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Using an approach based on a time domain analysis, a method of equivalent linearization is applied for an estimation of the strain response of complex nonlinear structures having nearly arbitrary complexity. Fatigue lives estimated for a nonlinear beam with random excitation using the approximate method were compared with results obtained using a conventional numerical simulation, yielding nearly identical results.
The principal objective of this research is to develop, test, and implement coarse-grained, parallel-processing strategies for nonlinear dynamic simulations of practical structural problems. There are contributions to four main areas: finite element modeling and analysis of rotational dynamics, numerical algorithms for parallel nonlinear solutions, automatic partitioning techniques to effect load-balancing among processors, and an integrated parallel analysis system.
An embedded-boundary, Cartesian-mesh flow solver is coupled with a three degree-of-freedom structural model to perform static, aeroelastic analysis of complex aircraft geometries. The approach solves a nonlinear, aerostructural system of equations using a loosely-coupled strategy. An open-source, 3-D discrete-geometry engine is utilized to deform a triangulated surface geometry according to the shape predicted by the structural model under the computed aerodynamic loads. The deformation scheme is capable of modeling large deflections and is applicable to the design of modern, very-flexible transport wings. The coupling interface is modular so that aerodynamic or structural analysis methods can be easily swapped or enhanced. After verifying the structural model with comparisons to Euler beam theory, two applications of the analysis method are presented as validation. The first is a relatively stiff, transport wing model which was a subject of a recent workshop on aeroelasticity. The second is a very flexible model recently tested in a low speed wind tunnel. Both cases show that the aeroelastic analysis method produces results in excellent agreement with experimental data.
This paper presents high fidelity Navier-Stokes simulations of the Boeing Subsonic Ultra Green Aircraft Research truss-braced wing wind-tunnel model and compares the results to linear MSC. Nastran flutter analysis and preliminary data from a recent wind-tunnel test of that model at the NASA Langley Research Center Transonic Dynamics Tunnel. The simulated conditions under consideration are zero angle of attack, so that structural nonlinearity can be neglected. It is found that, for Mach number greater than 0.78, the linear flutter analysis predicts flutter onset dynamic pressure below the wind-tunnel test and that predicted by the Navier-Stokes analysis. Furthermore, the wind-tunnel test revealed that the majority of the high structural dynamics cases were wing limit cycle oscillation (LCO) rather than flutter. Most Navier-Stokes simulated cases were also LCO rather than hard flutter. There is dip in the wind-tunnel test flutter/LCO onset in the Mach 0.76-0.80 range. Conditions tested above that Mach number exhibited no aeroelastic instability at the dynamic pressures reached in the tunnel. The linear flutter analyses do not show a flutter/LCO dip. The Navier-Stokes simulations also do not reveal a dip; however, the flutter/LCO onset is at a significantly higher dynamic pressure at Mach 0.90 than at lower Mach numbers. The Navier-Stokes simulations indicate a mild LCO onset at Mach 0.82, then a more rapidly growing instability at Mach 0.86 and 0.90. Finally, the modeling issues and their solution related to the use of a beam and pod finite element model to generate the Navier-Stokes structure mode shapes are discussed.
Among the topics discussed are developments in structural engineering hardware and software, computation for fracture mechanics, trends in numerical analysis and parallel algorithms, mechanics of materials, advances in finite element methods, composite materials and structures, determinations of random motion and dynamic response, optimization theory, automotive tire modeling methods and contact problems, the damping and control of aircraft structures, and advanced structural applications. Specific topics covered include structural design expert systems, the evaluation of finite element system architectures, systolic arrays for finite element analyses, nonlinear finite element computations, hierarchical boundary elements, adaptive substructuring techniques in elastoplastic finite element analyses, automatic tracking of crack propagation, a theory of rate-dependent plasticity, the torsional stability of nonlinear eccentric structures, a computation method for fluid-structure interaction, the seismic analysis of three-dimensional soil-structure interaction, a stress analysis for a composite sandwich panel, toughness criterion identification for unidirectional composite laminates, the modeling of submerged cable dynamics, and damping synthesis for flexible spacecraft structures.
Here, we present a novel finite element analysis of inelastic structures containing Shape Memory Alloys (SMAs). Phenomenological constitutive models for SMAs lead to material nonlinearities, that require substantial computational effort to resolve. Finite element analysis methods, which rely on Gauss quadrature integration schemes, must solve two sets of coupled differential equations: one at the global level and the other at the local, i.e. Gauss point level. In contrast to the conventional return mapping algorithm, which solves these two sets of coupled differential equations separately using a nested Newton procedure, we propose a scheme to solve the local and global differential equations simultaneously. In the process we also derive closed-form expressions used to update the internal/constitutive state variables, and unify the popular closest-point and cutting plane methods with our formulas. Numerical testing indicates that our method allows for larger thermomechanical loading steps and provides increased computational efficiency, over the standard return mapping algorithm.
