An integrated approach to the optimum design of actively controlled composite wings

The importance of interactions among the various disciplines in airplane wing design has been recognized for quite some time. With the introduction of high gain, high authority control systems and the design of thin, flexible, lightweight composite wings, the integrated treatment of control systems, flight mechanics and dynamic aeroelasticity became a necessity. A research program is underway now aimed at extending structural synthesis concepts and methods to the integrated synthesis of lifting surfaces, spanning the disciplines of structures, aerodynamics and control for both analysis and design. Mathematical modeling techniques are carefully selected to be accurate enough for preliminary design purposes of the complicated, built-up lifting surfaces of real aircraft with their multiple design criteria and tight constraints. The presentation opens with some observations on the multidisciplinary nature of wing design. A brief review of some available state of the art practical wing optimization programs and a brief review of current research effort in the field serve to illuminate the motivation and support the direction taken in our research. The goals of this research effort are presented, followed by a description of the analysis and behavior sensitivity techniques used. The presentation concludes with a status report and some forecast of upcoming progress

The 1/r singularity in weakly nonlinear fracture mechanics

Material failure by crack propagation essentially involves a concentration of large displacement-gradients near a crack's tip, even at scales where no irreversible deformation and energy dissipation occurs. This physical situation provides the motivation for a systematic gradient expansion of general nonlinear elastic constitutive laws that goes beyond the first order displacement-gradient expansion that is the basis for linear elastic fracture mechanics (LEFM). A weakly nonlinear fracture mechanics theory was recently developed by considering displacement-gradients up to second order. The theory predicts that, at scales within a dynamic lengthscale $\ell$ from a crack's tip, significant $\log{r}$ displacements and $1/r$ displacement-gradient contributions arise. Whereas in LEFM the $1/r$ singularity generates an unbalanced force and must be discarded, we show that this singularity not only exists but is {\em necessary} in the weakly nonlinear theory. The theory generates no spurious forces and is consistent with the notion of the autonomy of the near-tip nonlinear region. The J-integral in the weakly nonlinear theory is also shown to be path-independent, taking the same value as the linear elastic J-integral. Thus, the weakly nonlinear theory retains the key tenets of fracture mechanics, while providing excellent quantitative agreement with measurements near the tip of single propagating cracks. As $\ell$ is consistent with lengthscales that appear in crack tip instabilities, we suggest that this theory may serve as a promising starting point for resolving open questions in fracture dynamics.Comment: 12 pages, 2 figure