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NUMERICAL CALCULATION TECHNIQUE FOR LARGE ELASTIC-PLASTIC TRANSIENT DEFORMATIONS OF THIN SHELLS

AIAA JOURNAL 1968年第12期6卷 2352-&页

作者： LEECH, JW WITMER, EA PIAN, THH Massachusetts Institute of Technology Cambridge Mass.

Studies of explosive forming of structures must often include the large-deformation transient and permanent-deflection responses of the structure. To aid in studies of this nature, a large-deflection elastic- plastic transient response prediction method has been developed. The accuracy and reliability of this method have been demonstrated by comparisons of theoretical predictions with experimental measurements. The large-deflection large- rotation small-strain equations of motion for a thin shell including elastic, elastic- plastic, strainhardening, and strain-rate material behavior are presented in tensor form. These equations are then cast into numerical form by finite differencing. The step-by-step numerical-integration technique is applied to the case of a cylindrical panel;dynamic-deformation predictions are compared with experimentally observed deformation histories of an explosively loaded cylindrical panel tested at the Picatinny Arsenal. © 1968 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.

关键词： Principal Stresses Transient Response Numerical Integration Explosive Forming Young's Modulus finite difference approximation Cylindrical Shells Structural Dynamics Detonation Waves Air Forces

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SENSITIVITY ANALYSIS OF DISCRETE STRUCTURAL SYSTEMS

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AIAA JOURNAL 1986年第5期24卷 823-832页

作者： ADELMAN, HM HAFTKA, RT VIRGINIA POLYTECH INST & STATE UNIV DEPT AEROSP & OCEAN ENGNBLACKSBURGVA 24061

Sensitivity analysis is emerging as a fruitful area of engineering research. The reason for this interest is the recognition of the variety of uses for sensitivity derivatives. In its early stages, sensitivity analysis found its predominant use in assessing the effect of varying parameters in mathematical models of control systems. This article surveys methods for calculating sensitivity derivatives for discrete structural systems and primarily covers literature published during the past two decades. Methods are described for calculating derivatives of static displacements and stresses, eigenvalues and eigenvectors, transient structural response, and derivatives of optimum structural designs with respect to problem parameters.

关键词： Second Order Differential Equations Structural System finite Element Modeling Numerical Integration Structural Response Distributed Parameter System Structural Optimization finite difference approximation Structural Sensitivity Analysis Material Derivatives

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Numerical Solution of Two-Dimensional Compressible Radiating Flowfields

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JOURNAL OF THERMOPHYSICS AND HEAT TRANSFER 1990年第3期4卷 285-291页

作者： Chen, Yih-Kanq Varghese, Philip L. Howell, John R. Univ Texas Austin Dept Mech Engn Austin TX 78712 USA

A two-dimensional numerical model for flows with coupled radiation from an emitting, absorbing, and scattering fluid is developed. The continuity, momentum, and energy equations are approximated by a finite-difference method, and the radiative transfer equation is discretized by the product-integration method in which the shape function is taken to be piecewise-constant. The numerical grid for the radiation field is matched with the flowfield grid, and the continuity, momentum, and energy equations are coupled with the radiative transfer equation to obtain steady-state solutions. The model is verified by comparison with existing solutions for a laminar Poiseuille flow. Some sample calculations of inviscid supersonic flow of an ideal gas through a two-dimensional diffuser are presented to show the effect of radiation on the temperature field in the diffuser.

关键词： Temperature Fields Radiative Transfer Incompressible Flow Numerical Integration Gas Constant finite difference approximation Shape Functions Absorption Coefficient Radiative Heating Oblique Shock

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A MONOTONICITY PROCEDURE FOR THE ACCURATE, EFFICIENT SOLUTION OF CERTAIN HEAT-TRANSFER PROBLEMS WITH VARIABLE THERMAL-PROPERTIES

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 1995年第1期58卷 89-101页

作者： MOONEY, JW GLASGOW CALEDONIAN UNIV DEPT MATHGLASGOW G4 0BALANARKSCOTLAND

An efficient solution procedure of high accuracy is described for the numerical solution of nonlinear boundary value problems associated with heat-transfer and reaction-diffusion processes. Constructive existence-uniqueness theorems lead to Newton/Picard iterative schemes for bounding the positive solutions of these problems. The iteration schemes are discretised as matrix tridiagonal systems of error order O(h(2)). Richardson extrapolation can be exploited to produce very accurate results;comparisons are made with the results of other methods on specific examples.