Two kinds of finite-element analyses are developed for the geometrically nonlinear study of the large deformations in laminated composite structures, especially shells. The first kind of finite-element analysis utilizes the general incremental variational formulation as well as the total Lagrangian description of motion, and a three-dimensional degenerate element is adopted. The second kind of analysis employs a formulation based on deformable shell theory, and the plate-bending element is used. Numerical results for bending are presented for five plate and shell structures of isotropic as well as orthotropic composition, including an isotropic cylindrical panel with uniform loading and a laminated cylindrical panel with uniform loading. The results obtained using these analyses are found to be in good agreement with those available in the literature.
A two-parameter class of time-stepping algorithms for nonlinear structural dynamics is investigated. What sets the present method apart from other concurrent algorithms is the fact that it can be used to some advantage in sequential machines as well. Thus, substantial speed-ups are obtained on a single processor as the number of subdomains is increased. An additional O(p) speed-up is obtained when p processors are utilized. The test case discussed is being repeated for a mesh comprising four times as many elements, in an effort to understand how the large scale asymptotic speed-ups are attained. A three dimensional example involving finite deformations and free body motions is also being pursued. A code optimized for concurrency in the Alliant FX8 computer is being finalized. This will provide the means for testing the performance of the algorithm in a multiprocessor environment.
A time domain approach is used to determine the dynamic aeroelastic stability of a cascade of blades. The structural model for each blade is a typical section with two degrees of freedom. The aerodynamic model is the unsteady, two-dimensional, full-potential flow through the cascade of airfoils. The unsteady equations of motion for the structure and the fluid are integrated simultaneously in time starting with the steady flowfield and a small initial disturbance applied to the airfoils. The motion of each blade is analyzed to determine the aeroelastic stability of the cascade. The effect of interblade phase angle is included in the analysis by allowing each blade to have an independent motion and considering a number of blade passages. Calculations are made using an airfoil section and structural parameters that are representative of a propfan. The results are compared with those from a separate frequency domain analysis. Good agreement between the results is observed. With the time domain approach, it is possible to consider nonlinear structural models and nonlinear force-displacement relations. The method allows a realistic simulation of the motion of the fluid and the cascade blades for a better physical understanding and it also has the potential for saving computational time when compared to the frequency domain approach for the flutter analysis of cascades.
Finite element analysis is used to investigate Triangular Rollable and Collapsible (TRAC) composite booms. The TRAC booms are subjected to a suite of loading conditions, including in-plane bending, out-of-plane bending, and axial compression. Simulations containing as-designed boom geometry are performed, as are simulations with geometric deviations associated with the as-built conditions of a sample TRAC boom. Namely, a cross-sectional twist along the length of the boom is incorporated into the analysis to study the effect of the twist on the deformation characteristics of the boom. Twisting in the sample boom was observed after short-term storage in a rolled configuration and may be attributed to differential creep deformation between the inner and outer flanges of the TRAC boom. Simulations are conducted with and without the effects of gravity to understand the significance of gravity on testing conditions. Booms of three lengths are evaluated: 3 meters, 7.5 meters and 30 meters. The mechanical responses of the TRAC booms are discussed with reference to the effects of gravity, boom length and cross-sectional twisting. Gravity is found to have a more significant effect on boom mechanical response as boom length is increased. Cross-sectional twisting is found to have a more significant effect on boom mechanical response in the shorter booms.
Finite element analysis is used to investigate Triangular Rollable and Collapsible (TRAC) composite booms. The TRAC booms are subjected to a suite of loading conditions, including in-plane bending, out-of-plane bending, and axial compression. Simulations containing as-designed boom geometry are performed, as are simulations with geometric deviations associated with the as-built conditions of a sample TRAC boom. Namely, a cross-sectional twist along the length of the boom is incorporated into the analysis to study the effect of the twist on the deformation characteristics of the boom. Twisting in the sample boom was observed after short-term storage in a rolled configuration and may be attributed to differential creep deformation between the inner and outer flanges of the TRAC boom. Simulations are conducted with and without the effects of gravity to understand the significance of gravity on testing conditions. Booms of three lengths are evaluated: 3 meters, 7.5 meters and 30 meters. The mechanical responses of the TRAC booms are discussed with reference to the effects of gravity, boom length and cross-sectional twisting. Gravity is found to have a more significant effect on boom mechanical response as boom length is increased. Cross-sectional twisting is found to have a more significant effect on boom mechanical response in the shorter booms.
