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At least 37 records · Page 2

Equivalent plate structural modeling for wing shape optimization including transverse shear

A new technique for structural modeling of airplanes wings is presented taking transverse shear effects into account. The kinematic assumptions of first-order shear deformation plate theory in combination with numerical analysis, where simple polynomials are used to define geometry, construction, and displacement approximations, lead to analytical expressions for elements of the stiffness and mass matrices and load vector. Contributions from the cover skins, spar and rib caps, and spar and rib webs are included as well as concentrated springs and concentrated masses. Limitations of wing modeling techniques based on classical plate theory are discussed, and the improved accuracy of the new equivalent plate technique is demonstrated through comparison with finite element analysis and test results. Expressions for analytical derivatives of stiffness, mass, and load terms with respect to wing shape are given. Based on these, it is possible to obtain analytic sensitivities of displacements, stresses, and natural frequencies with respect to planform shape and depth distribution. This makes the new capability an effective structural tool for wing shape optimization.

Livne, Eli↗

Equivalent Plate Structural Modeling for Wing Shape Optimization Including Transverse Shear

A new technique for structural modeling of airplane wings is presented taking transverse shear effects into account. The kinematic assumptions of first-order shear deformation plate theory In combination with numerical analysis, where simple polynomials are used to define geometry, construction, and displacement approximations, lead to analytical expressions for elements of the stiffness and mass matrices and load vector. Contributions from the cover skins, spar and rib caps, and spar and rib webs are included as well as concentrated springs and concentrated masses. Limitations of wing modeling techniques based on classical plate theory are discussed, and the Improved accuracy of the new equivalent plate technique is demonstrated through comparison with finite element analysis and test results. Expressions for analytical derivatives of stiffness, mass, and load terms with respect to wing shape are given. Based on these, it is possible to obtain analytic sensitivities of displacements, stresses, and natural frequencies with respect to planform shape and depth distribution. This makes the new capability an effective structural tool for wing shape optimization.

Livne, Eli↗

Hierarchic models for laminated plates

Structural plates and shells are three-dimensional bodies, one dimension of which happens to be much smaller than the other two. Thus, the quality of a plate or shell model must be judged on the basis of how well its exact solution approximates the corresponding three-dimensional problem. Of course, the exact solution depends not only on the choice of the model but also on the topology, material properties, loading and constraints. The desired degree of approximation depends on the analyst's goals in performing the analysis. For these reasons models have to be chosen adaptively. Hierarchic sequences of models make adaptive selection of the model which is best suited for the purposes of a particular analysis possible. The principles governing the formulation of hierarchic models for laminated plates are presented. The essential features of the hierarchic models described models are: (1) the exact solutions corresponding to the hierarchic sequence of models converge to the exact solution of the corresponding problem of elasticity for a fixed laminate thickness; and (2) the exact solution of each model converges to the same limit as the exact solution of the corresponding problem of elasticity with respect to the laminate thickness approaching zero. The formulation is based on one parameter (beta) which characterizes the hierarchic sequence of models, and a set of constants whose influence was assessed by a numerical sensitivity study. The recommended selection of these constants results in the number of fields increasing by three for each increment in the power of beta. Numerical examples analyzed with the proposed sequence of models are included and good correlation with the reference solutions was found. Results were obtained for laminated strips (plates in cylindrical bending) and for square and rectangular plates with uniform loading and with homogeneous boundary conditions. Cross-ply and angle-ply laminates were evaluated and the results compared with those of MSC/PROBE. Hierarchic models make the computation of any engineering data possible to an arbitrary level of precision within the framework of the theory of elasticity.