关键词： NONLINEAR BOUNDARY VALUE PROBLEM HEAT-TRANSFER EQUATION REACTION-DIFFUSION PROCESS MONOTONIC NEWTON AND PICARD SCHEME finite difference approximation RICHARDSON EXTRAPOLATION

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EFFICIENT ALGORITHM FOR SOLUTION OF THE UNSTEADY TRANSONIC SMALL-DISTURBANCE EQUATION

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JOURNAL OF AIRCRAFT 1988年第7期25卷 598-605页

作者： BATINA, JT NASA Langley Research Center Hampton Virginia

A time-accurate approximate factorization (AF) algorithm is formulated for solution of the three-dimensional unsteady transonic small-disturbance equation. The AF algorithm consists of a Newton linearization procedure coupled with an internal iteration technique. Superior stability characteristics of the new algorithm are demonstrated through applications to steady and oscillatory flows at subsonic and supersonic freestream conditions for an F-5 fighter wing. For steady flow calculations, the size of the time step is cycled to achieve rapid convergence. For unsteady flow calculations, the AF algorithm is sufficiently robust to allow the step size to be selected based on accuracy rather than on stability considerations. Therefore, accurate solutions are obtained in only several hundred time steps yielding a significant computational cost savings when compared to alternative methods. © 1988 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.

关键词： Freestream Mach Number Unsteady Transonic Flow Numerical Stability Tapered Wings Angle of Attack Pressure Coefficient Aspect Ratio Swept Wing finite difference approximation Droop Nose

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MULTIGRID TRANSONIC COMPUTATIONS ABOUT ARBITRARY AIRCRAFT CONFIGURATIONS

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JOURNAL OF AIRCRAFT 1989年第8期26卷 751-759页

作者： EPSTEIN, B LUNTZ, AL NACHSHON, A Israel Aircraft Industries Lod Israel

A three-dimensional full-potential code that is able to handle arbitrary aircraft configurations is described. This code is based on the use of Cartesian grids, local refinement, and multigrid calculations. The configuration is treated as an assembly of elements (bodies, wings, pylons, etc.). The algorithm incorporates the body boundary condition implementation for nonaligned grids. Multigrid treatment of local refinement and grid overlapping is described. Three application cases are discussed. First, a fighter configuration including body, wing, fairing, and canard;this example shows the importance of the grid-to-shock alignment. Second, a fighter configuration including body, wing, fairing, canard, and external fuel tank;the analysis shows an unexpectedly strong interference between body, wing, and fuel tank. Third, a civil aircraft configuration with different wing root fairings. © 1988 by ICAS and AIAA. All rights reserved.

关键词： Aircraft Configurations Wing Twist Wing Root Angle of Attack Cartesian Coordinates Specific Heat Drag Reduction Aspect Ratio International Council of the Aeronautical Sciences finite difference approximation

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COMPUTATIONAL MODEL OF FLEXIBLE MEMBRANE WINGS IN STEADY LAMINAR-FLOW

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AIAA JOURNAL 1995年第10期33卷 1769-1777页

作者： SMITH, R SHYY, W University of Florida Gainesville Florida 32611

A computational procedure is presented that models the interaction of a two-dimensional flexible membrane wing and laminar, high-Reynolds-number fluid Row. The membrane wing model is derived by combining a spatial-coordinate based finite difference formulation of the equilibrium statement for an elastic membrane with a pressure-based control volume formulation of the incompressible Navier-Stokes equations written in general curvilinear body-fitted coordinates. The model is applied to initially Rat membrane wings of both vanishing and finite material stiffness as well as to flexible inextensible wings with excess length. Computational results are presented for Reynolds numbers between 2 X 10(3) and 10(4). The results from the viscous-flow based membrane wing model are compared with predictions using a potential-Row-based model as well as with experimental data for membrane wings in turbulent flow, Although the assumption of laminar flow precludes a quantitative comparison with the available experimental data, the solutions obtained capture many of the significant features of the aeroelastic interaction that are unaccounted for with a potential flow description of the fluid dynamics.