State-of-the-art nonlinear finite element analysis techniques are evaluated by applying them to a realistic aircraft structural component. A wing panel from the V-22 tiltrotor aircraft is chosen because it is a typical modern aircraft structural component for which there is experimental data for comparison of results. From blueprints and drawings, a very detailed finite element model containing 2284 9-node Assumed Natural-Coordinate Strain elements was generated. A novel solution strategy which accounts for geometric nonlinearity through the use of corotating element reference frames and nonlinear strain-displacement relations is used to analyze this detailed model. Results from linear analyses using the same finite element model are presented in order to illustrate the advantages and costs of the nonlinear analysis as compared with the more traditional linear analysis.
The constructed SRB math model was used for the analysis of the 85/32/5(VV/VH/theta) cavity collapse load condition for the aft end of the SRB structure. Linear, nonlinear collapse and bifurcation buckling analyses were performed. The linear and bifurcation buckling analyses showed that structural integrity and positive margins of safety are maintained for the applied maximum load case using a design factor of 1.25. The nonlinear collapse analysis predicts stresses in the skirt above the yield for a load factor of 1.0. Applying the 1.25 design factor gives a negative margin of safety against the material ultimate. The predicted collapse occurs at a load factor higher than 1.25.
A concept for enhancing the design of control fins for supersonic tactical missiles is described. The concept makes use of aeroelastic tailoring to create fin designs (for given planforms) that limit the variations in hinge moments that can occur during maneuvers involving high load factors and high angles of attack. It combines supersonic nonlinear aerodynamic load calculations with finite-element structural modeling, static and dynamic structural analysis, and optimization. The problem definition is illustrated. The fin is at least partly made up of a composite material. The layup is fixed, and the orientations of the material principal axes are allowed to vary; these are the design variables. The objective is the magnitude of the difference between the chordwise location of the center of pressure and its desired location, calculated for a given flight condition. Three types of constraints can be imposed: upper bounds on static displacements for a given set of load conditions, lower bounds on specified natural frequencies, and upper bounds on the critical flutter damping parameter at a given set of flight speeds and altitudes. The idea is to seek designs that reduce variations in hinge moments that would otherwise occur. The block diagram describes the operation of the computer program that accomplishes these tasks. There is an option for a single analysis in addition to the optimization.
Nonlinear finite element analysis techniques are evaluated by applying them to a realistic aircraft structural component. A wing panel from the V-22 tiltrotor aircraft is chosen because it is a typical modern aircraft structural component for which there is experimental data for comparison of results. From blueprints and drawings supplied by the Bell Helicopter Textron Corporation, a very detailed finite element model containing 2284 9-node Assumed Natural-Coordinate Strain (ANS) elements was generated. A novel solution strategy which accounts for geometric nonlinearity through the use of corotating element reference frames and nonlinear strain displacements relations is used to analyze this detailed model. Results from linear analyses using the same finite element model are presented in order to illustrate the advantages and costs of the nonlinear analysis as compared with the more traditional linear analysis. Strain predictions from both the linear and nonlinear stress analyses are shown to compare well with experimental data up through the Design Ultimate Load (DUL) of the panel. However, due to the extreme nonlinear response of the panel, the linear analysis was not accurate at loads above the DUL. The nonlinear analysis more accurately predicted the strain at high values of applied load, and even predicted complicated nonlinear response characteristics, such as load reversals, at the observed failure load of the test panel. In order to understand the failure mechanism of the panel, buckling and first ply failure analyses were performed. The buckling load was 17 percent above the observed failure load while first ply failure analyses indicated significant material damage at and below the observed failure load.
A large deflection analysis was developed for NASTRAN level 16 as an alternative to Rigid Format 4. A progress report is presented for a long term, general nonlinear analysis NASTRAN project, which contains (1) the theory of the structural analysis and numerical analysis methods presently used, and (2) some simple test problems comparing the new analysis with Rigid Format 4.
A two step hybrid analysis technique to predict the nonlinear steady state temperature distribution in structures and solids is presented. The technique is based on the regular perturbation expansion and the classical Bubnov-Galerkin approximation. The functions are obtained by using the regular perturbation method. These functions are selected as coordinate functions and the classical Bubnov-Galerkin technique is used to compute their amplitudes. The potential of the proposed hybrid technique for the solution of nonlinear thermal problems is discussed. The effectiveness of this technique is demonstrated by the effects of conduction, convection, and radiation modes of heat transfer. It is indicated that the hybrid technique overcomes the two major drawbacks of the classical techniques: (1) the requirement of using a small parameter in the regular perturbation method; and (2) the arbitrariness in the choice of the coordinate functions in the Bubnov-Galerkin technique. The proposed technique extends the range of applicability of the regular perturbation method and enhances the effectiveness of the Bubnov-Galerkin technique.
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.