Actis, Ricardo Luis↗

Compact, Two-Sided Structural Cold Plate Configuration

In two-sided structural cold plates, typically there is a structural member, such as a honeycomb panel, that provides the structural strength for the cold plates that cool equipment. The cold plates are located on either side of the structural member and thus need to have the cooling fluid supplied to them. One method of accomplishing this is to route the inlet and outlet tubing to both sides of the structural member. Another method might be to supply the inlet to one side and the outlet to the other. With the latter method, an external feature such as a hose, tube, or manifold must be incorporated to pass the fluid from one side of the structural member to the other. Although this is a more compact design than the first option, since it eliminates the need for a dedicated supply and return line to each side of the structural member, it still poses problems, as these external features can be easily damaged and are now new areas for potential fluid leakage. This invention eliminates the need for an external feature and instead incorporates the feature internally to the structural member. This is accomplished by utilizing a threaded insert that not only connects the cold plate to the structural member, but also allows the cooling fluid to flow through it into the structural member, and then to the cold plate on the opposite side. The insert also employs a cap that acts as a cover to seal the open area needed to install the insert. There are multiple options for location of o-ring style seals, as well as the option to use adhesive for redundant sealing. Another option is to weld the cap to the cold plate after its installation, thus making it an integral part of the structural member. This new configuration allows the fluid to pass from one cold plate to the other without any exposed external features.

Zaffetti, Mark↗

Detection of Non-Symmetrical Damage in Smart Plate-Like Structures

A two-dimensional model for in-plane vibrations of a cantilever plate with a non-symmetrical damage is used in the context of defect identification in materials with piezoelectric ceramic patches bonded to their surface. These patches can act both as actuators and sensors in a self-analyzing fashion, which is a characteristic of smart materials. A Galerkin method is used to approximate the dynamic response of these structures. The natural frequency shifts due to the damage are estimated numerically and compared to experimental data obtained from tests on cantilever aluminum plate-like structures damaged at different locations with defects of different depths. The damage location and extent are determined by an enhanced least square identification method. Efficacy of the frequency shift based algorithms is demonstrated using experimental data.

Blanks, H. T.↗

Power flow analysis of two coupled plates with arbitrary characteristics

In the last progress report (Feb. 1988) some results were presented for a parametric analysis on the vibrational power flow between two coupled plate structures using the mobility power flow approach. The results reported then were for changes in the structural parameters of the two plates, but with the two plates identical in their structural characteristics. Herein, limitation is removed. The vibrational power input and output are evaluated for different values of the structural damping loss factor for the source and receiver plates. In performing this parametric analysis, the source plate characteristics are kept constant. The purpose of this parametric analysis is to determine the most critical parameters that influence the flow of vibrational power from the source plate to the receiver plate. In the case of the structural damping parametric analysis, the influence of changes in the source plate damping is also investigated. The results obtained from the mobility power flow approach are compared to results obtained using a statistical energy analysis (SEA) approach. The significance of the power flow results are discussed together with a discussion and a comparison between the SEA results and the mobility power flow results. Furthermore, the benefits derived from using the mobility power flow approach are examined.

Cuschieri, J. M.↗

Development of an engineering analysis of progressive damage in composites during low velocity impact

A computerized, analytical methodology was developed to study damage accumulation during low velocity lateral impact of layered composite plates. The impact event was modeled as perfectly plastic with complete momentum transfer to the plate structure. A transient dynamic finite element approach was selected to predict the displacement time response of the plate structure. Composite ply and interlaminar stresses were computed at selected time intervals and subsequently evaluated to predict layer and interlaminar damage. The effects of damage on elemental stiffness were then incorporated back into the analysis for subsequent time steps. Damage predicted included fiber failure, matrix ply failure and interlaminar delamination.

Humphreys, E. A.↗

Combined, nonlinear aerodynamic and structural method for the aeroelastic design of a three-dimensional wing in supersonic flow

An iterative procedure for the static aeroelastic design of a flexible wing at supersonic speeds has been developed. The procedure combines a nonlinear, full-potential solver (NCOREL) with an equivalent plate structural analysis method. The NCOREL method yields significantly improved aerodynamic estimates compared to linear theory. The equivalent plate structural analysis method demonstrates an order of magnitude reduction in computer memory and execution time compared to finite-element methods. A highly swept wing is analyzed at high lift using this aeroelastic procedure. The results indicate that the wing deforms favorably due to aerodynamic loading and, consequently, that the inviscid drag levels do not vary at the required lift coefficient although the angle of attack varies significantly. A sensitivity analysis of the type required for optimization studies was also performed with the aeroelastic design procedure.

