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An investigation of heuristic failure theories based on the Shanley-Ryder (S-R) stress ratio formulations and their extensions to ratios of stress invariants is undertaken. The deterministic structural margin (MS) and factor of safety (FoS) are re-examined and their multiple valued relevances to probabilistic analyses based on statistical loads as well as statistical material failure properties are discussed. MS's have no unique meaning in stochastic analyses while factors of safety effectively increase allowable loads thereby decreasing failure probabilities. [ABSTRACT FROM AUTHOR]

The application of chaos theory to forces inducing rolling maneuvers by acting on linear or nonlinear temperature dependent viscoelastic wings with actual widely scattered random material properties is investigated in detail. Published experimental data shows widely scattered 1-D viscoelastic moduli and small excursions from average or beginning values - the basis for chaos theory - is realistically inapplicable and would simply constitute a purely academic exercise excursion. While conventional approaches have been associated with applied forces, such as probability theory, to characterize these deterministic and stochastic properties, chaos theory is offered as an additional alternate generalized protocol to characterize viscoelastic responses to chaotic flight loads. At this time unfortunately no deterministic, stochastic or chaotic experimental data seems to be available, nor experimental data on aero-viscoelastic structural responses to flight vehicle maneuvers at any temperature. [ABSTRACT FROM AUTHOR]

The present paper is a continuation and expansion of a previous Part I [1] emphasizing material failure modeling and visualization protocols in conjunction with aero - elastic/viscoelastic phenomena. Failure is defined in terms of the Shanley-Ryder stress ratio relations and through the generalization based on the first three stress invariant ratios. Both deterministic and stochastic stress and strain as well as failure analyses are carried out. Visualization examples of multi-dimensional failure surfaces depending on possibly more than 35 elastic and 47 viscoelastic parallel coordinates is formulated, presented and discussed. Separate analyses are formulated for elastic and viscoelastic combined unsymmetrical bendingtorsion during level flight and for vehicle rolling motion. The overall bending degrees of freedom considered are plunging, in plane and chord-wise motions. Bending-torsion effects on and changes in angles of attack due the rolling velocity as well as the infiuence of moving shear centers and neutral axes and of material failures are considered during simultaneous occurrences. The final goal is to establish conditions for bending and torsional flutter, torsional divergence, control effectiveness and ultimate survival time of the wing due to material failures and structural instabilities (buckling) with future extensions to the entire vehicle under the rubric of system of systems approach, leading to a single pair of critical velocities and frequencies including material failure effects. The original Shanley-Ryder stress ratio failure criterion as well as its successor three stress invariant formulations are utilized. The latter has the advantage of having an unlimited number of arbitrary coefficients to be used to in fitting analytical expressions to stochastic experimental data. The multi-D numerical example results are displayed as a single figure of multiple 2-D parallel coordinates (1 1-cor(is) as opposed to numerous simultaneous, but separate, 2-D trace plots of a multi-D aeroelastic/aero-viscoelastic combined stability, buckling and material failure surface. In the present analyses, the use of Inselberg's parallel coordinates protocols clearly demonstrates in a single graph the individual and collective influences of many parameters on critical velocities without recourse to multiple 3-D critical surface representations. The critical velocities are also displayed as separate 2-D traces for each of the divers parameters, as well as in H-coords renderings. A small sample of randomly chosen subsonic wing parametric variation calculations show that compared to the free standing bending-torsion configuration, combinations involving plunging and in-plane bending, control effectiveness and reversal, with or without positive or negative roll velocities, and absent or present Timoshenko effects, produce substantially altered fiutter velocities and their paired frequencies. Finally, it noteworthy to mention that failure conditions can be improved by introducing morphing to the structure. Morphing [2], 13] airfoil shapes, although not treated here in detail, can produces significant improvements in aerodynamic, aeroelastic, aero-viscoelastic and structural performances, and delay as well as reduce their failure probabilities - all with relatively little energy expenditures. Additionally, the optimizing process that leads to the design of high performance Liebeck airfoils [4] contributes in equal measures. [ABSTRACT FROM AUTHOR]

Following the unified approach to viscoelastic Timoshenko beams (spars) formulated in [1], similar inclusive analyses are formulated for elastic and viscoelastic combined unsymmetrical bending-torsion during level flight and for vehicle rolling motion. The overall bending degrees of freedom considered are plunging, in plane and chord-wise motions. Bending-torsion effects on and changes in angles of attack due the rolling velocity as well as the influence of moving shear centers and neutral axes and of material failures are considered during simultaneous occurrences. The final goal is to establish conditions for bending and torsional flutter, torsional divergence, control effectiveness and ultimate survival time of the wing due to material failures and structural instabilities (buckling) with future extensions to the entire vehicle under the rubric of system of systems (SoS) approach, leading to a single pair of critical velocities and frequencies including material failure effects. A new stress invariant stochastic generalization to the original Shanley-Ryder stress ratio failure criterion is derived and utilized. The latter has the advantage of having an unlimited number of arbitrary coefficients to be used to in fitting analytical expressions to stochastic experimental data. The multi-D numerical example results are displayed as a single figure of multiple 2-D parallel coordinates (ǁ-coords), as opposed to numerous simultaneous, but separate, 2-D traces of a multi-D aeroelastic/aero-viscoelastic combined stability, buckling and material failure surface. In the present analyses, the use of ǁ-coords clearly graphically demonstrates the individual and collective influences of many parameters on critical velocities without recourse to a multidimensional critical surface representation. The critical velocities are also displayed as separate 2-D traces for each of the divers parameters, as well as in ǁ-coords renderings. A small sample of randomly chosen subsonic wing parametric variation calculations show that compared to the free standing bending-torsion configuration, combinations involving plunging and inplane bending, control effectiveness and reversal, with or without positive or negative roll velocities, and absent or present Timoshenko effects, produce substantially altered flutter velocities and their paired frequencies. [ABSTRACT FROM AUTHOR]

A unified bending/shear beam (spar) theory has been formulated by merging a number of previously completed theoretical segments into a comprehensive analytical treatment of linear non-homogenous viscoelastic Timoshenko beams (spars) with stochastic properties and random dynamic loads including shear center and neutral axis spatial and temporal motions due to bending, and including realistic physical starting load transients. These inverse problem analyses are framed entirely in terms of relaxation moduli or creep compliances, excluding any dependence on Poisson's ratios. The deterministic and stochastic effects of unequal tension and compression relaxation moduli/compliances on normal and shear bending stresses are derived and evaluated. The influences of all these phenomena on combined bending and shear stress distributions, structural instabilities, material failures and structural survival times also are formulated and discussed. [ABSTRACT FROM AUTHOR]