关键词： Incompressible Flow Aerodynamic Characteristics Stagnation Pressure Viscous Fluid Navier Stokes Equations finite difference approximation Lift Coefficient Camber Boundary Value Problems Vortex Strength

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Optimal two-dimensional finite difference grids providing superconvergence

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SIAM JOURNAL ON SCIENTIFIC COMPUTING 2002年第5期23卷 1707-1730页

作者： Yamaleev, NK NASA Natl Res Council Langley Res Ctr Hampton VA 23681 USA

A novel multidimensional grid adaptation method based on minimization of the leading truncation error term of arbitrary second- and higher-order finite difference approximations is proposed. The method does not explicitly require the truncation error estimate, but increases the design order of approximation globally by one, so that the same finite difference operator is superconvergent on the optimal grid. If the differential operator and the metric coefficients are evaluated identically by some hybrid approximation, the single optimal grid generator can be used in the entire computational domain and does not depend on points where the hybrid discretization switches from one approximation to another. If one family of the coordinate lines is given a priori, then the analytical optimal mapping is constructed for any consistent second-order finite difference approximation of delf in two dimensions. The present approach can be extended directly to nonlinear partial differential equations and three dimensions. Numerical calculations show that the truncation error obtained on the two-dimensional optimal grid is both superconvergent and reduced by several orders of magnitude in comparison with the uniform grid results for all the test examples considered.

关键词： truncation error optimal grid finite difference approximation

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IMPROVED METHOD FOR CALCULATING BOOSTER TO LAUNCH PAD INTERFACE TRANSIENT FORCES

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JOURNAL OF SPACECRAFT AND ROCKETS 1988年第6期25卷 433-438页

作者： HENKEL, EE MAR, R Rockwell International Seal Beach California

This paper presents a methodology for the calculation of the transient interface forces between a launch vehicle and its launch pad. The method presented is closed form and, thus, is mathematically exact. The method uses variable constraint equations to couple the launch vehicle to the pad. The resulting interface forces are monitored each time step, and as the launch vehicle separates from the pad, the constraint equations are modified accordingly. The only assumption in the method is that the forces acting on the booster and pad, including the subject interface forces, vary linearly between integration time steps. This is the same assumption used in standard linear transient loads analyses. In addition, the nature of the constraint equations allows a great reduction in the number of coupled equations to be solved. Solving the resulting small system of equations yields the interface forces, which are then used to solve for the booster and pad response by the standard linear transient solution method. Use of constraint equations also frees the analyst from calculating coupled booster-pad systems modes, which are a necessity in some methodologies currently in use. (Author)

关键词： Launch Pad Launch Vehicles Condensation Nastran Vandenberg Air Force Base Space Shuttle finite difference approximation Structural Element Dynamic Response Payload System

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ROTOR BLADE AEROELASTICITY IN FORWARD FLIGHT WITH AN IMPLICIT AERODYNAMIC FORMULATION

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AIAA JOURNAL 1988年第12期26卷 1425-1433页

作者： CELI, R FRIEDMANN, PP UNIV CALIF LOS ANGELES DEPT MECH AEROSP & NUCL ENGNLOS ANGELESCA 90024

This paper describes a new methodology for formulating the aeroelastic stability and response problem for helicopter rotor blades. The mathematical expressions for the aerodynamic loads heed not be explicit functions of the blade displacement quantities. The methodology is combined with a finite-element model of the blade and a quasilinearization solution technique. The resulting computer program is used to study the behavior of blades with noncoincident elastic axis, aerodynamic centers, and centers of mass. © 1988 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.

关键词： Aeroelastic Stability Rotor Blades Aerodynamic Center finite Element Analysis Computer Programs Helicopter Rotor Numerical Integration finite difference approximation Rotary Wing Compressibility Effect

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