Pittman, J. L.↗

Thick plate bending wave transmission using a mobility power flow approach

The mobility power flow (MPF) approach is used in this paper to describe the flexural behavior of an L-shaped plate structure consisting of thick plates with rotary inertia and shear deformation effects included in the analysis. The introduction of the thick plate effects significantly increases the complexity of the structural mobility functions used in the definitions of the power flow terms; however, because of the substructuring that is used in the MPF approach, the complexity of the problem is significantly reduced as compared to solving for the global structure. Additionally, with the MPF approach the modal behavior is described. The MPF analysis of the L-shaped plate is performed for the case of point force excitation on one plate, with the two plates being identical in both size and thickness. The results of this analysis are compared to results from the finite-element analysis (FEA) and the statistical energy analysis (SEA) and show very good agreement in the low- and high-frequency regimes, respectively.

Mccollum, M. D.↗

Silicate coprecipitation reduces green rust crystal size and limits dissolution-precipitation during air oxidation

Green rusts (GR) are mixed-valence iron (Fe) hydroxides which form in reducing redox environments like riparian and wetland soils and shallow groundwater. In these environments, silicon (Si) can influence Fe oxides’ chemical and physical properties but its role in GR formation and subsequent oxidative transformation have not been studied starting at initial nucleation. Green rust sulfate [GR(SO 4 )] and green rust carbonate [GR(CO 3 )] were both coprecipitated from salts by base titration in increasing % mol Si (0, 1, 10, and 50). The minerals were characterized before and after rapid (24 h) aqueous air-oxidation by x-ray diffraction (XRD), scanning electron microscopy (SEM), Fe extended x-ray absorption fine structure spectroscopy (EXAFS), and N 2 -BET surface area. Results showed that only GR(SO4) or GR(CO3) was formed at every tested Si concentration. Increasing % mol Si caused decreased plate size and increased surface area in GR(CO3) but not GR(SO4). GR plate basal thickness was not changed at any condition indicating a lack of Si interlayering. Air oxidation of GR(SO4) at all % mol Si contents transformed by dissolution and reprecipitation into lepidocrocite and goethite, favoring ferrihydrite with higher % Si content. Air oxidation of GR(CO3) transformed into magnetite and goethite but increasing Si caused GR to oxidize while retaining its hexagonal plate structure via solid-state oxidation. Our results indicate that Si has the potential to cause GR to form in smaller particles and upon air oxidation, Si can either stabilize the plate structure or alter transformation to ferrihydrite.

36 MATERIALS SCIENCE↗

Sensitivity Analysis of Wing Aeroelastic Responses

Design for prevention of aeroelastic instability (that is, the critical speeds leading to aeroelastic instability lie outside the operating range) is an integral part of the wing design process. Availability of the sensitivity derivatives of the various critical speeds with respect to shape parameters of the wing could be very useful to a designer in the initial design phase, when several design changes are made and the shape of the final configuration is not yet frozen. These derivatives are also indispensable for a gradient-based optimization with aeroelastic constraints. In this study, flutter characteristic of a typical section in subsonic compressible flow is examined using a state-space unsteady aerodynamic representation. The sensitivity of the flutter speed of the typical section with respect to its mass and stiffness parameters, namely, mass ratio, static unbalance, radius of gyration, bending frequency, and torsional frequency is calculated analytically. A strip theory formulation is newly developed to represent the unsteady aerodynamic forces on a wing. This is coupled with an equivalent plate structural model and solved as an eigenvalue problem to determine the critical speed of the wing. Flutter analysis of the wing is also carried out using a lifting-surface subsonic kernel function aerodynamic theory (FAST) and an equivalent plate structural model. Finite element modeling of the wing is done using NASTRAN so that wing structures made of spars and ribs and top and bottom wing skins could be analyzed. The free vibration modes of the wing obtained from NASTRAN are input into FAST to compute the flutter speed. An equivalent plate model which incorporates first-order shear deformation theory is then examined so it can be used to model thick wings, where shear deformations are important. The sensitivity of natural frequencies to changes in shape parameters is obtained using ADIFOR. A simple optimization effort is made towards obtaining a minimum weight design of the wing, subject to flutter constraints, lift requirement constraints for level flight and side constraints on the planform parameters of the wing using the IMSL subroutine NCONG, which uses successive quadratic programming.

Issac, Jason Cherian↗