks and subjected to bending and tension loads is considered. The problem is formulated by using Reissner's plate bending theory and considering three-dimensional material orthotropy. The Line-spring model developed by Rice and Levy is used to formulate the surface crack problem in which a total of nine material constants were used. The effects of material orthotropy on the stress intensity factors was determined, the interaction between two asymmetrically arranged collinear cracks was investigated, and extensive numerical results regarding the stress intensity factors are provided. The problem is reduced to a system of singular integral equations which is solved by using the Gauss-Chebyshev quadrature formulas. The calculated results show that the material orthotropy does have a significant effect on the stress intensity factor.
Wu, Bing-Hua↗
The surface crack problem in an orthotropic plate under bending and tension
The elasticity problem for an infinite orthotropic flat plate containing a series of through and part-through cracks and subjected to bending and tension loads is considered. The problem is formulated by using Reissner's plate bending theory and considering three dimensional materials orthotropy. The Line-spring model developed by Rice and Levy is used to formulate the surface crack problem in which a total of nine material constants has been used. The main purpose of this study is to determine the effect of material orthotropy on the stress intensity factors, to investigate the interaction between two asymmetrically arranged collinear cracks, and to provide extensive numerical results regarding the stress intensity factors. The problem is reduced to a system of singular integral equations which is solved by using the Gauss-Chebyshev quadrature formulas. The calculated results show that the material orthotropy does have a significant effect on the stress intensity factor.
Wu, B. H.↗
Determination of two elastic constants of platelike bodies
Bending tests with plate strip in pure bending and square plate in pure shearing stress, and determination of moduli of elasticity and plate rigidity
BENDING MOMENT↗
Numerical fracture simulation of compact and bend specimens
An elastic-plastic finite-element analysis with a critical crack-tip-opening displacement criterion was used to simulate fracture of various size compact and bend specimens made of HY-130 steel. From the calculated load-crack-extension and load-displacement curves, J-resistance (J-R) curves were determined by several methods. The simulated 3-R curves were insensitive to specimen size up to maximum load but were sensitive to specimen configuration for crack extensions greater than 10 percent of the initial uncracked ligament length.
Shivakumar, K. N.↗
Stresses and deformations in thin shells of revolution Seventh progress report
Stresses and deformations in thin shells of revolution - dynamic response of shells of revolution and bending analysis of elastic plastic circular plates
THIN WALLED SHELL↗
Scalability in SLA lattice through lattice orientation and hybrid frame and plate architectures
Lightweighting has been a key goal for engineers and designers, with lattice structures widely explored as the building blocks for structural components. Cellular structure-inspired lattice truss frame designs made of struts, have been extensively studied. All plate-based lattice designs have superior mechanical performance. Limits in scalability occur from formation of closed pockets limiting uv curing in processes like stereolithography (SLA). We examine hybrid frame and plate body-centered cubic-simply cubic (BCC-SC) lattices under compression. Unit cells and scaled up lattice exhibit an increase in yield stress and modulus with the addition of plates. The loading direction on the hybrid frame and plate unit cells affected the magnitude of improvement. Simulations and measurements indicated that the optimal lightweight lattice was determined to be when two plates were placed opposite each other with plates buttressing the struts, inhibiting buckling of the struts aligned with the loading direction. This lattice resulted in 63% improvement in specific modulus, a 137% improvement in specific yield point, and a 360% improvement in specific energy absorption (SEA) and the scaled up 4 × 4 × 4 scaled-up structures, showed a 107%, 148%, and 297% in specific modulus, specific yield point, and SEA, respectively A combined stretching-bending behavior was identified in optimal orientations reflecting the delayed buckling mechanism paired to a rising stress-strain curve past the elastic yield indicating bending resistance. The mass moment of inertia was found to be a key parameter correlating optimum orientation for the same number of plates added to the BCC-SC frame.
Mahan Ghosh↗
Effect of helicopter blade dynamics on blade aerodynamic and structural loads
The effect of rotor blade dynamics on aerodynamic and structural loads is examined for a conventional, main-rotor helicopter using a comprehensive rotorcraft analysis (CAMRAD) and flight-test data. The impact of blade dynamics on blade section lift-coefficient time histories is studied by comparing predictions from a rigid-blade analysis and an elastic-blade analysis with helicopter flight test data. The elastic blade analysis better predicts high-frequency behavior of section lift. In addition, components of the blade angle of attack such as elastic blade twist, blade flap rate, blade slope velocity, and inflow are examined as a function of blade mode. Elastic blade motion changed blade angle of attack by a few tenths of a degree, and up to the sixth rotor harmonic. A similar study of the influence of blade dynamics on bending and torsion moments was also conducted. A correlation study comparing predictions from several elastic-blade analyses with flight-test data revealed that an elastic-blade model consisting of only three elastic bending modes (first and second flap and first lag), and two elastic torsion modes was sufficient for good correlation.
Heffernan, Ruth M.↗
Thin-walled composite beams under bending, torsional, and extensional loads
Symmetric and antisymmetric layup graphite-epoxy composite beams with thin-walled rectangular cross sections are fabricated using an autoclave molding technique and tested under bending, torsional, and extensional loads. The bending slope and elastic twist at a station are measured using an optical system, and the results correlated with predicted values from a simple beam analysis as well as a refined finite element analysis. A symmetric ply layup results in bending-twist coupling whereas an antisymmetric layup causes extension-twist coupling. Simple analytical results with plane-stress assumption agree better with measured data as well as finite element predictions than with plane-strain assumption. For symmetric layup beams, the bending-induced twist and torsion-induced bending slope are predicted satisfactorily using simple analytical solution. Correlations with measured data, however, are generally improved using a finite element solution. For antisymmetric beams, axial force-induced twist is predicted satisfactorily by both methods.
Chandra, Ramesh↗
Analysis of elastic-plastic circular plates.
Bending analysis of elastoplastic circular plates for small deflection and axisymmetric loadings and support conditions, based on Kirchhoff hypothesis
Khojesteh-Bakht, M.↗
Unique considerations in the design and experimental evaluation of tailored wings with elastically produced chordwise camber
Some of the unique considerations that are associated with the design and experimental evaluation of chordwise deformable wing structures are addressed. Since chordwise elastic camber deformations are desired and must be free to develop, traditional rib concepts and experimental methodology cannot be used. New rib design concepts are presented and discussed. An experimental methodology based upon the use of a flexible sling support and load application system has been created and utilized to evaluate a model box beam experimentally. Experimental data correlate extremely well with design analysis predictions based upon a beam model for the global properties of camber compliance and spanwise bending compliance. Local strain measurements exhibit trends in agreement with intuition and theory but depart slightly from theoretical perfection based upon beam-like behavior alone. It is conjectured that some additional refinement of experimental technique is needed to explain or eliminate these (minor) departures from asymmetric behavior of upper and lower box cover strains. Overall, a solid basis for the design of box structures based upon the bending method of elastic camber production has been confirmed by the experiments.
Rehfield, Lawrence W.↗
Analysis of plate structures by a dual finite element method
Stretching and bending of linearly elastic orthotropic plate analysis by dual finite element method with computer program
Ho, P. K.-K.↗
Stresses near a flat inclusion in bonded dissimilar materials.
The plane elastostatic problem for bonded materials containing a flat inclusion is considered. It is assumed that the inclusion is located parallel to or on the interface and may be rigid or elastic with negligible bending rigidity. The integral equations for various cases are derived and their solutions are described. The stress state around the singular points are investigated and a pair of stress intensity factors similar to that for crack problems are defined. A series of numerical examples for two bonded half planes and for a half plane is worked out. The stress intensity factors are presented as functions of the ratio of the distance from the interface to the length of the inclusion.
Erdogan, F.↗
Analysis of foil bearings for high speed operation in cryogenic applications
The general objective of this project is to develop analysis tools which are required for the design of foil bearings to be used in cryogenic applications. During the second year of this project, a general analysis approach and code for journal bearings operating under steady state conditions will be completed. This will be followed by the initiation of an investigation into transient behavior of foil bearings to determine their performance in rotor systems. Foil bearings have been proposed as an alternative to rolling element bearings for use in cryogenic turbopumps in liquid propellant rocket engines. This type of bearing offers several advantages over rolling element bearings since they would use the cryogenic pump fluid for a lubricant and have structural flexibility. These bearings have the potential of high reliability and long life. The bearing surface is constructed of a 'foil' which resists deflection by a combination of bending, membrane, and elastic foundation effects. The relative motion between the rotating shaft and the foil causes pressure in the fluid film to develop. This pressure deflects the the foil surface away from the shaft. Once a full fluid film is established between the foil and the rotor shaft, contact no longer takes place and there is no subsequent wear of the surfaces. The flexible foil structure of the bearing allows it to compensate for minor tolerance and manufacturing defects. This same flexibility also has a significant effect on the dynamic performance of the rotor-bearing system.
Carpino, Marc↗